Why is a day 24 hours and an hour 60 minutes?

The 24-hour day traces to ancient Egypt, where daylight and darkness were each divided into 12 parts, tracked by sundials during the day and by the rising of particular stars at night. The choice of 12 likely reflects a counting method using the three joints on each of the four fingers of one hand, giving twelve countable segments per hand, a system that also shows up in other ancient cultures. Those Egyptian hours were seasonal and unequal, stretching and shrinking as daylight changed through the year, and fixed equal hours came much later with mechanical clocks.

The 60-minute hour and 60-second minute come from Babylonian mathematics, which used a sexagesimal, base-60 system. The appeal of 60 is divisibility: it divides evenly by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30, which makes fractions vastly easier than base 10, where thirds produce repeating decimals. That same Babylonian inheritance is why circles have 360 degrees and why degrees subdivide into minutes and seconds of arc. So the modern clock is a composite artifact: Egyptian twelves, Babylonian sixties, and mechanical clockmaking's insistence on equal intervals, which is why the units feel arbitrary against a metric world and have resisted every attempt at decimalization, including a serious one during the French Revolution.