What is the unit of measurement for force?
Force
In physics, a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F.
Bending moment
Moments and torques are measured as a force multiplied by a distance so they have as unit newton-metres (N·m), or pound-foot (lbf·ft). The concept of bending moment is very important in engineering (particularly in civil and mechanical engineering) and physics.
Metric system
In SI, which is a coherent system, the unit of power is the "watt", which is defined as " joule per second". In the US customary system of measurement, which is non-coherent, the unit of power is the "horsepower", which is defined as "550 foot-pounds per second" (the pound in this context being the pound-force). Similarly, neither the US gallon nor the imperial gallon is cubic foot or cubic yard— the US gallon is 231 cubic inches and the imperial gallon is 277.42 cubic inches.
Joule per mole
The joule per mole (symbol: J·mole or J/mol) is an SI derived unit of energy per amount of material. Energy is measured in joules, and the amount of material is measured in moles. For example, Gibbs free energy is quantified as joules per mole.
Metric system
Gravitational metric systems use the kilogram-force (kilopond) as a base unit of force, with mass measured in a unit known as the hyl, "Technische Mass Einheit" (TME), mug or metric slug. Although the CGPM passed a resolution in 1901 defining the standard value of acceleration due to gravity to be 980.665 cm/s, gravitational units are not part of the International System of Units (SI).
Foot-pound (energy)
The foot-pound is often used to specify the muzzle energy of a bullet in small arms ballistics, particularly in the United States.
"Foot-pound" is also used as a unit of torque (see "pound-foot (torque)"). In the United States this unit is often used to specify, for example, the tightness of a bolt or the output of an engine. Although they are dimensionally equivalent, energy (a scalar) and torque (a vector) are distinct physical quantities. Both energy and torque can be expressed as a product of a force vector with a displacement vector (hence pounds and feet); energy is the scalar product of the two, and torque is the vector product.
List of unusual units of measurement
A foe is a unit of energy equal to  joules (≈9.478 BTU) that was coined by physicist Gerry Brown of Stony Brook University. To measure the staggeringly immense amount of energy produced by a supernova, specialists occasionally use the "foe", an acronym derived from the phrase [ten to the power of] fifty-one ergs, or  ergs. This unit of measure is convenient because a supernova typically releases about one foe of observable energy in a very short period of time (which can be measured in seconds).
Tension (physics)
In physics, tension, as a transmitted force, as an action-reaction pair of forces, or as a restoring force, may be a force and has the units of force measured in newtons (or sometimes pounds-force). The ends of a string or other object transmitting tension will exert forces on the objects to which the string or rod is connected, in the direction of the string at the point of attachment. These forces due to tension are also called "passive forces". There are two basic possibilities for systems of objects held by strings: either acceleration is zero and the system is therefore in equilibrium, or there is acceleration, and therefore a net force is present in the system.
Force field (physics)
In physics a force field is a vector field that describes a non-contact force acting on a particle at various positions in space. Specifically, a force field is a vector field formula_1, where formula_2 is the force that a particle would feel if it were at the point formula_3.As a particle moves through a force field along a path "C", the work done by the force is a line integral
This value is independent of the velocity/momentum that the particle travels along the path. For a conservative force field, it is also independent of the path itself, depending only on the starting and ending points. Therefore, if the starting and ending points are the same, the work is zero for a conservative field:
If the field is conservative, the work done can be more easily evaluated by realizing that a conservative vector field can be written as the gradient of some scalar potential function:
Force
A static equilibrium between two forces is the most usual way of measuring forces, using simple devices such as weighing scales and spring balances. For example, an object suspended on a vertical spring scale experiences the force of gravity acting on the object balanced by a force applied by the "spring reaction force", which equals the object's weight. Using such tools, some quantitative force laws were discovered: that the force of gravity is proportional to volume for objects of constant density (widely exploited for millennia to define standard weights); Archimedes' principle for buoyancy; Archimedes' analysis of the lever; Boyle's law for gas pressure; and Hooke's law for springs. These were all formulated and experimentally verified before Isaac Newton expounded his Three Laws of Motion.
Work (physics)
For moving objects, the quantity of work/time (power) is integrated along the trajectory of the point of application of the force. Thus, at any instant, the rate of the work done by a force (measured in joules/second, or watts) is the scalar product of the force (a vector), and the velocity vector of the point of application. This scalar product of force and velocity is known as instantaneous power. Just as velocities may be integrated over time to obtain a total distance, by the fundamental theorem of calculus, the total work along a path is similarly the time-integral of instantaneous power applied along the trajectory of the point of application.
Moment (physics)
Moments are usually defined with respect to a fixed reference point; they deal with physical quantities as measured at some distance from that reference point. For example, the moment of force acting on an object, often called torque, is the product of the force and the distance to the object (i.e., the reference point). In principle, any physical quantity can be multiplied by distance to produce a moment; commonly used quantities include forces, masses, and electric charge distributions.
Rolling resistance
formula_3 is the force needed to push (or tow) a wheeled vehicle forward (at constant speed on a level surface, or zero grade, with zero air resistance) per unit force of weight. It is assumed that all wheels are the same and bear identical weight. Thus: formula_6 means that it would only take 0.01 pounds to tow a vehicle weighing one pound. For a 1000-pound vehicle, it would take 1000 times more tow force, i.e. 10 pounds. One could say that formula_3 is in lb(tow-force)/lb(vehicle weight). Since this lb/lb is force divided by force, formula_3 is dimensionless. Multiply it by 100 and you get the percent (%) of the weight of the vehicle required to maintain slow steady speed. formula_3 is often multiplied by 1000 to get the parts per thousand, which is the same as kilograms (kg force) per metric ton (tonne = 1000 kg ), which is the same as pounds of resistance per 1000 pounds
of load or Newtons/kilo-Newton, etc. For the US railroads, lb/ton has been traditionally used; this is just formula_10. Thus, they are all just measures of resistance per unit vehicle weight. While they are all "specific resistances", sometimes they are just called "resistance" although they are really a coefficient (ratio)or a multiple thereof. If using pounds or kilograms as force units, mass is equal to weight (in earth's gravity a kilogram a mass weighs a kilogram and exerts a kilogram of force) so one could claim that formula_3 is also the force per unit mass in such units. The SI system would use N/tonne (N/T, N/t), which is formula_12 and is force per unit mass, where "g" is the acceleration of gravity in SI units (meters per second square).
Pressure
Various units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre; similarly, the pound-force per square inch (psi) is the traditional unit of pressure in the imperial and US customary systems. Pressure may also be expressed in terms of standard atmospheric pressure; the atmosphere (atm) is equal to this pressure, and the torr is defined as of this. Manometric units such as the centimetre of water, millimetre of mercury, and inch of mercury are used to express pressures in terms of the height of column of a particular fluid in a manometer.
Newton (unit)
Newton's second law of motion states that , where is the force applied, is the mass of the object receiving the force, and is the acceleration of the object. The newton is therefore:
where the following symbols are used for the units: N for newton, kg for kilogram, m for metre, and s for second.
Coherence (units of measurement)
Isaac Asimov wrote, "In the cgs system, a unit force is described as one that will produce an acceleration of 1 cm/sec on a mass of 1 gm. A unit force is therefore 1 cm/sec multiplied by 1 gm." These are independent statements. The first is a definition; the second is not. The first implies that the constant of proportionality in the force law has a magnitude of one; the second implies that it is dimensionless. Asimov uses them both together to prove that it is the pure number one.
International System of Units
Combinations of base and derived units may be used to express other derived units. For example, the SI unit of force is the newton (N), the SI unit of pressure is the pascal (Pa)—and the pascal can be defined as one newton per square metre (N/m).
Strength of materials
Ultimate strength is an attribute related to a material, rather than just a specific specimen made of the material, and as such it is quoted as the force per unit of cross section area (N/m). The ultimate strength is the maximum stress that a material can withstand before it breaks or weakens. For example, the ultimate tensile strength (UTS) of AISI 1018 Steel is 440 MN/m. In general, the SI unit of stress is the pascal, where 1 Pa = 1 N/m. In Imperial units, the unit of stress is given as lbf/in² or pounds-force per square inch. This unit is often abbreviated as psi. One thousand psi is abbreviated ksi.
Physical geodesy
Gravity is commonly measured in units of m·s (metres per second squared). This also can be expressed (multiplying by the gravitational constant G in order to change units) as newtons per kilogram of attracted mass.
Planck force
Planck force is the derived unit of force resulting from the definition of the base Planck units for time, length, and mass. It is equal to the natural unit of momentum divided by the natural unit of time.
International System of Units
The early metric systems defined a unit of weight as a base unit, while the SI defines an analogous unit of mass. In everyday use, these are mostly interchangeable, but in scientific contexts the difference matters. Mass, strictly the inertial mass, represents a quantity of matter. It relates the acceleration of a body to the applied force via Newton's law, : force equals mass times acceleration. A force of 1 N (newton) applied to a mass of 1 kg will accelerate it at 1 m/s. This is true whether the object is floating in space or in a gravity field e.g. at the Earth's surface. Weight is the force exerted on a body by a gravitational field, and hence its weight depends on the strength of the gravitational field. Weight of a 1 kg mass at the Earth's surface is ; mass times the acceleration due to gravity, which is 9.81 newtons at the Earth's surface and is about 3.5 newtons at the surface of Mars. Since the acceleration due to gravity is local and varies by location and altitude on the Earth, weight is unsuitable for precision measurements of a property of a body, and this makes a unit of weight unsuitable as a base unit.
Measurement
The metric system is a decimal system of measurement based on its units for length, the metre and for mass, the kilogram. It exists in several variations, with different choices of base units, though these do not affect its day-to-day use. Since the 1960s, the International System of Units (SI) is the internationally recognised metric system. Metric units of mass, length, and electricity are widely used around the world for both everyday and scientific purposes.
Magnetic moment
The unit for magnetic moment in terms of the International System of Units (SI) base units is A⋅m, where A is the ampere (the SI unit of current) and m is the meter (the SI unit of distance). This has equivalents in other units used in SI including:
English Engineering units
In English Engineering units, the pound mass and the pound force are distinct base units, and Newton's Second Law of Motion takes the form "F" = "ma"/"g", where "g" = 32.174 lb·ft/(lbf·s).
Gravimeter
The term for the "force constant" changes if the restoring force is electrostatic, magnetostatic, electromagnetic, optical, microwave, acoustic, or any of dozens of different ways to keep the mass stationary. The "force constant" is just the coefficient of the displacement term in the equation of motion:
Conventional electrical unit
A conventional electrical unit (or conventional unit where there is no risk of ambiguity) is a unit of measurement in the field of electricity which is based on the so-called "conventional values" of the Josephson constant and the von Klitzing constant agreed by the International Committee for Weights and Measures (CIPM) in 1988. These units are very similar in scale to their corresponding SI units, but are not identical because of their different definition. They are distinguished from the corresponding SI units by setting the symbol in italic typeface and adding a subscript "90" – e.g., the conventional volt has the symbol "V" – as they came into international use on 1 January 1990.
Measurement
Units of measurement are generally defined on a scientific basis, overseen by governmental or independent agencies, and established in international treaties, pre-eminent of which is the General Conference on Weights and Measures (CGPM), established in 1875 by the Metre Convention, overseeing the International System of Units (SI) and having custody of the International Prototype Kilogram. The metre, for example, was redefined in 1983 by the CGPM in terms of light speed, while in 1960 the international yard was defined by the governments of the United States, United Kingdom, Australia and South Africa as being "exactly" 0.9144 metres.
SI base unit
The International System of Units (SI) defines seven units of measure as a basic set from which all other SI units can be derived. The SI base units and their physical quantities are the meter for measurement of length, the kilogram for mass, the second for time, the ampere for electric current, the kelvin for temperature, the candela for luminous intensity, and the mole for amount of substance.
Kilogram-force
The kilogram-force (kgf or kg), or kilopond (kp, from Latin "pondus" meaning "weight"), is a gravitational metric unit of force. It is equal to the magnitude of the force exerted on one kilogram of mass in a gravitational field (standard gravity, a conventional value approximating the average magnitude of gravity on Earth). Therefore, one kilogram-force is by definition equal to . Similarly, a gram-force is , and a milligram-force is . One kilogram-force is approximately 2.204622 pound-force.
Natural units
In physics, natural units are physical units of measurement based only on universal physical constants. For example, the elementary charge is a natural unit of electric charge, and the speed of light is a natural unit of speed. A purely natural system of units has all of its units defined in this way, and usually such that the numerical values of the selected physical constants in terms of these units are exactly "dimensionless" . These constants are then typically omitted from mathematical expressions of physical laws, and while this has the apparent advantage of simplicity, it may entail a loss of clarity due to the loss of information for dimensional analysis. It precludes the interpretation of an expression in terms of fundamental physical constants, such as and , unless it is "known" which units (in dimensionful units) the expression is supposed to have. In this case, the reinsertion of the correct powers of , , etc., can be uniquely determined.
Centimetre–gram–second system of units
In measurements of purely mechanical systems (involving units of length, mass, force, energy, pressure, and so on), the differences between CGS and SI are straightforward and rather trivial; the unit-conversion factors are all powers of 10 as and . For example, the CGS unit of force is the dyne which is defined as , so the SI unit of force, the newton (), is equal to 100,000 dynes.
Kibble balance
A Kibble balance (previously watt balance) is an electromechanical measuring instrument that measures the weight of a test object very precisely by the strength of the electric current and voltage needed to produce a compensating force. It is a metrological instrument that can realize the new definition of the kilogram unit of mass based on fundamental constants, termed an "electronic" or "electrical" kilogram. The name "watt balance" came from the fact that the weight of the test mass is proportional to the product of the current and the voltage, which is measured in units of watts. In June 2016, two months after the death of the inventor of the balance, Bryan Kibble, metrologists of the Consultative Committee for Units of the International Committee for Weights and Measures agreed to rename the device in his honor.
Metre per second squared
Newton's Second Law states that force equals mass multiplied by acceleration.
The unit of force is the newton (N), and mass has the SI unit kilogram (kg). One newton equals one kilogram metre per second squared. Therefore, the unit metre per second squared is equivalent to newton per kilogram, N·kg, or N/kg.
Bryan Kibble
In 1990, the Mark II watt balance was built, with a view to measuring the Planck constant accurately enough to redefine the S.I. unit of the kilogramme from fundamental constants. Such an instrument equalises one force with another, specifically the weight of a [one-kilogramme, typically] test mass and the force produced by an electric current in a moving coil in a magnetic field. The magnitude of the upward force on the coil is controlled by changes to the current. The power of the moving mass is equal to the product of the current and potential difference measured in the coil, hence the term 'watt' balance (as the S.I. unit of power is the watt (W)).
Metrology
There is a proposed redefinition of the SI base units that was formally voted on in November 2018, and will come into effect in May 2019. The motivation in the change of the base units is to make the entire system derivable from physical constants, which requires the removal of the prototype kilogram as it is the last artefact the unit definitions depend on. Scientific metrology plays an important role in this redefinition of the units as precise measurements of the physical constants is required to have accurate definitions of the base units. To redefine the value of a kilogram without an artefact the value of the Planck constant must be known to twenty parts per billion. Scientific metrology, through the development of the Kibble balance and the Avogadro project, has produced a value of Planck constant with low enough uncertainty to allow for a redefinition of the kilogram.
Statics
Force is the action of one body on another. A force is either a push or a pull. A force tends to move a body in the direction of its action. The action of a force is characterized by its magnitude, by the direction of its action, and by its point of application. Thus, force is a vector quantity, because its effect depends on the direction as well as on the magnitude of the action.
Weight
In most modern scientific work, physical quantities are measured in SI units. The SI unit of weight is the same as that of force: the newton (N) – a derived unit which can also be expressed in SI base units as kg⋅m/s (kilograms times meters per second squared).
Planck constant
It is currently planned to redefine certain of the SI base units in terms of fundamental physical constants. This has already been done for the metre, which since 1983 has been defined in terms of a fixed value of the speed of light. The most urgent unit on the list for redefinition is the kilogram, whose value has been fixed for all science (since 1889) by the mass of a small cylinder of platinum–iridium alloy kept in a vault just outside Paris. While nobody knows if the mass of the International Prototype Kilogram has changed since 1889 – the value 1 kg of its mass expressed in kilograms is by definition unchanged and therein lies one of the problems – it is known that over such a timescale the many similar Pt–Ir alloy cylinders kept in national laboratories around the world have changed their relative masses by several tens of parts per billion, however carefully they are stored. A change of several tens of micrograms in one kilogram is equivalent to the current uncertainty in the value of the Planck constant in SI units.
Hooke's law
In SI units, displacements are measured in meters (m), and forces in newtons (N or kg·m/s). Therefore, the spring constant , and each element of the tensor , is measured in newtons per meter (N/m), or kilograms per second squared (kg/s).
Pound (force)
In some contexts, the term "pound" is used almost exclusively to refer to the unit of force and not the unit of mass. In those applications, the preferred unit of mass is the slug, i.e. lbf⋅s/ft. In other contexts, the unit "pound" refers to a unit of mass. The international standard symbol for the pound as a unit of mass is lb. 
In the "engineering" systems (middle column), the weight of the mass unit (pound-mass) on Earth's surface is approximately equal to the force unit (pound-force). This is convenient because one pound mass exerts one pound force due to gravity. Note, however, unlike the other systems the force unit is not equal to the mass unit multiplied by the acceleration unit—the use of Newton's Second Law, , requires another factor, "g", usually taken to be 32.174049 (lb⋅ft)/(lbf⋅s).
"Absolute" systems are "coherent" systems of units: by using the slug as the unit of mass, the "gravitational" FPS system (left column) avoids the need for such a constant. The SI is an "absolute" metric system with kilogram and meter as base units.
Unit of measurement
A unit of measurement is a standardised quantity of a physical property, used as a factor to express occurring quantities of that property. Units of measurement were among the earliest tools invented by humans. Primitive societies needed rudimentary measures for many tasks: constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials.
Energy
In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton.
Power (physics)
In physics, power is the rate of doing work or transferring heat, the amount of energy transferred or converted per unit time. Having no direction, it is a scalar quantity. In the International System of Units, the unit of power is the joule per second (J/s), known as the watt in honour of James Watt, the eighteenth-century developer of the condenser steam engine. Another common and traditional measure is horsepower (comparing to the power of a horse). Being the rate of work, the equation for power can be written:
Janka hardness test
The results are stated in various ways, which can lead to confusion, especially when the actual units employed are often not attached. Overall, the resulting measure is always one of force. In the United States, the measurement is in pounds-force (lbf). In Sweden it is in kilograms-force (kgf), and in Australia, either in newtons (N) or kilonewtons (kN). This confusion is greatest when the results are treated as units, for example "660 Janka".
Pound (force)
The pound-force is equal to the gravitational force exerted on a mass of one avoirdupois pound on the surface of Earth. Since the 18th century, the unit has been used in low-precision measurements, for which small changes in Earth's gravity (which varies from place to place by up to half a percent) can safely be neglected.
Vacuum permittivity
One now adds the requirement that one wants force to be measured in newtons, distance in metres, and charge to be measured in the engineers' practical unit, the coulomb, which is defined as the charge accumulated when a current of 1 ampere flows for one second. This shows that the parameter "ε" should be allocated the unit C⋅N⋅m (or equivalent units – in practice "farads per metre").
Newton (unit)
In 1946, Conférence Générale des Poids et Mesures (CGPM) Resolution 2 standardized the unit of force in the MKS system of units to be the amount needed to accelerate 1 kilogram of mass at the rate of 1 metre per second squared. In 1948, the 9th CGPM Resolution 7 adopted the name "newton" for this force. The MKS system then became the blueprint for today's SI system of units. The newton thus became the standard unit of force in the (SI), or International System of Units.
Grave (unit)
The modern kilogram has its origins in the Age of Enlightenment and the French Revolution. In 1790 an influential proposal by Talleyrand called for a new system of units, including a unit of length derived from an invariable length in nature, and a unit of mass (then called "weight") equal to the mass of a unit volume of water. In 1791, the Commission of Weights and Measures, appointed by the French Academy of Sciences, chose one ten-millionth of the quarter meridian as the unit of length, and named it "metre". Initially a "provisional" value was used, based on the old meridian measurement by Lacaille (1740).
Gravitational metric system
In Germany, the kilopond lost its legal status as a unit of force on the first of January 1978 and is replaced by SI units. A kilopond can be converted to the SI unit Newton by multiplication with the standard acceleration "g":
Ohm
The ohm (symbol: Ω) is the SI derived unit of electrical resistance, named after German physicist Georg Simon Ohm. Although several empirically derived standard units for expressing electrical resistance were developed in connection with early telegraphy practice, the British Association for the Advancement of Science proposed a unit derived from existing units of mass, length and time and of a convenient size for practical work as early as 1861. The definition of the ohm was revised several times. Today, the definition of the ohm is expressed from the quantum Hall effect.
Kilogram-force per square centimetre
kg/cm remains active as a measurement of force primarily due to older torque measurement devices still in use.
Gravimetry
Gravity is usually measured in units of acceleration. In the SI system of units, the standard unit of acceleration is 1 metre per second squared (abbreviated as m/s). Other units include the gal (sometimes known as a "galileo", in either case with symbol Gal), which equals 1 centimetre per second squared, and the "g" ("g"), equal to 9.80665 m/s. The value of the "g" approximately equals the acceleration due to gravity at the Earth's surface (although the value of "g" varies by location).
Specific strength
Tenacity is the customary measure of strength of a fiber or yarn. In the U.S. it is usually defined as the ultimate (breaking) force of the fiber (in gram-force units) divided by the denier.
Because denier is a measure of the linear density, the tenacity works out to be not a measure of force per unit area, but rather a quasi-dimensionless measure analogous to specific strength. 
A tenacity of formula_1 corresponds to: formula_2
Kilogram
The stability of the IPK is crucial because the kilogram underpins much of the SI system of measurement as it is currently defined and structured. For instance, the newton is defined as the force necessary to accelerate one kilogram at one metre per second squared. If the mass of the IPK were to change slightly then the newton would also change proportionally. In turn, the pascal, the SI unit of pressure, is defined in terms of the newton. This chain of dependency follows to many other SI units of measure. For instance, the joule, the SI unit of energy, is defined as that expended when a force of one newton acts through one metre. Next to be affected is the SI unit of power, the watt, which is one joule per second. The ampere too is defined relative to the newton.
Gravimetry
An instrument used to measure gravity is known as a gravimeter, or gravinometer. For a small body, general relativity predicts gravitational effects indistinguishable from the effects of acceleration by the equivalence principle. Thus, gravimeters can be regarded as special-purpose accelerometers. Many weighing scales may be regarded as simple gravimeters. In one common form, a spring is used to counteract the force of gravity pulling on an object. The change in length of the spring may be calibrated to the force required to balance the gravitational pull. The resulting measurement may be made in units of force (such as the newton), but is more commonly made in units of gals.
Thrust
Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction on that system.
The force applied on a surface in a direction perpendicular or normal to the surface is also called thrust. Force, and thus thrust, is measured using the International System of Units (SI) in newtons (symbol: N), and represents the amount needed to accelerate 1 kilogram of mass at the rate of 1 meter per second per second. In mechanical engineering, force orthogonal to the main load (such as in parallel helical gears) is referred to as thrust.
Specific force
Specific force (also called g-force and mass-specific force) is measured in meters/second² (m·s) which is the units for acceleration. Thus, specific force is not actually a force, but a type of acceleration. However, the (mass-)specific force is not a coordinate-acceleration, but rather a proper acceleration, which is the acceleration relative to free-fall. Forces, specific forces, and proper accelerations are the same in all reference frames, but coordinate accelerations are frame-dependent. For free bodies, the specific force is the cause of, and a measure of, the body's proper acceleration.
Body force
A body force is simply a type of force, and so it has the same dimensions as force, [M][L][T]. However, it is often convenient to talk about a body force in terms of either the force per unit volume or the force per unit mass. If the force per unit volume is of interest, it is referred to as the force density throughout the system.
Gauss (unit)
The gauss, abbreviated as G or Gs, is the cgs unit of measurement of magnetic flux density (or "magnetic induction") (B). It is named after German mathematician and physicist Carl Friedrich Gauss. One gauss is defined as one maxwell per square centimeter. The cgs system has been superseded by the International System of Units (SI), which uses the tesla (symbol T) as the unit of magnetic flux density. One gauss equals 1 tesla (100 μT), so 1 tesla = 10,000 gauss.
Coherence (units of measurement)
The history of the measurement of length dates back to the early civilisations of the Middle East (10000 BC – 8000 BC). Archeologists have been able to reconstruct the units of measure in use in Mesopotamia, India, the Jewish culture and many others. Archaeological and other evidence shows that in many civilisations, the ratios between different units for the same quantity of measure were adjusted so that they were integer numbers. In many early cultures such as Ancient Egypt, multiples of 2, 3 and 5 were not always used—the Egyptian royal cubit being 28 fingers of 7 hands. In 2150 BC, the Akkadian emperor Naram-Sin rationalised the Babylonian system of measure, adjusting the ratios of many units of measure to multiples of 2, 3 or 5, for example there were 6 "she" (barleycorns) in a "shu-si" (finger) and 30 shu-si in a "kush" (cubit).
Non-commensurable quantities have different physical dimensions which means that adding or subtracting them is not meaningful. For instance, adding the mass of an object to its volume has no physical meaning. However, new quantities (and, as such, units) can be derived via multiplication and exponentiation of other units. As an example, the SI unit for force is the newton, which is defined as kg⋅m⋅s. Since a coherent derived unit is one which is defined by means of multiplication and exponentiation of other units but not multiplied by any scaling factor other than 1, the pascal is a coherent unit of pressure (defined as kg⋅m⋅s), but the bar (defined as ) is not.
International Practical Shooting Confederation
The official unit used for the power factor is the imperial unit "kilo grain feet per second" (kgr·ft/s). "Grain feet per second" (gr·ft/s) can be obtained by measuring the "mass" in grain (gr) (equal to pound), and "velocity" in feet per second (ft/s), but since their product yields a very large number it is common to multiply by a factor of , obtaining the power factor in ""kilo" grain feet per second" instead.
Kilogram-force
Prior to this, the unit was widely used in much of the world and it is still in use for some purposes. The thrust of a rocket engine, for example, was measured in kilograms-force in 1940s Germany, in the Soviet Union (where it remained the primary unit for thrust in the Russian space program until at least the late 1980s), and it is still used today in China and sometimes by the European Space Agency.
Pressure measurement
Pressure measurement is the analysis of an applied force by a fluid (liquid or gas) on a surface. Pressure is typically measured in units of force per unit of surface area. Many techniques have been developed for the measurement of pressure and vacuum. Instruments used to measure and display pressure in an integral unit are called pressure gauges or vacuum gauges. A manometer (not to be confused with nanometer) is a good example, as it uses a column of liquid to both measure and indicate pressure. Likewise the widely used Bourdon gauge is a mechanical device, which both measures and indicates and is probably the best known type of gauge.
Weight
In United States customary units, the pound can be either a unit of force or a unit of mass. Related units used in some distinct, separate subsystems of units include the poundal and the slug. The poundal is defined as the force necessary to accelerate an object of one-pound "mass" at 1 ft/s, and is equivalent to about 1/32.2 of a pound-"force". The slug is defined as the amount of mass that accelerates at 1 ft/s when one pound-force is exerted on it, and is equivalent to about 32.2 pounds (mass).
Coherence (units of measurement)
A variant of this system applies the unit s/ft to the proportionality constant. This has the effect of identifying the pound-force with the pound. The pound is then both a base unit of mass and a coherent derived unit of force. One may apply any unit one pleases to the proportionality constant. If one applies the unit s/lb to it, then the foot becomes a unit of force. In a four-unit system (English engineering units), the pound and the pound-force are distinct base units, and the proportionality constant has the unit lbf⋅s/(lb⋅ft).
Proper acceleration
The total (mechanical) force that is calculated to induce the proper acceleration on a mass at rest in a coordinate system that has a proper acceleration, via Newton's law F = "m" a, is called the proper force. As seen above, the proper force is equal to the opposing reaction force that is measured as an object's "operational weight" (i.e. its weight as measured by a device like a spring scale, in vacuum, in the object's coordinate system). Thus, the proper force on an object is always equal and opposite to its measured weight.
Size
Although the size of an object may be reflected in its mass or its weight, each of these is a different concept. In scientific contexts, mass refers loosely to the amount of "matter" in an object (though "matter" may be difficult to define), whereas weight refers to the force experienced by an object due to gravity. An object with a mass of 1.0 kilogram will weigh approximately 9.81 newtons (newton is the unit of force, while kilogram is the unit of mass) on the surface of the Earth (its mass multiplied by the gravitational field strength). Its weight will be less on Mars (where gravity is weaker), more on Saturn, and negligible in space when far from any significant source of gravity, but it will always have the same mass. Two objects of equal size, however, may have very different mass and weight, depending on the composition and density of the objects. By contrast, if two objects are known to have roughly the same composition, then some information about the size of one can be determined by measuring the size of the other, and determining the difference in weight between the two. For example, if two blocks of wood are equally dense, and it is known that one weighs ten kilograms and the other weighs twenty kilograms, and that the ten kilogram block has a volume of one cubic foot, then it can be deduced that the twenty kilogram block has a volume of two cubic feet.
Force density
In fluid mechanics, the force density is the negative gradient of pressure. It has the physical dimensions of force per unit volume. Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid. Force density is represented by the symbol f 
, and given by the following equation, where "P" is the pressure:
Momentum
In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction in three-dimensional space. If is an object's mass and is the velocity (also a vector), then the momentum is
In SI units, it is measured in kilogram meters per second (kg⋅m/s). Newton's second law of motion states that a body's rate of change in momentum is equal to the net force acting on it.
Kilogram-force per square centimetre
In SI units, the unit is converted to the SI derived unit pascal (Pa), which is defined as one newton per square metre (N/m). A newton is equal to a kg·m/s, and a kilogram-force is 9.80665 newtons, meaning that 1 kgf/cm equals 98.0665 kilopascals (kPa).
Units of measurement in France
During the early part of the twentieth century, the French introduced their own units of power - the "poncelet", which was defined as being the power required to raise a mass of 100 kg against standard gravity with a velocity of 1 m/s giving a value of 980.665 W. However, many other European countries defined their units of power (the "Pferdestärke" in Germany, the "paardekracht" in the Netherlands and the "cavallo vapore" in Italy) using 75 kg rather than 100 kg, which gave a value of 735.49875 W (about 0.985 HP). Eventually, the "poncelet" was replaced with the "cheval vapeur", which was identical to equivalent units of measure in neighbouring countries. In 1977, these units, along with the "stere" and the "livre" (and amongst others, the German "pfund") were proscribed by EEC Directive 71/354/EEC
Weighting
In each field of measurement, special units are used to indicate a weighted measurement as opposed to a basic physical measurement of energy level. For sound, the unit is the phon (1 kHz equivalent level).
Gc (engineering)
In unit systems where force is a derived unit, like in SI units, "g" is equal to 1 and is not needed. In unit systems where force is a primary unit, like in English units, "g" is not equal to 1, and is required to obtain correct results.
Introduction to the metric system
On the eve of the French Revolution, France had an estimated quarter of a million different units of measurement. In many cases the value of a unit differed from town to town and even from trade to trade even though they might have the same name. While certain standards, such as the "pied du roi" (the King's foot) had a degree of pre-eminence and were used by savants (scientists), many traders used their own measuring devices. This gave scope for fraud and hindered commerce and industry. The metric system was designed to replace this confusion with a radical new system with fixed values.
In England, Magna Carta in 1215 decreed that "there shall be one unit of measure throughout the realm", However, France and the rest of Europe had a multitude of measurement units. The differences were like those between United States customary units and United Kingdom imperial units that measure liquids a US pint consists of 16 US fluid ounces while an imperial pint is 20 UK fluid ounces and the US fluid ounce is about 4% larger than the UK fluid ounce. Differences such as these occurred across Europe.
Units of energy
Because energy is defined via work, the SI unit for energy is the same as the unit of work – the joule (J), named in honor of James Prescott Joule and his experiments on the mechanical equivalent of heat. In slightly more fundamental terms, 1 joule is equal to 1 newton metre and, in terms of SI base units
Electric field
The Coulomb force on a charge of magnitude formula_25 at any point in space is equal to the product of the charge and the electric field at that point
The units of the electric field in the SI system are newtons per coulomb (N/C), or volts per meter (V/m); in terms of the SI base units they are kg⋅m⋅s⋅A
Force
An alternative unit of force in a different foot-pound-second system, the absolute fps system, is the poundal, defined as the force required to accelerate a one-pound mass at a rate of one foot per second squared. The units of slug and poundal are designed to avoid a constant of proportionality in Newton's Second Law.
Introduction to the metric system
The metric system was developed during the French Revolution to replace the various measures previously used in France. The metre (sometimes spelled "meter" in American English) is the unit of length in the metric system and was originally based on the dimensions of the earth, as far as it could be measured at the time. The litre (also spelled "liter"), is the unit of volume and was defined as one thousandth of a cubic metre. The metric unit of mass is the kilogram and it was defined as the mass of one litre of water. The metric system was, in the words of French philosopher Marquis de Condorcet, "for all people for all time".
Ultimate tensile strength
Tensile strength is defined as a stress, which is measured as force per unit area. For some non-homogeneous materials (or for assembled components) it can be reported just as a force or as a force per unit width. In the International System of Units (SI), the unit is the pascal (Pa) (or a multiple thereof, often megapascals (MPa), using the SI prefix "mega"); or, equivalently to pascals, newtons per square metre (N/m²). A United States customary unit is pounds per square inch (lb/in² or psi), or kilo-pounds per square inch (ksi, or sometimes kpsi), which is equal to 1000 psi; kilo-pounds per square inch are commonly used in one country (US), when measuring tensile strengths.
Kilogram-force
Kilogram-force is a non-standard unit and is classified in SI Metric System as a unit that is unacceptable for use with SI.
G-force
The term g-force is technically incorrect as it is a measure of "acceleration", not force. While acceleration is a vector quantity, g-force accelerations ("g-forces" for short) are often expressed as a scalar, with positive g-forces pointing downward (indicating upward acceleration), and negative g-forces pointing upward. Thus, a g-force is a vector of acceleration. It is an acceleration that must be produced by a mechanical force, and cannot be produced by simple gravitation. Objects acted upon "only" by gravitation experience (or "feel") no g-force, and are weightless.
Force gauge
A force gauge (also force gage) is a small measuring instrument used across all industries to measure the force during a push or pull test. Applications exist in research and development, laboratory, quality, production and field environment. There are two kinds of force gauges today: mechanical and digital force gauges. Force Gauges usually measure pressure in stress increments and other dependant human factors.
Torque
Torque has dimension force times distance, symbolically . Official SI literature suggests using the unit "newton metre" (N⋅m) or the unit "joule per radian". The unit "newton metre" is properly denoted N⋅m or N m. This avoids ambiguity with mN, millinewtons.
Metrication in the United States
Other units are based on customary units, but use power-of-ten factors and metric prefixes. For example, distance to target for a U.S. submarine is expressed in kiloyards rather than some combination of miles, yards, and feet. Telephone transmission line length and loop distances are measured in kilofeet. In some fields of civil engineering (especially structural engineering), and architecture, large loads and forces (such as the weight of a building or the amount of load applied to a column) are measured in kips (kilopounds or 1000 pounds-force) instead of short tons-force (2000 pounds-force), which are used in virtually all other non-metric industries in the United States, as well as in common usage among the public, when dealing with large values of force.
Gurley Precision Instruments
The Gurley unit is a measure of the stiffness of a material. Since the measurement device holds a piece of material vertically and tests the force required to deflect the material a given amount. One Gurley unit is equivalent to one milligram of force
, however the Gurley unit also implies measurement with this apparatus. A related unit, the Taber, is highly correlated but uses a different apparatus (manufactured by Taber Industries) for performing measurements.
Net force
A force is known as a bound vector—which means it has a direction and magnitude and a point of application. A convenient way to define a force is by a line segment from a point "A" to a point "B". If we denote the coordinates of these points as A=(A, A, A) and B=(B, B, B), then the force vector applied at "A" is given by
The length of the vector B-A defines the magnitude of F and is given by
International System of Units
The base units are derived from invariant constants of nature, such as the speed of light in vacuum and the triple point of water, which can be observed and measured with great accuracy, and one physical artefact. The artefact is the international prototype kilogram, certified in 1889, and consisting of a cylinder of platinum-iridium, which nominally has the same mass as one litre of water at the freezing point. Its stability has been a matter of significant concern, culminating in a revision of the definition of the base units entirely in terms of constants of nature, scheduled to be put into effect on 20 May 2019.
Mass versus weight
Because mass and weight are separate quantities, they have different units of measure. In the International System of Units (SI), the kilogram is the basic unit of mass, and the newton is the basic unit of force. The non-SI kilogram-force is also a unit of force typically used in the measure of weight. Similarly, the avoirdupois pound, used in both the Imperial system and U.S. customary units, is a unit of mass, and its related unit of force is the pound-force.
Kilogram-force
It is also used for tension of bicycle spokes, for informal references to pressure in kilograms per square centimeter (1 kp/cm) which is the technical atmosphere (at) and very close to 1 bar and the standard atmosphere (atm), for the draw weight of bows in archery, and to define the "metric horsepower" (PS) as 75 metre-kiloponds per second. In addition, kilograms force is the standard unit used for Vickers hardness testing.
The tonne-force, metric ton-force, megagram-force, and megapond (Mp) are each 1000 kilograms-force.
Poundal
English units require re-scaling of either force or mass to eliminate a numerical proportionality constant in the equation "F = ma". The poundal represents one choice, which is to rescale units of force. Since a pound of "force" (pound force) accelerates a pound of "mass" (pound mass) at 32.174 049 ft/s (9.80665 m/s; the acceleration of gravity, "g"), we can scale down the unit of force to compensate, giving us one that accelerates 1 pound mass at 1 ft/s rather than at 32.174 049 ft/s; and that is the poundal, which is approximately of a pound force.
Acceleration
In physics, acceleration is the rate of change of velocity of an object with respect to time. An object's acceleration is the net result of all forces acting on the object, as described by Newton's Second Law. The SI unit for acceleration is metre per second squared Accelerations are vector quantities (they have magnitude and direction) and add according to the parallelogram law. The vector of the net force acting on a body has the same direction as the vector of the body's acceleration, and its magnitude is proportional to the magnitude of the acceleration, with the object's mass (a scalar quantity) as proportionality constant.
Imperial and US customary measurement systems
Imperial and US customary units have long been used in many branches of engineering. 
Two of the earliest such units of measure to come into use were the "horsepower" and the "degree Fahrenheit". The "horsepower" was defined by James Watt in 1782 as the power required to raise 33,000 pounds of water through a height of one foot in one minute and the degree Fahrenheit was first defined by Daniel Fahrenheit in about 1713 as being a temperature scale having its lower calibration point (0 °F) at temperature where a supersaturated salt/ice mixture froze and its upper calibration point at body temperature (96 °F). In 1777 the Royal Society, under the chairmanship of Henry Cavendish, proposed the definition of the Fahrenheit scale be modified such that the temperature corresponding to the melting point of ice be 32 °F and the boiling point of water under standard atmospheric conditions be 212 °F.
The British thermal unit (Btu) is defined as the heat needed to raise the temperature of one pound of water by one degree Fahrenheit. It was in use before 1859 as a unit of heat based on imperial units rather than the metric units used by the French—Clément-Desormes having defined the calorie in terms of the kilogram and degrees centigrade in 1824.
Joule-second
The joule-second also appears as the unit of measure in classical mechanics for the angular momentum of a rotating object and in quantum mechanics within the definition of Planck's constant. Angular momentum is the product of an object’s moment of inertia, in units of kg∙m and its rotational velocity in units of m∙s∙m, or simply s (i.e., Hz). This product of moment of inertia and rotational velocity yields kg∙m∙ s or the joule-second. Planck's constant represents the energy of a wave, in units of joule, divided by the frequency of that wave, in units of s. This quotient of energy and frequency also yields the joule-second (J∙s).
Kip (unit)
The name comes from combining the words "kilo" and "pound"; it is occasionally called a "kilopound". Its symbol is kip, or less frequently, klb. When it is necessary to clearly distinguish it as a unit of force rather than mass, it is sometimes called the "kip-force" (symbol kipf or klbf).
Note that the symbol kp usually stands for a different unit of force, the "kilopond" or kilogram-force used primarily in Europe prior to the introduction of SI units.
Ounce
The "ounce" in "ounce-force" is equivalent to an avoirdupois ounce; ounce-force is a measurement of force using avoirdupois ounces. However, it is not necessary to identify it as such or to differentiate it in that way because there is no equivalent measure of force using troy or any other "ounce".
Newton metre
The newton metre (also newton-metre, symbol N m or N⋅m) is a unit of torque (also called ) in the SI system. One newton metre is equal to the torque resulting from a force of one newton applied perpendicularly to the end of a moment arm that is one metre long.
Coherence (units of measurement)
All these systems are coherent. One that is not is a three-unit system (also called English engineering units) in which "F" = "ma" that uses the pound and the pound-force, one of which is a base unit and the other, a noncoherent derived unit. In place of an explicit proportionality constant, this system uses conversion factors derived from the relation 1 lbf = 32.174 lb⋅ft/s. In numerical calculations, it is indistinguishable from the four-unit system, since what is a proportionality constant in the latter is a conversion factor in the former. The relation among the numerical values of the quantities in the force law is {"F"} = 0.031081 {"m"} {"a"}, where the braces denote the numerical values of the enclosed quantities. Unlike in this system, in a coherent system, the relations among the numerical values of quantities are the same as the relations among the quantities themselves.
2019 redefinition of SI base units
During the early years of the French Revolution, the leaders of the French National Constituent Assembly decided to introduce a completely new system of measurement based on the principles of logic and natural phenomena. Specifically, the metre was defined as one ten-millionth of the distance from the North Pole to the Equator, and the kilogram as the mass of one thousandth of a cubic metre of pure water. Although these definitions were chosen so that nobody would "own" the units, they could not be measured with sufficient convenience or precision for practical use. Instead, realisations were created in the form of the ' and ' which were a "best attempt" at fulfilling these principles.
Physical constant
On November 16, 2018, the International Bureau of Weights and Measures voted to redefine several base units in the International System of Units (SI) by fixing the SI value of several physical constants, including the Planck constant, "h", elementary charge, "e", Boltzmann constant, "k", Avogadro constant, "N", and the speed of light, "c". The new fixed values are based on the best measurements of the constants based on the earlier definitions, including the kilogram, to ensure minimal impact.
G-force
The unit of measure of acceleration in the International System of Units (SI) is m/s. However, to distinguish acceleration relative to free fall from simple acceleration (rate of change of velocity), the unit g (or g) is often used. One "g" is the acceleration due to gravity at the Earth's surface and is the standard gravity (symbol: "g"), defined as  metres per second squared, or equivalently  newtons of force per kilogram of mass. Note that the "unit definition" does not vary with location—the g-force when standing on the moon is about 0.181 g.
Pound (force)
The pound of force or pound-force (symbol: lbf, sometimes lb,) is a unit of force or weight used in some systems of measurement including English Engineering units and the British Gravitational System. Pound-force should not be confused with foot-pound, a unit of energy, or pound-foot, a unit of torque, that may be written as "lbf⋅ft"; nor should these be confused with pound-mass (symbol: lb), often simply called "pound," which is a unit of mass.