<p>One key side effect of the French Revolution was the introduction of the metric system. Prior to that revolution, how length, area, volume, mass, and money were measured varied not only from country to country but from town to town. It was an absolute mess. The metric system addressed all of these.</p>
<p>Two things that people measured were not an absolute mess: time and angle. With regard to time, the scientific community had universally settled on 24 hours per day, 60 minutes per hour, and 60 seconds per minute long before the French Revolution. The scientific community had also settled on 360 degrees of arc per rotation, 60 minutes of arc per degree, and 60 seconds of arc per arc minute. These measures date back to ancient Egypt and Babylonia, so very, very old.</p>
<p>The French Revolution's attempts at metricizing time and angle failed because these were the well established de facto standards. Were the goofy standards? Arguably so, but the standards did exist. That there were no standards (de facto or official) for length, area, volume, or mass were key in the rapid advancement of the metric system -- except for time and angle.</p>

CC BY-SA 4.0
2023-06-01T13:03:27.303Z
2023-06-01T13:03:27.303Z
David Hammen
<p>Historical reasons.</p>
<p>Yet your base assumption that 24 hours or 360° equal <em>two</em> revolutions is wrong in an astronomical sense: An hour equals approximately 15 degrees of movement of stars or the Sun if you are dealing with astronomy. Yet that's inconsequential here:</p>
<p>60 is nicely divisible by 2,3,4,5,6,10,12,15, and 30. So subdivisions of degree were chosen with base-12 in mind, making coarse calculations without floating point numbers easy and also marking easily 1/2, 1/3, 1/4, 1/5, 1/6, 1/10, 1/12, 1/15, 1/30 on geometric tools. And the same holds true for dividing each minute into 60 seconds. On the same reasoning the full circle has 360° degrees... nicely divisible without leftover by many numbers, too, introduced this way already thousands of years ago in mesopotamia by the Sumerians and Bablyonians. See also <a href="https://math.stackexchange.com/questions/340467/why-is-a-full-circle-360-degrees">this answer in the math SE</a> or the wiki article on the <a href="https://en.wikipedia.org/wiki/Sexagesimal" rel="nofollow noreferrer">sexagesimal (60-base) system</a>.</p>
<p>Generally, in former times quantities easily divisible were traded, especially of goods where the unit 1 is not easily split, like a complete oxen or eggs. Eggs are here often sold in units of 6, 10 or 12.</p>
<p>While the traditional unit systems usually are a mess and PITA, they sometimes use the factor 12 as well for the conversion between different units like between foot and inch (but not others; just look at the funky conversions between e.g. fingers, yards, miles, furlongs or queen's chains).</p>

CC BY-SA 4.0
2023-05-31T12:39:09.657Z
As you said, an hour equals 15 degrees in astronomical sense. So again, how does each degree equals to 60 minutes (an hour)?! It should have been "each degree equals to 4 minutes"
Snack Exchange
CC BY-SA 4.0
2023-05-31T13:07:57.777Z
Why? The hours of time do not relate to degrees of angle. The similarity is just that each hour of time has 60 minutes and 60 seconds to a minute. The same is for angles: the each degree has 60 arc-minutes and each arc-minute has 60 arc-seconds.
planetmaker
CC BY-SA 4.0
2023-06-01T11:36:04.127Z
But there is still a relationship between hours of time to degrees of angle. Of course, I am convinced that minutes of arc have nothing to do with minutes of time. But surely we both agree that the Earth turns through 15 degrees of arc (degrees for short) in one hour of time (hour for short). This is the relationship.
Snack Exchange
CC BY-SA 4.0
2023-06-01T15:27:14.580Z
Sure. But that's the same kind of relation that I drive with my car 50km / hour in built-up areas. It's just a velocity. For Earth its its rotational velocity which defines the day: 15° per hour. It's somewhat arbitrary and only matches because we defined at some point in history the hour (or minute or second) the way it is: 24 hours in one Earth rotation.
planetmaker
CC BY-SA 4.0
2023-06-01T15:33:54.457Z
But Earth's rotation is too much subject to change (tides, but also seasons, earthquakes, etc) that it is not a good measure of time by todays standard. Time is the most precisely defined and measurable property there is currently to better than 1/10^(-14). (thus better than 20 minutes in duration equal to the age of Earth itself)
planetmaker
CC BY-SA 4.0
2023-05-31T12:29:21.127Z
2023-05-31T12:38:05.143Z
2023-05-31T12:38:05.143Z
planetmaker
<p>The Earth does not turn through a minute of arc or an arcminute during a minute of time, nor does it turn through a second of arc or an arcsecond during a second of time.</p>
<p>Assuming that ther is a connection between arcminutes and minutes of time is an error.</p>
<p>In angular measurement:</p>
<p>A circle is divided into 360 arc degrees, each arc degree being 1/360, or 0.002777, of a circle.</p>
<p>Each arc degree is divided into 60 arcminutes, each arc minute being 1/(360-X 60) or 1/21,600 or 0.000046296, of a circle.</p>
<p>Each arcminute is divided into 60 arcseconds, each arcsecond being 1/(360 X 60 X 60), or 1/1,296,000, or 0.000000771, of a circle.</p>
<p>In time measurement:</p>
<p>One day is divided into 24 hours, each being 1/24, or 0.0416666, of a day.</p>
<p>One hour is divided into 60 minutes of time, each minute of time being 1/(24 X 60), or 1/1,440, or 0.000694444, of a day.</p>
<p>One minute of time is divided into 60 seconds of time, each second of time being  1/(24 X 60 X 60), or 1/96,400, or 0.000011574, of a day.</p>
<p>The Earth turns 360 degrees of arc in one 24 hour day of time.</p>
<p>So the Earth turns through 15 degrees of arc in one hour of time.</p>
<p>And thus the Earth turns through 15 arcminutes during one minute of time.</p>
<p>And so the Earth turns through 15 arcseconds in one second of time.</p>
<p>So any source implying that an arcminute is equal to the angle that Earth turns in a minute of time is incorrect.</p>
<p>The Earth does not turn through one arcminute in one minute of time, nor through one arcsecond in one second of time.  So a different number of arcminutes fits into a  full circle than the number of minutes of time during a day.</p>

CC BY-SA 4.0
2023-06-01T11:30:35.573Z
But it is true to say that the Earth turns each degree of arc (degree for short) in 4 minutes of time (minute for short). Isn't it a way to relate angle to time?
Snack Exchange
CC BY-SA 4.0
2023-06-01T01:51:09.327Z
2023-06-01T01:51:09.327Z
M. A. Golding
<p>The terms &quot;minute&quot; and &quot;second&quot; were likely more commonly used to refer to fractions of a degree than for time back when they were invented.  The meaning and pronunciation have slightly morphed over the years and are generally synonymous with time now.</p>
<p>But if you think of the homographs of the words (words that are spelled the same, but have a different meaning), <a href="https://www.dictionary.com/browse/minute#:%7E:text=%2F%20(ma%C9%AA%CB%88nju%CB%90t)%20%2F,unimportant%3B%20petty" rel="noreferrer">minute</a> pronounced in the way that rhymes with &quot;my newt&quot; just means &quot;very tiny&quot;.  So a &quot;minute of a degree&quot; just means a &quot;tiny fraction of a degree&quot;, or more specifically &quot;<strong>minute division</strong>&quot;.</p>
<p>Similarly the homograph of &quot;second&quot;, as in &quot;not first&quot;, &quot;not third&quot;, but <span class="math-container">$2^{nd}$</span>.  So a &quot;second of a degree&quot;, just means &quot;<strong>second division</strong>&quot;.</p>
<p>Before the age of computing machines, division was time consuming, so it made sense to choose a base which was easily divisible by many numbers, and 60 fits that quite well, and is the basis for the <a href="https://en.wikipedia.org/wiki/Sexagesimal" rel="noreferrer">sexagesimal system</a>.  And we still use this system today in that a &quot;minute part of an hour&quot; is 1/60th of an hour, and the &quot;second division of an hour&quot; is 1/60th of a minute.</p>
<p><strong>So the meaning of the words still holds today, in that they mean 1/60th of something</strong>.  It's just that what they are 1/60th of changes depending on context.</p>
<p>In astronomy, the words arcminute and arcsecond are generally used to disambiguate the terms.  But in celestial navigation and land surveying, it is still quite common to just use minute and second to refer to fractions of a degree.</p>
<p>The <a href="https://en.wikipedia.org/wiki/Minute#History" rel="noreferrer">history section</a> of the Wikipedia entry on the minute contains some of this explanation, and expands on to &quot;thirds&quot; and &quot;fourths&quot;.</p>

CC BY-SA 4.0
2023-05-31T14:50:37.640Z
Thank you for your answer. It enlightened me very much. But I still can't get the quoted text that I extracted from a website to my question body. Is that nonesense in fact?
Snack Exchange
CC BY-SA 4.0
2023-05-31T16:45:47.147Z
Snack Exchange - Yes, it is nonsense. I think the author was unaware of the information provided here. An etymological dictionary will confirm Greg's very well-written answer.
Mark Foskey
CC BY-SA 4.0
2023-05-31T17:06:26.303Z
@MarkFoskey I think that was nonesense in two parts! One for not knowing there are two kind of minutes and seconds. And one for the formula they have given: Why should we divide 720 degrees to 12 in order to reach 60? And how does dividing degrees to a number yields minutes? Even if the number's unit is hour, still doesn't make sense. And then the site says well, it's proven that each degree equals to 60 minutes!
Snack Exchange
CC BY-SA 4.0
2023-06-01T02:58:06.467Z
Yea, the link is nonsense, I chose to focus on explaining it correctly to answer the question in the title.
Greg Miller
CC BY-SA 4.0
2023-05-31T14:13:56.650Z
2023-05-31T14:33:45.923Z
2023-05-31T14:33:45.923Z
Greg Miller
<p>I was searching in the internet to find the reason each degree equals to 60 minutes and I found <a href="https://byjusexamprep.com/how-is-1-degree-equal-to-60-minutes-i_amp" rel="nofollow noreferrer">this</a>:</p>
<blockquote>
<p>60 seconds make up a minute. One day is equal to 24 hours, and the hour hand completes two 360-degree circles around the clock in a single day, for a total of 720 degrees. One degree (2 x 360)/12 equals one hour.</p>
</blockquote>
<p>But does it make sense? Why should we divide it by 12? An hour itself equals 30 degrees. So each second equals 6 degrees and thus, each degree should equal 1/6 seconds.</p>

CC BY-SA 4.0
2023-05-31T12:21:27.177Z
"and thus, each degree should equal 1/6 seconds." ???  The title of your question and what follows don't seem to match up.
ProfRob
CC BY-SA 4.0
2023-05-31T13:06:49.257Z
Each degree equals 1/6 seconds on a clock. Each degree equals 4 minutes on the Earth rotation. But I don't know how each degree equals 60 minutes.
Snack Exchange
CC BY-SA 4.0
2023-05-31T13:10:09.490Z
Don't conflate minutes and hours on the clock with arc-minutes and arc-seconds as units of angle. It's different things with (nearly) identical names - for historical reasons as they give the same *fraction* of the unit they divide respectively
planetmaker
CC BY-SA 4.0
2023-05-31T14:13:06.827Z
Related: https://astronomy.stackexchange.com/q/44109/16685
PM 2Ring
CC BY-SA 4.0
2023-06-02T17:44:30.063Z
60-oriented or 360-oriented mensuration systems seem to have been popular with Babylonians, for example, in their astronomy, and other things. I'd speculate that relatively precise time-keeping's close relationship with astronomy partly encouraged re-use of the terminology... but I don't know. (The reason being that these numbers have many small divisors... )
paul garrett
<mathematics>
How does each degree equal to 60 minutes?
Snack Exchange
# How does each degree equal to 60 minutes?

(Asked by: username_0 on 2023-05-31)

I was searching in the internet to find the reason each degree equals to 60 minutes and I found [this](https://byjusexamprep.com/how-is-1-degree-equal-to-60-minutes-i_amp):

> 60 seconds make up a minute. One day is equal to 24 hours, and the hour hand completes two 360-degree circles around the clock in a single day, for a total of 720 degrees. One degree (2 x 360)/12 equals one hour.

But does it make sense? Why should we divide it by 12? An hour itself equals 30 degrees. So each second equals 6 degrees and thus, each degree should equal 1/6 seconds.

**Tags:** mathematics
> **Comments:**
> **username_1**: "and thus, each degree should equal 1/6 seconds." ???  The title of your question and what follows don't seem to match up.  
> **username_0**: Each degree equals 1/6 seconds on a clock. Each degree equals 4 minutes on the Earth rotation. But I don't know how each degree equals 60 minutes.  
> **username_2**: Don't conflate minutes and hours on the clock with arc-minutes and arc-seconds as units of angle. It's different things with (nearly) identical names - for historical reasons as they give the same *fraction* of the unit they divide respectively  
> **username_3**: Related: https://astronomy.stackexchange.com/q/44109/16685  
> **username_4**: 60-oriented or 360-oriented mensuration systems seem to have been popular with Babylonians, for example, in their astronomy, and other things. I'd speculate that relatively precise time-keeping's close relationship with astronomy partly encouraged re-use of the terminology... but I don't know. (The reason being that these numbers have many small divisors... )  

---

## 4 answers

### Answer by username_7 on 2023-05-31. Score: 7 | Accepted answer

The terms "minute" and "second" were likely more commonly used to refer to fractions of a degree than for time back when they were invented. The meaning and pronunciation have slightly morphed over the years and are generally synonymous with time now.

But if you think of the homographs of the words (words that are spelled the same, but have a different meaning), [minute](https://www.dictionary.com/browse/minute#:%7E:text=%2F%20(ma%C9%AA%CB%88nju%CB%90t)%20%2F,unimportant%3B%20petty) pronounced in the way that rhymes with "my newt" just means "very tiny". So a "minute of a degree" just means a "tiny fraction of a degree", or more specifically "**minute division**".

Similarly the homograph of "second", as in "not first", "not third", but $2^{nd}$. So a "second of a degree", just means "**second division**".

Before the age of computing machines, division was time consuming, so it made sense to choose a base which was easily divisible by many numbers, and 60 fits that quite well, and is the basis for the [sexagesimal system](https://en.wikipedia.org/wiki/Sexagesimal). And we still use this system today in that a "minute part of an hour" is 1/60th of an hour, and the "second division of an hour" is 1/60th of a minute.

**So the meaning of the words still holds today, in that they mean 1/60th of something**. It's just that what they are 1/60th of changes depending on context.

In astronomy, the words arcminute and arcsecond are generally used to disambiguate the terms. But in celestial navigation and land surveying, it is still quite common to just use minute and second to refer to fractions of a degree.

The [history section](https://en.wikipedia.org/wiki/Minute#History) of the Wikipedia entry on the minute contains some of this explanation, and expands on to "thirds" and "fourths".

> **Comments:**
> **username_0**: Thank you for your answer. It enlightened me very much. But I still can't get the quoted text that I extracted from a website to my question body. Is that nonesense in fact?  
> **username_8**: Snack Exchange - Yes, it is nonsense. I think the author was unaware of the information provided here. An etymological dictionary will confirm Greg's very well-written answer.  
> **username_0**: @MarkFoskey I think that was nonesense in two parts! One for not knowing there are two kind of minutes and seconds. And one for the formula they have given: Why should we divide 720 degrees to 12 in order to reach 60? And how does dividing degrees to a number yields minutes? Even if the number's unit is hour, still doesn't make sense. And then the site says well, it's proven that each degree equals to 60 minutes!  
> **username_7**: Yea, the link is nonsense, I chose to focus on explaining it correctly to answer the question in the title.  

---

### Answer by username_5 on 2023-06-01. Score: 4

One key side effect of the French Revolution was the introduction of the metric system. Prior to that revolution, how length, area, volume, mass, and money were measured varied not only from country to country but from town to town. It was an absolute mess. The metric system addressed all of these.

Two things that people measured were not an absolute mess: time and angle. With regard to time, the scientific community had universally settled on 24 hours per day, 60 minutes per hour, and 60 seconds per minute long before the French Revolution. The scientific community had also settled on 360 degrees of arc per rotation, 60 minutes of arc per degree, and 60 seconds of arc per arc minute. These measures date back to ancient Egypt and Babylonia, so very, very old.

The French Revolution's attempts at metricizing time and angle failed because these were the well established de facto standards. Were the goofy standards? Arguably so, but the standards did exist. That there were no standards (de facto or official) for length, area, volume, or mass were key in the rapid advancement of the metric system -- except for time and angle.


---

### Answer by username_2 on 2023-05-31. Score: 4

Historical reasons.

Yet your base assumption that 24 hours or 360° equal *two* revolutions is wrong in an astronomical sense: An hour equals approximately 15 degrees of movement of stars or the Sun if you are dealing with astronomy. Yet that's inconsequential here:

60 is nicely divisible by 2,3,4,5,6,10,12,15, and 30. So subdivisions of degree were chosen with base-12 in mind, making coarse calculations without floating point numbers easy and also marking easily 1/2, 1/3, 1/4, 1/5, 1/6, 1/10, 1/12, 1/15, 1/30 on geometric tools. And the same holds true for dividing each minute into 60 seconds. On the same reasoning the full circle has 360° degrees... nicely divisible without leftover by many numbers, too, introduced this way already thousands of years ago in mesopotamia by the Sumerians and Bablyonians. See also [this answer in the math SE](https://math.stackexchange.com/questions/340467/why-is-a-full-circle-360-degrees) or the wiki article on the [sexagesimal (60-base) system](https://en.wikipedia.org/wiki/Sexagesimal).

Generally, in former times quantities easily divisible were traded, especially of goods where the unit 1 is not easily split, like a complete oxen or eggs. Eggs are here often sold in units of 6, 10 or 12.

While the traditional unit systems usually are a mess and PITA, they sometimes use the factor 12 as well for the conversion between different units like between foot and inch (but not others; just look at the funky conversions between e.g. fingers, yards, miles, furlongs or queen's chains).

> **Comments:**
> **username_0**: As you said, an hour equals 15 degrees in astronomical sense. So again, how does each degree equals to 60 minutes (an hour)?! It should have been "each degree equals to 4 minutes"  
> **username_2**: Why? The hours of time do not relate to degrees of angle. The similarity is just that each hour of time has 60 minutes and 60 seconds to a minute. The same is for angles: the each degree has 60 arc-minutes and each arc-minute has 60 arc-seconds.  
> **username_0**: But there is still a relationship between hours of time to degrees of angle. Of course, I am convinced that minutes of arc have nothing to do with minutes of time. But surely we both agree that the Earth turns through 15 degrees of arc (degrees for short) in one hour of time (hour for short). This is the relationship.  
> **username_2**: Sure. But that's the same kind of relation that I drive with my car 50km / hour in built-up areas. It's just a velocity. For Earth its its rotational velocity which defines the day: 15° per hour. It's somewhat arbitrary and only matches because we defined at some point in history the hour (or minute or second) the way it is: 24 hours in one Earth rotation.  
> **username_2**: But Earth's rotation is too much subject to change (tides, but also seasons, earthquakes, etc) that it is not a good measure of time by todays standard. Time is the most precisely defined and measurable property there is currently to better than 1/10^(-14). (thus better than 20 minutes in duration equal to the age of Earth itself)  

---

### Answer by username_6 on 2023-06-01. Score: 2

The Earth does not turn through a minute of arc or an arcminute during a minute of time, nor does it turn through a second of arc or an arcsecond during a second of time.

Assuming that ther is a connection between arcminutes and minutes of time is an error.

In angular measurement:

A circle is divided into 360 arc degrees, each arc degree being 1/360, or 0.002777, of a circle.

Each arc degree is divided into 60 arcminutes, each arc minute being 1/(360-X 60) or 1/21,600 or 0.000046296, of a circle.

Each arcminute is divided into 60 arcseconds, each arcsecond being 1/(360 X 60 X 60), or 1/1,296,000, or 0.000000771, of a circle.

In time measurement:

One day is divided into 24 hours, each being 1/24, or 0.0416666, of a day.

One hour is divided into 60 minutes of time, each minute of time being 1/(24 X 60), or 1/1,440, or 0.000694444, of a day.

One minute of time is divided into 60 seconds of time, each second of time being 1/(24 X 60 X 60), or 1/96,400, or 0.000011574, of a day.

The Earth turns 360 degrees of arc in one 24 hour day of time.

So the Earth turns through 15 degrees of arc in one hour of time.

And thus the Earth turns through 15 arcminutes during one minute of time.

And so the Earth turns through 15 arcseconds in one second of time.

So any source implying that an arcminute is equal to the angle that Earth turns in a minute of time is incorrect.

The Earth does not turn through one arcminute in one minute of time, nor through one arcsecond in one second of time. So a different number of arcminutes fits into a full circle than the number of minutes of time during a day.

> **Comments:**
> **username_0**: But it is true to say that the Earth turns each degree of arc (degree for short) in 4 minutes of time (minute for short). Isn't it a way to relate angle to time?  

---

