What is the minute [unit of time] based on?

Tradition. But 60 divides by 4 and by 3 evenly, and with 60 minutes in an hour, there are 60×60 = 360 seconds in an hour, which matches 360 degrees in a circle.

This is an excerpt from a much longer article that goes into the details of how the use of 60 came about:

“In today’s world, the most widely used numeral system is decimal (base 10), a system that probably originated because it made it easy for humans to count using their fingers. The civilizations that first divided the day into smaller parts, however, used different numeral systems, specifically duodecimal (base 12) and sexagesimal (base 60).

Thanks to documented evidence of the Egyptians’ use of sundials, most historians credit them with being the first civilization to divide the day into smaller parts. As early as 1500 B.C., the Egyptians had developed a more advanced sundial. A T-shaped bar placed in the ground, this instrument was calibrated to divide the interval between sunrise and sunset into 12 parts. This division reflected Egypt’s use of the duodecimal system—the importance of the number 12 is typically attributed either to the fact that it equals the number of lunar cycles in a year or the number of finger joints on each hand (three in each of the four fingers, excluding the thumb), making it possible to count to 12 with the thumb.”

12 is also used for inches in feet. Interesting. Base 10 is so much easier and better in my opinion. But, I cannot imagine changing over the clock to base 10. Everything else I am all in favor of metric, bit the clock would be a hold out for me.

@Zaku – 60 can be divided by 2, 3, 4, 5, 6, 10, ... That is very convenient. Also note: 60×60 = 3600, which is analogous but not the same as 360° of a circle.

Minutes are made up of 60 seconds mainly because timekeeping was developed in conjunction with astronomy. If you’re looking for a consistent event upon which to measure time, the earth’s rotation (and observations of the heavenly objects that swing by) is pretty darn good, but not perfect.

Some of the earliest astronomers were the ancient Sumerians – circa 3,000 B.C. – who used base 60 for their calculations. The Babylonians and Egyptians built upon that standard, followed by the Greeks, on and on until we get where we are today.

60 has 12 factors, 1,2,3,4,5,6,10,12,15,20,30 and 60, more than any smaller number (such numbers are called highly composite), making it highly convenient for breaking into smaller parts.

@RocketGuy Um, right, 3600, thanks. :-)