<p>Your trigonometry book isn't wrong: both &quot;minute&quot; and &quot;arcminute&quot; can refer to  <span class="math-container">$\frac1{60}$</span> of a degree. It's certainly a very good idea to use the term &quot;arcminute&quot; when referring to <span class="math-container">$\frac1{60}$</span> of a degree, but it's not essential if there's no ambiguity, eg, in a static geometry problem where there's no mention of time.</p>
<p>The term &quot;arcminute&quot; is <em>relatively</em> new. According to Google Ngrams, &quot;arcminute&quot; and &quot;arcsecond&quot; started becoming popular around 1970-1980. FWIW, I went to high school in the 1970s, and I can't remember any of my books or teachers using those terms.</p>
<p>From the <a href="https://books.google.com/ngrams/graph?content=arcminute&amp;year_start=1850&amp;year_end=2019&amp;corpus=26&amp;smoothing=3&amp;direct_url=t1%3B%2Carcminute%3B%2Cc0" rel="noreferrer">arcminute Ngram</a></p>
<p><a href="https://i.sstatic.net/vLC95.jpg" rel="noreferrer"><img src="https://i.sstatic.net/vLC95.jpg" alt="arcminute Ngram" /></a></p>
<p>Here's the <a href="https://books.google.com/ngrams/graph?content=arcsecond&amp;year_start=1850&amp;year_end=2019&amp;corpus=26&amp;smoothing=3&amp;direct_url=t1%3B%2Carcsecond%3B%2Cc0" rel="noreferrer">arcsecond Ngram</a></p>
<p><a href="https://i.sstatic.net/EvjZZ.jpg" rel="noreferrer"><img src="https://i.sstatic.net/EvjZZ.jpg" alt="arcsecond Ngram" /></a></p>
<p>The results for &quot;arc minute&quot;, &quot;arc-minute&quot;, etc, are similar.</p>
<p>However, the terms &quot;minutes of arc&quot; and &quot;seconds of arc&quot; were quite popular before that era, and it appears they have mostly been displaced by &quot;arcminute&quot; and &quot;arcsecond&quot;.</p>
<p><a href="https://books.google.com/ngrams/graph?content=minutes+of+arc&amp;year_start=1850&amp;year_end=2019&amp;corpus=26&amp;smoothing=3&amp;direct_url=t1%3B%2Cminutes%20of%20arc%3B%2Cc0" rel="noreferrer">minutes of arc</a></p>
<p><a href="https://i.sstatic.net/krFrf.jpg" rel="noreferrer"><img src="https://i.sstatic.net/krFrf.jpg" alt="minutes of arc Ngram" /></a></p>
<p><a href="https://books.google.com/ngrams/graph?content=seconds+of+arc&amp;year_start=1850&amp;year_end=2019&amp;corpus=26&amp;smoothing=3&amp;direct_url=t1%3B%2Cseconds%20of%20arc%3B%2Cc0" rel="noreferrer">seconds of arc</a></p>
<p><a href="https://i.sstatic.net/sV5Xg.jpg" rel="noreferrer"><img src="https://i.sstatic.net/sV5Xg.jpg" alt="seconds of arc Ngram" /></a></p>
<hr />
<p>As the Wikipedia <a href="https://en.wikipedia.org/wiki/Sexagesimal" rel="noreferrer">Sexagesimal</a> article mentions, people have been using the base 60 system to represent fractional quantities since the 3rd millennium BC. The Chaldeans (Babylonians) inherited it from the Sumerians, and they used it to record celestial positions.</p>
<p>The Babylonian <a href="https://en.wikipedia.org/wiki/Babylonian_astronomical_diaries" rel="noreferrer">Astronomical diaries</a> span 7 centuries, and Babylonian data was one of the sources used in Ptolemy's <a href="https://en.wikipedia.org/wiki/Almagest" rel="noreferrer">Almagest</a>. The trigonometry tables in the Almagest use base 60 both for the angles and for the values of the trig functions (Ptolemy trig tables used chord length, which is closely related to the sine function).</p>
<p>European mathematicians continued to use sexagesimal for recording and computing with fractional quantities up to the late 17th century, but it was gradually displaced by decimal fractions.</p>

CC BY-SA 4.0
2021-06-02T12:52:24.710Z
The word in latin was minuta/minutus, which means "made small". Likely it was convenient for them to define these 1/60ths as "small parts" and here we are - same root for the time division and the angle division, same measurement name. *pars minuta prima*, the first part made small. It is then fairly clear to see where also the second came from - dividing again into a "second" part.
Stian
CC BY-SA 4.0
2021-06-02T05:14:14.667Z
2021-06-02T07:25:26.347Z
2021-06-02T07:25:26.347Z
PM 2Ring
<p>One minute has two definitions. One is 1/60th of an hour, or 60 seconds, while the other is 1/60th of a degree. Typically, one minute is shorthand for &quot;arcminute.&quot; You can tell between the two by replacing the word with &quot;60 seconds.&quot; If it makes sense, then it means that. If not, then it is one arcminute.</p>
<p>An exception is the use of &quot;minute&quot; as an adjective (means tiny), but it is obvious that when used in a sentence, you can distinguish its meaning.</p>

CC BY-SA 4.0
2021-06-02T08:51:05.490Z
I don't see how your proposed test can tell between the two - a minute can be replaced with "60 seconds" for both meanings of the words: [ 1 arcminute = 1 minute (of arc) = 60 seconds (of arc) = 60 arcseconds ] vs [ 1 minute (of time) = 60 seconds (of time) ]
Steve
CC BY-SA 4.0
2021-06-02T18:44:14.853Z
@Steve Exactly, I don't know why does this have so many upvotes.
User123
CC BY-SA 4.0
2021-06-01T17:05:17.570Z
2021-06-01T17:05:17.570Z
WarpPrime
<p><a href="https://i.sstatic.net/PEIZn.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/PEIZn.png" alt="The four N-gram traces of @PM 2Ring's answer" /></a></p>
<p>Put into perspective, it becomes clear that the traditional terms are still competitive. I would prefer them.</p>

CC BY-SA 4.0
2021-06-04T12:34:47.013Z
This seems very similar to [@PM2Ring's answer](https://astronomy.stackexchange.com/a/44126/31410). What makes yours different?
WarpPrime
CC BY-SA 4.0
2021-06-07T17:58:34.900Z
The difference is the common scale, whereas theirs have no scale at all. The difference in noise at peak level made me suspect that the scales could be very different. It no longer "appears they have mostly been displaced by arcminute and arcsecond."
Rainald62
CC BY-SA 4.0
2021-06-04T10:02:08.593Z
2021-06-04T10:02:08.593Z
Rainald62
<p>This can get a bit confusing, because &quot;arcminute&quot; and &quot;minute&quot; are both sometimes used in celestial coordinate systems but mean two different things.</p>
<p>An <em>arcminute</em> is 1/60th of a degree, and an <em>arcsecond</em> is 1/60th of an arcminute. That's simple enough, and when talking about small angular distances, it's often much handier to refer to something as being, say, 140 arcseconds across, rather than 0.0389 degrees. So you're likely to see angular sizes or scales quoted in degrees, arcminutes and arcseconds.</p>
<p>If you're trying to state the position of an object on the sky, things get a little more complicated, thanks to the commonly-used <a href="https://en.wikipedia.org/wiki/Equatorial_coordinate_system" rel="noreferrer">equatorial coordinate system</a>, which states an object's position on the celestial sphere in terms of its declination and its right ascension. The declination of an object is usually given in degrees, arcminutes and arcseconds. Its right ascension, on the other hand, is usually given in hours, minutes and seconds. Here, one &quot;hour&quot; corresponds to 1/24th of a circle, or 15 degrees. One <em>minute</em> is then 1/60th of an hour, and one <em>second</em> is 1/60th of a minute. So as units of angular separation in this context, an arcminute is different from a minute, and an arcsecond is different from a second.</p>

CC BY-SA 4.0
2021-06-03T14:55:53.673Z
I actually made a [riddle on Puzzling.SE](https://puzzling.stackexchange.com/questions/23376/simple-riddle-involving-time-travel) about exactly this discrepancy several years ago.  Looking at it after reading this question is probably a spoiler for the answer, but it was long enough ago so whatever.
Darrel Hoffman
CC BY-SA 4.0
2021-06-01T17:23:05.927Z
2021-06-02T13:18:19.307Z
2021-06-02T13:18:19.307Z
HDE 226868
<p>I read in trigonometry class that 1 minute is equal to 1/60 degrees. So, 'minute' is an angular unit. But also 'arcminutes' are used to measure seperation between celestial objects and also equals to 1/60 degrees.
Are they any similar? If not, then what's the difference?</p>

CC BY-SA 4.0
2021-06-01T17:00:33.240Z
"Minute" is a length of time. Your trig teacher meant to say arcminute.
Daddy Kropotkin
CC BY-SA 4.0
2021-06-02T11:19:56.717Z
@DaddyKropotkin: "Minute" is not just a length of time: it can also mean the same as "arcminute"; this is confusing, but not incorrect.
psmears
CC BY-SA 4.0
2021-06-02T12:45:10.443Z
@DaddyKropotkin To follow up on psmears comment: Minute, as used in measurement, is a magnitude adjustment just like "hekto", "mega" or "deci" - it specifically means one sixtyeth. It is also used figuratively: *a minute adjustment*, meaning "tiny". It is more than a measure of time.
Stian
CC BY-SA 4.0
2021-06-02T12:49:20.477Z
@psmears and @ Stian Yttervik thank you both for clarifying
Daddy Kropotkin
CC BY-SA 4.0
2021-06-02T12:57:00.017Z
@StianYttervik: Note that "minute" as in "a minute adjustment" is a different word (it's an adjective rather than a noun, and it is pronounced differently too).
psmears
CC BY-SA 4.0
2021-06-02T12:59:44.567Z
@psmears You are correct, I was pointing to their common appearance in writing. It would be imprecise to claim that the (written) word "minute" has one meaning, it has at least these 3.
Stian
CC BY-SA 4.0
2021-06-02T13:26:16.573Z
@StianYttervik How big are minutemen then?
Mast
CC BY-SA 4.0
2021-06-02T17:49:54.813Z
Not only the terms are confusing, but also the symbols. For time, the only acceptable symbol is **min** (with no period after), while for angle, the symbol is **′**. However, some people use them interchangeably, which is improper use. The same goes for seconds of time, symbol s, and seconds of arc, symbol ″. Note also that ′ and ″ (which are straight angled) are not the same as ' and " (which are straight vertical) or as ’ and ” (which, depending on the font, are curly).
Pierre Paquette
CC BY-SA 4.0
2021-06-03T12:23:34.497Z
@StianYttervik, you got it the wrong way around. Etymologically, a minute is a small part, and you can see the same root in the adjective “minute”. And a second refers to the second subdivision into parts.
Carsten S
CC BY-SA 4.0
2021-06-03T12:31:20.370Z
@CarstenS Yes - but that is what I am saying? It all came from the sexagesimal system the babylonians used to count. Their astronomy, and thus time was based on 12/60. The partitioning into 60 sized lots got absorbed into the latin language, making the word for "small parts" over time to mean both a measurement of time, and a measurement of angle. But its root is the sexagesimals.
Stian
<observational-astronomy><distances><right-ascension>
What's the difference between minutes and arcminutes?
Tanya
# What's the difference between minutes and arcminutes?

(Asked by: username_0 on 2021-06-01)

I read in trigonometry class that 1 minute is equal to 1/60 degrees. So, 'minute' is an angular unit. But also 'arcminutes' are used to measure seperation between celestial objects and also equals to 1/60 degrees.
Are they any similar? If not, then what's the difference?

**Tags:** observational-astronomy, distances, right-ascension
> **Comments:**
> **username_1**: "Minute" is a length of time. Your trig teacher meant to say arcminute.  
> **username_2**: @DaddyKropotkin: "Minute" is not just a length of time: it can also mean the same as "arcminute"; this is confusing, but not incorrect.  
> **username_3**: @DaddyKropotkin To follow up on psmears comment: Minute, as used in measurement, is a magnitude adjustment just like "hekto", "mega" or "deci" - it specifically means one sixtyeth. It is also used figuratively: *a minute adjustment*, meaning "tiny". It is more than a measure of time.  
> **username_1**: @psmears and @ Stian Yttervik thank you both for clarifying  
> **username_2**: @StianYttervik: Note that "minute" as in "a minute adjustment" is a different word (it's an adjective rather than a noun, and it is pronounced differently too).  
> **username_3**: @psmears You are correct, I was pointing to their common appearance in writing. It would be imprecise to claim that the (written) word "minute" has one meaning, it has at least these 3.  
> **username_4**: @StianYttervik How big are minutemen then?  
> **username_5**: Not only the terms are confusing, but also the symbols. For time, the only acceptable symbol is **min** (with no period after), while for angle, the symbol is **′**. However, some people use them interchangeably, which is improper use. The same goes for seconds of time, symbol s, and seconds of arc, symbol ″. Note also that ′ and ″ (which are straight angled) are not the same as ' and " (which are straight vertical) or as ’ and ” (which, depending on the font, are curly).  
> **username_6**: @StianYttervik, you got it the wrong way around. Etymologically, a minute is a small part, and you can see the same root in the adjective “minute”. And a second refers to the second subdivision into parts.  
> **username_3**: @CarstenS Yes - but that is what I am saying? It all came from the sexagesimal system the babylonians used to count. Their astronomy, and thus time was based on 12/60. The partitioning into 60 sized lots got absorbed into the latin language, making the word for "small parts" over time to mean both a measurement of time, and a measurement of angle. But its root is the sexagesimals.  

---

## 4 answers

### Answer by username_12 on 2021-06-01. Score: 35 | Accepted answer

This can get a bit confusing, because "arcminute" and "minute" are both sometimes used in celestial coordinate systems but mean two different things.

An *arcminute* is 1/60th of a degree, and an *arcsecond* is 1/60th of an arcminute. That's simple enough, and when talking about small angular distances, it's often much handier to refer to something as being, say, 140 arcseconds across, rather than 0.0389 degrees. So you're likely to see angular sizes or scales quoted in degrees, arcminutes and arcseconds.

If you're trying to state the position of an object on the sky, things get a little more complicated, thanks to the commonly-used [equatorial coordinate system](https://en.wikipedia.org/wiki/Equatorial_coordinate_system), which states an object's position on the celestial sphere in terms of its declination and its right ascension. The declination of an object is usually given in degrees, arcminutes and arcseconds. Its right ascension, on the other hand, is usually given in hours, minutes and seconds. Here, one "hour" corresponds to 1/24th of a circle, or 15 degrees. One *minute* is then 1/60th of an hour, and one *second* is 1/60th of a minute. So as units of angular separation in this context, an arcminute is different from a minute, and an arcsecond is different from a second.

> **Comments:**
> **username_13**: I actually made a [riddle on Puzzling.SE](https://puzzling.stackexchange.com/questions/23376/simple-riddle-involving-time-travel) about exactly this discrepancy several years ago.  Looking at it after reading this question is probably a spoiler for the answer, but it was long enough ago so whatever.  

---

### Answer by username_7 on 2021-06-02. Score: 16

Your trigonometry book isn't wrong: both "minute" and "arcminute" can refer to $\frac1{60}$ of a degree. It's certainly a very good idea to use the term "arcminute" when referring to $\frac1{60}$ of a degree, but it's not essential if there's no ambiguity, eg, in a static geometry problem where there's no mention of time.

The term "arcminute" is *relatively* new. According to Google Ngrams, "arcminute" and "arcsecond" started becoming popular around 1970-1980. FWIW, I went to high school in the 1970s, and I can't remember any of my books or teachers using those terms.

From the [arcminute Ngram](https://books.google.com/ngrams/graph?content=arcminute&year_start=1850&year_end=2019&corpus=26&smoothing=3&direct_url=t1%3B%2Carcminute%3B%2Cc0)

[![arcminute Ngram](https://i.sstatic.net/vLC95.jpg)](https://i.sstatic.net/vLC95.jpg)

Here's the [arcsecond Ngram](https://books.google.com/ngrams/graph?content=arcsecond&year_start=1850&year_end=2019&corpus=26&smoothing=3&direct_url=t1%3B%2Carcsecond%3B%2Cc0)

[![arcsecond Ngram](https://i.sstatic.net/EvjZZ.jpg)](https://i.sstatic.net/EvjZZ.jpg)

The results for "arc minute", "arc-minute", etc, are similar.

However, the terms "minutes of arc" and "seconds of arc" were quite popular before that era, and it appears they have mostly been displaced by "arcminute" and "arcsecond".

[minutes of arc](https://books.google.com/ngrams/graph?content=minutes+of+arc&year_start=1850&year_end=2019&corpus=26&smoothing=3&direct_url=t1%3B%2Cminutes%20of%20arc%3B%2Cc0)

[![minutes of arc Ngram](https://i.sstatic.net/krFrf.jpg)](https://i.sstatic.net/krFrf.jpg)

[seconds of arc](https://books.google.com/ngrams/graph?content=seconds+of+arc&year_start=1850&year_end=2019&corpus=26&smoothing=3&direct_url=t1%3B%2Cseconds%20of%20arc%3B%2Cc0)

[![seconds of arc Ngram](https://i.sstatic.net/sV5Xg.jpg)](https://i.sstatic.net/sV5Xg.jpg)

---

As the Wikipedia [Sexagesimal](https://en.wikipedia.org/wiki/Sexagesimal) article mentions, people have been using the base 60 system to represent fractional quantities since the 3rd millennium BC. The Chaldeans (Babylonians) inherited it from the Sumerians, and they used it to record celestial positions.

The Babylonian [Astronomical diaries](https://en.wikipedia.org/wiki/Babylonian_astronomical_diaries) span 7 centuries, and Babylonian data was one of the sources used in Ptolemy's [Almagest](https://en.wikipedia.org/wiki/Almagest). The trigonometry tables in the Almagest use base 60 both for the angles and for the values of the trig functions (Ptolemy trig tables used chord length, which is closely related to the sine function).

European mathematicians continued to use sexagesimal for recording and computing with fractional quantities up to the late 17th century, but it was gradually displaced by decimal fractions.

> **Comments:**
> **username_3**: The word in latin was minuta/minutus, which means "made small". Likely it was convenient for them to define these 1/60ths as "small parts" and here we are - same root for the time division and the angle division, same measurement name. *pars minuta prima*, the first part made small. It is then fairly clear to see where also the second came from - dividing again into a "second" part.  

---

### Answer by username_8 on 2021-06-01. Score: 1

One minute has two definitions. One is 1/60th of an hour, or 60 seconds, while the other is 1/60th of a degree. Typically, one minute is shorthand for "arcminute." You can tell between the two by replacing the word with "60 seconds." If it makes sense, then it means that. If not, then it is one arcminute.

An exception is the use of "minute" as an adjective (means tiny), but it is obvious that when used in a sentence, you can distinguish its meaning.

> **Comments:**
> **username_9**: I don't see how your proposed test can tell between the two - a minute can be replaced with "60 seconds" for both meanings of the words: [ 1 arcminute = 1 minute (of arc) = 60 seconds (of arc) = 60 arcseconds ] vs [ 1 minute (of time) = 60 seconds (of time) ]  
> **username_10**: @Steve Exactly, I don't know why does this have so many upvotes.  

---

### Answer by username_11 on 2021-06-04. Score: -2

[![The four N-gram traces of @PM 2Ring's answer](https://i.sstatic.net/PEIZn.png)](https://i.sstatic.net/PEIZn.png)

Put into perspective, it becomes clear that the traditional terms are still competitive. I would prefer them.

> **Comments:**
> **username_8**: This seems very similar to [@PM2Ring's answer](https://astronomy.stackexchange.com/a/44126/31410). What makes yours different?  
> **username_11**: The difference is the common scale, whereas theirs have no scale at all. The difference in noise at peak level made me suspect that the scales could be very different. It no longer "appears they have mostly been displaced by arcminute and arcsecond."  

---

