We take it for granted that a day has 24 hours, an hour 60 minutes and a minute 60 seconds. The system is thousands of years old and was never designed by anyone in a single moment. It came from Egyptian sundials, Babylonian mathematics and a French revolution.
The Egyptians and the 24 hours
Ancient Egyptians divided the day into twelve parts of daylight and twelve of night. At night they used the rising of certain stars, called decans, to mark the hours, and in the day they used shadows and sundials. Twelve was a natural choice, and one popular explanation is that you can count to twelve on the three finger joints of each of the four fingers on one hand, using the thumb as a pointer.
In those days the hours were not equal. A summer daylight hour was longer than a winter daylight hour, because the day was always divided into twelve parts regardless of the season.
The Babylonians and base 60
The Babylonians used a number system based on 60, called sexagesimal. The number 60 is useful because it can be divided evenly by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. This makes fractions easy to work with, which is why it was the preferred base for astronomers and surveyors.
The traces of this system are still around us. A circle has 360 degrees, each degree is divided into 60 minutes of arc, and each minute into 60 seconds of arc.
The Greek astronomers
Greek astronomers such as Hipparchus, in the second century BC, wanted a standard system, and they used equal hours that are one twenty-fourth of a full day. They borrowed the Babylonian base-60 system to divide the hour into smaller parts. The Latin names for these parts were pars minuta prima, the first small part, and pars minuta secunda, the second small part, which became minute and second.
For most people, however, the equal hour was not very useful until there was a way of measuring it.
Mechanical clocks make hours equal
In Europe the church bells in the Middle Ages marked prayer times, and the length of the hours varied with the season. Mechanical clocks, which spread in the 14th century, ticked at a constant rate and made equal hours practical. Over a few generations, towns replaced seasonal hours with a 24-hour day divided the same way all year.
The minute hand became common later, and the second hand only after the pendulum clock was invented in the 1600s, when clocks were accurate enough for them to be useful.
Why a week has seven days
The seven-day week does not come from astronomy of the Sun but from the seven classical planets: the Sun, the Moon, Mars, Mercury, Jupiter, Venus and Saturn. The Babylonians and later the Greeks and Romans named the days after them, and the names are visible in the Romance languages, such as lundi for the Moon's day.
In English and the Scandinavian languages, four of the Roman gods were replaced by Norse gods, so Tuesday is Tyr's day, Wednesday is Odin's day, Thursday is Thor's day and Friday is Frigg's day, a goddess often linked to Freya.
Decimal time: the experiment that failed
In 1793, during the French Revolution, France decided to make time decimal. The day was divided into 10 hours, each with 100 minutes of 100 seconds, and the week had ten days. Clocks with decimal faces were made, but people did not like them, and the system was dropped in 1795 for hours and minutes, although the metric system for length and weight was a lasting success.
A similar idea has come up since then, for example Swatch Internet Time in 1998, but none has caught on.
Other ways of dividing the day
Not everyone has used the same system. Traditional Chinese timekeeping divided the day into twelve double hours, each named after an animal of the zodiac. The Maya used a complex calendar with units of 20. In Japan until the 1870s the length of an hour varied with the season, as in ancient Egypt, and it was only with the adoption of Western timekeeping that the equal hour became standard.
The second today
The second is no longer one 86,400th of a day. Since 1967 it has been defined by the radiation of cesium atoms, as described in the guide to UTC and atomic time. The old divisions, however, are still with us: 60 seconds, 60 minutes, 24 hours.
If you want to convert between the units, the minutes-to-hours tool on this site does it instantly, and the timer and stopwatch tools use the same units.