Why are There 60 Minutes in an Hour?
Published by We are all familiar with dividing our days into 24 hours and our hours into 60 minutes. But why do we use these particular units for measuring time?
To understand the units of time we need to investigate the number systems of ancient civilizations. How did the Sumerians count to 12 on one hand and to 60 on two? What advances did the Babylonians make and how did they use this number system for measurement? And what refinements did the Egyptians make to time measurement to give us the system we still use today?
Sumerian Counting
It is easy to see the origins of a decimal (base 10) number system. Our hands have 10 digits to count on, so a decimal system follows naturally. With the addition of the toes on our feet a vigesimal (base 20) number system, like that of the Maya, also makes sense. But understanding a sexagesimal (base 60) number system, as used by the Sumerians, takes a little more thought.
A quick glance at a hand shows us four fingers and a thumb that can be used for counting. But the human hand is a complex machine consisting of 27 bones, as shown in the diagram below.
Some of these features are evident externally, especially in the fingers. By using the thumb as a pointer, and marking off the distal phalanx, middle phalanx and proximal phalanx of each finger, we can count up to 12 on one hand, as shown below.
Furthermore, by using the other hand to mark five multiples of 12 we can extend the count up to 60. For instance, 32 (= 2 x 12 + 8 ) would appear as follows.
Babylonian Mathematics
The Sumerian number system was passed on to the Babylonians. Sexagesimal was a useful system as 60 has a large number of factors. Each collection of 60 objects could be divided into whole groups of 2, 3, 4, 5, 6, 10, 12, 15, 20 or 30.
The Babylonians used just two symbols for their mathematical notation. There was a 
for 1 and a 
for 10. All the numbers from 1 to 59 were written as combinations of these marks. For instance, 32 appeared as
A significant advance from earlier notation was the use by the Babylonians of a positional system. In our decimal notation we represent 10 as a column containing a 1 followed by a column containing a 0. In a similar way the Babylonians represented numbers over 59 in multiple columns. For instance, 64 was 1 x 60 + 4 or
Although there was no symbol for a zero it was shown as a larger gap between the columns.
Measurement and Time
The number 60 and its factors were used in the measurement of many things, several of which are still in use today. In length there are 12 inches to a foot. In angular measurement there are 6 x 60 = 360 degrees in a circle. In pre-decimalised currency in the UK there were 12 pence in a shilling.
But let us bring our attention back to time and the division of a day. The Babylonians divided each hour of the day into 60 minutes. Each minute they divided into 60 seconds. These are not, however, the minutes and seconds we would recognise today.
Each day was divided into a daylight portion and a night portion. These portions were then divided into 12 hours each. As the length of day and night varied throughout the year, so the length of the Babylonian hours, minutes and seconds varied too.
Egyptian Refinements
The Egyptians refined the measurement of time to remove these variations. They ignored the distinction between daylight hours and night hours but kept the total of 24. The whole day was then divided into 24 equal periods creating the hour that we still use today.
Despite occasional suggestions that we should adopt decimal time, this ancient system of measurement has survived for thousands of years. And so, the reason there are 60 minutes in an hour is due to the mathematics of the Sumerians, Babylonians and Egyptians and the structure of the human hand.
Further Reading
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47 Responses to “Why are There 60 Minutes in an Hour?”
On February 14, 2009 at 10:25 am
Very interesting!
On April 23, 2009 at 3:19 pm
this really makes things clear now 24 used to seem like such a random number but now it fits in lol but what about the aztecs im almost certain they gaves us some of todays measure ments in time ??
On May 24, 2009 at 12:13 pm
Excellent article. Very interesting. Thanks!
On June 26, 2009 at 12:43 am
12: divisible by 2, 3, 4, 6
60: divisible by 2, 3, 4, 5, 6, 12, 15, 20, 30
The point is that these numbers have the most factors (and secondary if you’re willing to accept the fractional use of 8, 16 and 24) and are therefore most easily broken down into simple fractions.
On June 26, 2009 at 4:24 am
If you find this kind of thing interesting I really recommend this book: ‘The Discoverers’ by Daniel Boorstin
http://en.wikipedia.org/wiki/The_Discoverers
On June 26, 2009 at 4:44 am
Very interesting!
On June 26, 2009 at 6:10 am
Using the Sumerian system described above, you can count to 72 not 60.
On June 26, 2009 at 6:20 am
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On June 26, 2009 at 7:23 am
Surely with both hands you can count up to 72?
5*12 on the one hand plus an additional 12 on the other.
On June 26, 2009 at 7:44 am
On June 26, 2009 at 8:14 am
Cool article. I think you should disable emoticons because the
is rendered as an emoticon.
On June 26, 2009 at 8:55 am
Please read my theory (in italian) of number system:
http://www.dnamagazine.it/loro.html
txs
BT
On June 26, 2009 at 9:02 am
Clearly we should throw away this barmy system and move to a hexedecimal system of time!
We may need to grow an extra joint in each of our fingers though..
On June 26, 2009 at 9:05 am
This isn\’t entirely accurate. The length of second was based on the heartbeat. And the length of seconds didn\’t change at certain times of the year. Some other books disagree with your sources.
On June 26, 2009 at 9:40 am
Francis Botha,
What ever you typed rendered as the hot smiley…
On June 26, 2009 at 9:55 am
32 = 2 x 12 + cool?
On June 26, 2009 at 9:59 am
If only they would have used the palm under the finger to add 4 more posible values in one hand. We would have a base 16 time and everything would we easier to compute.
On June 26, 2009 at 11:17 am
Nice Post
Very interesting read!
On June 26, 2009 at 11:21 am
@John: There is apparently an automatic smiley creator on this blog application. The smiley “8)” is the symbol for a smiley with sunglasses. If the author would put a space between the ‘8′ and the left parentheses it would be “32 (= 2 x 12 + 8 )”
On June 26, 2009 at 12:15 pm
According to this explanation, you can count up to 72 on two hands, not 60.
If you point to the lowest phalanx of the little finger on the left hand, that’s ‘12′. Holding up five fingers on the right hand is ‘60′.
So, if this article is accurate, the Sumerians could count to 72 on two hands, not just 60.
That seems to be a bit of an obvious error. It makes me wonder if this explanation is correct.
On June 26, 2009 at 12:32 pm
If you count in binary on both hands, you get 2^10 or 1024.
-Dan Barlow
On June 26, 2009 at 12:52 pm
Perhaps they placed their right thumb against one of their four right fingers to signify how many twelves they had counted on the other hand? Thus they could `store’ up to 4 twelves, and have one more twelve counted.
On June 26, 2009 at 1:02 pm
Come to think about it, assuming they were mostly right handed, might they have counted each twelve on the right hand?!
On June 26, 2009 at 1:13 pm
Thanks for all the comments. Four and a half months into the life of this article it seems to have taken off.
The issue with the smiley has occurred since Scienceray had its makeover. A fix has been submitted to correct the problem.
The suggestion by some people that using this method we could count to 72 on two hands can be disproved by considering the decimal system. Let’s assume for a moment that we have 10 fingers on each hand. We start counting from 1 to 10 on one hand. When we reach 10 we mark off 1 on our other hand and start counting again on the first hand. Once we have marked off 10 groups of 10 (i.e. 100) we stop and find some other way to store this new power of 10 (in written notation this would be a new column). What we don’t do is count off another group of 10 to give us a total of 110.
The same applies if we count to 12 on one hand and 5 on the other. When we get to 5 groups of 12 (i.e. 60) we stop and denote this value in some way. Again, what we don’t do is count off another group of 12 to give a total of 72. I hope this clears up the uncertainty.
@bog – Yes, this is one of several theories, but it does seem the most plausible. Basing the length of a second on the human heartbeat seems unlikely as this can vary from person to person. At rest, the average human heartbeat can be anywhere between 60 and 100 beats per minute.
@ JTL – True, this system could be used either way round
The usual assumption is that the right hand would have been in use, either for writing or holding something, so the counting was done on the left.
On June 26, 2009 at 2:04 pm
Awesome! Always wondered, very cool to know. Thanks!
On June 26, 2009 at 4:39 pm
Interesting reading – Thanks.
I always wondered about this.. If anyone ever consider changing it to 10x decimal number… please spare a thought for those involved in computer hardware/software. Would it be better to use number of power of 2… (0, 2, 4, 8, 16, 32, 64 … etc)
On June 26, 2009 at 5:21 pm
why are there seven days in a week?
On June 26, 2009 at 6:35 pm
Simon,
Because of the cycle of the moon being ~28 days. 4 phases of the moon (like four seasons) gives us 7 days.
On June 26, 2009 at 6:42 pm
you multiply the amount on the left hand by the number of 12\’s on the right. Yielding a maximum of 60. So to get 24, the left hand would be on the 2, and the right would show 2 fingers. 2×12=24. it wouldn\’t be 2 24. So the system does in fact go to a maximum of 60.
On June 26, 2009 at 8:06 pm
@Gary: but you still could count until 71 before you have to denote that value. disproved!
On June 27, 2009 at 5:08 pm
In addition to all this, isn’t it a pleasant coincidence that we have 24 hours in a day, 24,000 miles around the earth, and 24 time zones splitting the earth up every 15 degrees, or 1000 miles at the equator? So we had 24 hours in a day before we knew the earth was 24,000 miles around.
On June 28, 2009 at 12:47 am
Not that it would be practical, but this system could actually be used in a lot of other ways. You could use the same system as the left hand for counting 12’s on the right hand. That lets you track twelve 12s on the right hand plus another twelve on the left for a total of 156.
Additionally, you could use the right hand for tracking 13’s instead of 12s since you can count to 12 on the left. This just requires a method of showing zero on the left.
Not that the Sumerians had a huge need for counting bigger numbers.
Of couse, as Dan says, these days we can easily count to 1024 on ten fingers (assuming you’re reasonably coordinated).
On June 28, 2009 at 1:36 am
@ Light:
Actually, we had 24 hours in a day before a “mile” had been invented. Also, it’s closer to 25,000 miles.
But, I think it’s cool and probably not a coincidence that we have 360 degrees in a circle and roughly 365 days in a year.
@ Gary:
I think the only reason we wouldn’t count to 110 in your ten finger example is that it wouldn’t be as compatible with our decimal system. Ignoring the decimal system, you would count to 110. And actually, you would use the second hand to mark 11s… allowing you to count to 120.
That would give you the ability to count to higher numbers (potentially useful). Our decimal system is the reason for stopping at 100 in your example. In the Sumerian system, I figure it would be based on the factors of the number. 72 and 60 have the same number of factors, but 60 has the advantage that its factors include the numbers 1-6 where 72 loses 5 as a factor and replaces it with 8. To me, that would be a sensible reason to stop counting at 60.
On June 28, 2009 at 10:39 am
That’s neat! My private theory was that the Sumerians were 6-fingered mutants.
On June 28, 2009 at 10:01 pm
@Hannah
I wouldn’t have described 24 as a ‘random number’ – it has the advantage of being divisible by 2,3,4,6,8 and 12.
That makes it easy to divide into fractions.
I wouldn’t surprise me if the decision to use 24 came first, and later someone figured out how to use fingers to count up to 24.
On June 29, 2009 at 1:54 pm
With the Sumerian finger counting method you needn’t stop at 60 or 72, you could easily keep track all the way to 120. Since 12 is all four fingers (12 segments) of the left hand, you don’t need to use the right until you count 13. So 60 would be the twelve segments on the left hand and four fingers on the right, not just the five right hand digits with no left hand segments. 72 would be twelve segments on the right, and all five left hand digits. But you could continue if you then touched the thumb to the index finger on the right hand to represent 72, thumb to middle finger is 84, thumb to ring finger is 96, and thumb to pinkie is 108. At that point you add 12 segments from the left hand and your end point is 120.
On June 29, 2009 at 8:03 pm
The variable 12-hour clock did not end with Babylon. Medieval monasteries also used a variable-hour clock to time their prayers, counting 12 hours from sunrise to sunset and 12 from sunset to sunrise. See this article on the Cistercian hours of prayer: midmorning is terce (three), noon is sexte, and midafternoon is nones. You can measure those hours with a simple sundial, or just a pole and some marks scratched in the ground.
Of course, measuring such hours after dark is rather more complicated. If you can identify a star that is just rising at sunset, then it’s angle will give you the night-time Babylonian hours – but since you can’t see stars until an hour or so after sunset, the only people who could tell time that way were astronomers who knew how to calculate which constellation was rising at any given time, whether or not they could see it. Everyone else had to use some sort of approximation. For instance, stay up all night flipping an hour-glass every time it runs out, see how far off you are from a count of 12 flips when the sun rises, and re-calculate from that. (Remember, no two hand-made hour-glasses will be the same!) Or use a water-clock with an adjustable flow rate; someone has to re-adjust it at sunrise and sunset each day, but that’s easy compared to the hour glass.
But then someone went and invented the pendulum clock. It wasn’t much more expensive than a water clock, and it was potentially much more accurate, but it kept insisting that there were more hours in the day in the summer. (Just like the laborers who toted the rocks to build the cathedral had been claiming all along.) For a while, medieval inventors tried to find a way to adjust the swing twice a day to match the sundial hours. Finally, someone had a real inspiration: shift the starting point six hours. Noon to midnight and midnight to noon were then each twelve equal hours, although the time of sunrise and sunset varied. Once the pendulum length was properly adjusted, it stayed adjusted.
Finally, with these amazingly accurate clocks, some people went nuts and started subdividing the hour. Soon the town clocks were sporting minute hands. And your boss would pointedly remind you how many minutes you were late to work. Then the clockmakers started adding another divide-by-sixty gear and a second hand, and the early scientists discovered a fortunate coincidence; they had been attempting to time events by counting their pulse, and an average pulse (for a resting man in good physical condition) was pretty close to one second.
There are other near-coincidences. The Roman army estimated distances by counting double footsteps (e.g., every time the left heel hits the ground is one count). One thousand double steps became their unit of length for long distances, and the English adopted an approximation to that as the mile. And it just happened that the circumference of the Earth is reasonably close to 24,000 miles. But mariners were more interested in another number: 21,600 = 360 x 60, that is, the number of arc-minutes in a circle. So they defined the nautical mile to equal one arc-minute on a circle of latitude (that is, a circle passing through the poles). (Nowadays we can measure Earth’s deviation from the strictly spherical, so we’ve had to re-define the nautical mile more accurately, but the old definition was quite accurate enough for men who navigated by the sextant, books of tables, and hand calculations.) It was 15% longer than the traditional mile, but it made certain calculations so much easier…
On June 29, 2009 at 8:20 pm
Aside from counting tricks, two reasons for base 12 are it’s large number of divisors (often useful when you have to do division by pencil and paper methods), and there are (approximately) 12 lunar months in a year. Babylonian astronomer/priests were really into lunar cycles. But 12 is not divisible by 5 or 10; 60 is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30.
The variable hour did not end with Babylon. Medieval monasteries also used a variable-hour clock to time their prayers, counting 12 hours from sunrise to sunset and 12 from sunset to sunrise. See this article on the Cistercian hours of prayer:
http://cistercianvocation.wordpress.com/2008/06/21/the-hours-of-monastic-prayer
Midmorning is terce (three), noon is sexte (six), and midafternoon is nones (nine). Obviously, sunup was zero and sunset was 12. You can measure those hours with a simple sundial, or just a pole and some marks scratched in the ground.
Measuring the hours after dark is rather more complicated. If you can identify a star that is just rising at sunset, then its angle will give you the night-time Babylonian hours – but since you can’t see stars until an hour or so after sunset, the only people who could tell time that way were astronomers who knew how to calculate which constellation was rising at any given time, whether or not they could see it. Everyone else had to use some sort of approximation. For instance, stay up all night flipping an hour-glass every time it runs out, see how far off you are from a count of 12 flips when the sun rises, and re-calculate from that. (Remember, no two hand-made hour-glasses will be the same!) Or use a water-clock with an adjustable flow rate; someone has to re-adjust it at sunrise and sunset each day, but that\’s easy compared to the hour glass.
But then someone went and invented the pendulum clock. It wasn\’t much more expensive than a water clock, and it was potentially much more accurate, but it kept insisting that there were more hours in the day in the summer. (Just like the laborers who toted the rocks to build the cathedral had been claiming all along.) For a while, medieval inventors tried to find a way to adjust the swing twice a day to match the sundial hours. Finally, someone had a real inspiration: shift the starting point six hours. Noon to midnight and midnight to noon were then each twelve equal hours, although the time of sunrise and sunset varied. Once the pendulum length was properly adjusted, it stayed adjusted.
Finally, with these amazingly accurate clocks, some people went nuts and started subdividing the hour. Soon the town clocks were sporting minute hands. And your boss would pointedly remind you how many minutes you were late to work. Then the clockmakers started adding another divide-by-sixty gear and a second hand, and the early scientists discovered a fortunate coincidence; they had been attempting to time events by counting their pulse, and an average pulse (for a resting man in good physical condition) was pretty close to one second.
There are other near-coincidences. The Roman army estimated distances by counting double footsteps (e.g., every time the left heel hits the ground is one count). One thousand double steps became their unit of length for long distances, and the English adopted an approximation to that as the mile. And it just happened that the circumference of the Earth is reasonably close to 24,000 miles. But mariners were more interested in another number: 21,600 = 360 x 60, that is, the number of arc-minutes in a circle. So they defined the nautical mile to equal one arc-minute on a circle of latitude (that is, a circle passing through the poles). (Nowadays we can measure Earth’s deviation from the strictly spherical, so we had to re-define the nautical mile more accurately, but the old definition was quite accurate enough for men who navigated by the sextant, books of tables, and hand calculations.) It was 15% longer than the traditional mile, but it made certain calculations so much easier…
On July 1, 2009 at 12:59 am
I thought it had something to do with the convenience of driving 60 miles per hour–you would go one mile in one minute. Worked out great until that metric system came along tossed the whole thing into the weeds. How far do you go in one minute at 100 kph? Who cares.
On July 1, 2009 at 1:06 am
You can count to 31 on one hand using binary. On two hands you can count to 1023. Why would you use this complicated method instead?
On July 1, 2009 at 7:17 am
Very interesting!
On September 4, 2009 at 10:04 pm
wow this help a lot for my homework i now undrestand why is 60 secounds and minutes thanks for spicific reasons. and sry im just a sixth grader im not the best speller.
On November 19, 2009 at 6:39 pm
:O c00l interesting
i like it …. thanks this helped me with my egypt study questions… 6gr…. Thanks
On November 23, 2009 at 4:41 am
interesting.
watch this video
http://www.youtube.com/watch?v=Nc4yrFXw20Q
On November 23, 2009 at 1:56 pm
Thanks Ethioboi. That was a fascinating video.
On January 18, 2010 at 10:01 am
If the Sumerians used the thumb as an index for one hand, it is probable that it served the same use for the other. Thus the photo showing 24 as thumb and forefinger of the right hand is suspect. A consistent approach to showing 24 would be the thumb on the right hand touching the base of the second finger.
Under the consistent thumb usage system, 60 would be the appropriate count. As the author describes, 72 would be the appropriate count.
For those that would like to appeal to information density, yes there are systems that use normal hand configuration to represent system bases above 72 (left as an exercise for the reader). However, the Sumerian system is just like every other numeric system for general usage – it needs to be teachable to a large portion of the population and accessible to children.
On May 22, 2010 at 2:14 pm
We casually associate decimal system with 10 fingers. But if that were the case we should have ten symbols, excluding zero. Not 9 nonzero symbols as in decimal system!!
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