GNU Units
this page seriously undersells the versatility and utility of the units program<p>how long will my laptop take to charge at its current rate of charging?<p><pre><code>    You have: (22.8 Wh - 16.8 Wh)&#x2F;7.4W
    You want: time
            48 min + 38.918919 sec
</code></pre>
how long will a 2000mAh 18650 cell take to discharge at 2.5 watts, using a nominal voltage of 3.7 volts?<p><pre><code>    You have: 3.7 V 2 amp hour &#x2F; 2.5 watt
    You want: time
            2 hr + 57 min + 36 sec
</code></pre>
what energy density is that, so i can compare it to the volume needed for other forms of energy storage?<p><pre><code>    You have: 3.7 V 2 amp hour &#x2F; circlearea(half 18 mm) 65 mm
    You want: MJ&#x2F;ℓ
            * 1.6105936
            &#x2F; 0.62088909
</code></pre>
what&#x27;s the specific energy of stoichiometrically mixed oxyhydrogen fuel?<p><pre><code>    You have: 44000 J&#x2F;mol &#x2F; ((2 hydrogen + oxygen)g&#x2F;mol)
    You want: MJ&#x2F;kg
            * 2.4423711
            &#x2F; 0.40943818
</code></pre>
okay but how much volume?  say at atmospheric pressure?<p><pre><code>    You have: 3 mol gasconstant tempC(20) &#x2F; 1 atm
    You want: l
            * 72.165351
            &#x2F; 0.013857066
</code></pre>
so that&#x27;s how much energy density?<p><pre><code>    You have: 44kJ&#x2F;_
    You want: J&#x2F;l
            * 609.71089
            &#x2F; 0.0016401216
</code></pre>
(i may be off by a factor of 2 here)<p>how much energy can this capacitor hold?<p><pre><code>    You have: half (10V)**2 47 uF
    You want: mJ
            * 2.35
            &#x2F; 0.42553191
</code></pre>
how much energy density is that?<p><pre><code>    You have: half (10V)**2 47 μF &#x2F; 15mm circlearea(3mm)
    You want: J&#x2F;ℓ
            * 5.5409499
            &#x2F; 0.18047447
</code></pre>
how thick of a cable do i need to support me in a lightweight fabric-sling chair (or, from a different point of view, to pose a risk of accidental strangulation)?  suppose its tensile strength is 2.7 gigapascals<p><pre><code>    You have: 120kg gravity &#x2F; 2.7 GPa
    You want: mm2
            * 0.43585111
            &#x2F; 2.2943615
    You have: _
    You want: circlearea
            0.00037247244 m
    You have: _
    You want: mm
            * 0.37247244
            &#x2F; 2.6847624
</code></pre>
note that this is the <i>radius</i> of the cable, not its diameter!<p>the datasheet says this 400×240 display uses 175 μW if all the pixels flip once per second and 60 μW for a static display.  how much energy is that per pixel flip?<p><pre><code>    You have: (175 uW - 50 uW) &#x2F; 400 240 1 Hz
    You want: nJ
            * 1.3020833
            &#x2F; 0.768
</code></pre>
if i overclock it to 60 fps how much power will it use?<p><pre><code>    You have: 60 Hz 400 240 1.3nJ
    You want: μW
            * 7488
            &#x2F; 0.00013354701
</code></pre>
and how many pixels is its diagonal?<p><pre><code>    You have: 400**2+240**2
    You want: 
            Definition: 217600
    You have: _**.5
    You want: 
            Definition: 466.47615
</code></pre>
what is the visual angle subtended by the sun as seen from earth?<p><pre><code>    You have: 2 sunradius&#x2F;sundist
    You want: milliradians
            * 9.3049358
            &#x2F; 0.10746984
    You have: _
    You want: dms
            31 arcmin + 59.280781 arcsec
</code></pre>
okay, how does that compare to the moon?<p><pre><code>    You have: moonradius 2 &#x2F; moondist
    You want: 
            Definition: 0.0090426639
</code></pre>
on average the moon looks a little smaller, which is why annular eclipses are so common, but we can also calculate that total eclipses are possible because sometimes the moon looks bigger<p><pre><code>    You have: moonradius 2 &#x2F; moondist_min
    You want: 
            Definition: 0.0097530864
</code></pre>
what percentage of this copper sulfate is actual copper?<p><pre><code>    You have: copper &#x2F; (copper + (sulfur + 4 oxygen))
    You want: %
            * 39.813395
            &#x2F; 0.025117175
</code></pre>
how fast can i write to this slc flash chip without wearing it out in 53 years, assuming perfect wear leveling and no write amplification?<p><pre><code>    You have: 100 thousand 128 MiB&#x2F;53 years
    You want: bytes&#x2F;second
            * 8024.8943
            &#x2F; 0.00012461223
</code></pre>
how much fuel will this truck need to get across the country?<p><pre><code>    You have: 4000 km &#x2F; (6.5 miles&#x2F;gallon)
    You want: l
            * 1447.4744
            &#x2F; 0.00069085852
</code></pre>
how much is that per kilogram of lettuce or sodium lauryl sulfate or whatever?<p><pre><code>    You have: _&#x2F;28 tonnes
    You want: ml&#x2F;kg
            * 51.695513
            &#x2F; 0.019344039
</code></pre>
okay, but how much energy is 52 mℓ of diesel per kg of lettuce?<p><pre><code>    You have: _ 38.6 kJ&#x2F;l
    You want: kJ&#x2F;kg
            * 1.9954468
            &#x2F; 0.5011409
</code></pre>
how much data can i transfer overnight during unmetered hours on a 2400-baud modem?<p><pre><code>    You have: 8 hours 2400 bps
    You want: MB
            * 8.64
            &#x2F; 0.11574074
</code></pre>
how much power does the earth receive from the sun, assuming a solar constant of 1400 W&#x2F;m²?<p><pre><code>    You have: 1400 W&#x2F;m**2 * circlearea(earthradius)
    You want: petawatts
            * 178.52313
            &#x2F; 0.0056015152
</code></pre>
what would the equilibrium temperature of an object be if it were illuminated at that brightness and had a flat emission spectrum?<p><pre><code>    You have: (1400 W&#x2F;m**2 &#x2F; stefanboltzmann)**(1&#x2F;4)
    You want: tempC
            123.24583
</code></pre>
how about here in buenos aires at the winter solstice?  first, what angle is the sun at anyway?  we&#x27;re at 34°36’ south, and the sun&#x27;s latitude at the solstice is 23°26’<p><pre><code>    You have: 34° + 36&#x27; + 23° + 26&#x27;
    You want: dms
            58 deg + 2 arcmin
</code></pre>
so that reduces the peak insolation to how much?  here underneath the atmosphere we only get 1kW&#x2F;m²<p><pre><code>    You have: cos(_) 1000 W&#x2F;m^2
    You want: W&#x2F;m^2
            * 529.4258
            &#x2F; 0.0018888388
</code></pre>
and that would be what temperature in equilibrium?<p><pre><code>    You have: (_&#x2F;stefanboltzmann)**(1&#x2F;4)
    You want: tempC
            37.698189
</code></pre>
(integrating the sun&#x27;s angle over the course of the day as the earth rotates is sadly beyond its capacities)<p>how much money could a sensible heat storage reservoir of 15 kg of water save me over 16 years?  say power rates go down to only 2.5¢&#x2F;kWh because of solar<p><pre><code>    You have: 1500 kcal&#x2F;day * 16 years * 2.5 cents&#x2F;kWh
    You want: 
            Definition: 254.69556 US$
</code></pre>
what&#x27;s the surface area of a 300mm × 400mm × 150mm backpack?  like how much cloth?<p><pre><code>    You have: 2 (300mm 400mm + 400mm 150mm + 150mm 300mm)
    You want: 
            Definition: 0.45 m^2
</code></pre>
okay but in cm²<p><pre><code>    You have: _
    You want: cm2
            * 4500
            &#x2F; 0.00022222222
</code></pre>
what&#x27;s the electrical impedance of a 1000 μF cap at an audio highpass frequency of 20Hz?<p><pre><code>    You have: 1&#x2F;(2 pi 20 Hz 1000 uF)
    You want: ohms
            * 7.9577472
            &#x2F; 0.12566371
</code></pre>
what&#x27;s the time constant of 100 pF (roughly the smallest capacitance you can get in a macroscopic circuit with any degree of precision) and 1 MΩ?<p><pre><code>    You have: 100 pF 1 megohm
    You want: ms
            * 0.1
            &#x2F; 10
</code></pre>
okay.  so how long will an 0.1μF cap take to discharge through a 100kΩ resistor from 5 volts down to a 1.3 volt threshold?<p><pre><code>    You have: ln(5V&#x2F;1.3V) .1 uF 100kilohm
    You want: ms
            * 13.470736
            &#x2F; 0.074234991
</code></pre>
how many bits of precision does a linear adc need to be able to measure a difference of 1.8 millivolts if 1.5 volts is full-scale?<p><pre><code>    You have: log(1.8mV&#x2F;1.5V)&#x2F;log(2)
    You want: 
            Definition: -9.7027499
</code></pre>
if this oxygen absorber contains 7 grams of iron which oxidizes to Fe₂O₃, how much air can it remove all the oxygen from?  air is 21% oxygen by volume (and roughly by mass) and weighs 1.2 grams per liter<p><pre><code>    You have: 3 oxygen &#x2F; 2 iron * 7 g
    You want: g
            * 3.0082138
            &#x2F; 0.33242318
    You have: _&#x2F;21%&#x2F;(1.2g&#x2F;ℓ)
    You want: ℓ
            * 11.937356
            &#x2F; 0.083770641
</code></pre>
i&#x27;ve lost 7 kg over the last two months; how much of a caloric deficit does that represent in my diet?<p><pre><code>    You have: 7 kg 3500kcal&#x2F;pound &#x2F; 2 months
    You want: kcal&#x2F;day
            * 887.30034
            &#x2F; 0.0011270141
</code></pre>
if you were to spread the moon evenly over russia, how deep would it be?<p><pre><code>    You have: spherevol(moonradius) &#x2F; area_russia
    You want: 
            Definition: 1286134.4 m
</code></pre>
how big is nigeria compared to massachusetts?<p><pre><code>    You have: area_nigeria&#x2F;area_massachusetts
    You want: 
            Definition: 33.793093
</code></pre>
how many ounces of platinum is a ton of oil worth at 40 dollars per megawatt hour?<p><pre><code>    You have: tonoil 40 dollars&#x2F;MWh
    You want: platinumounce
            * 0.58368883
            &#x2F; 1.7132416
</code></pre>
or in grams?<p><pre><code>    You have: tonoil 40 dollars&#x2F;MWh &#x2F; platinumprice
    You want: g
            * 18.154752
            &#x2F; 0.055081997</code></pre>