How long is a second?

There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute - so surely a second is just 1/(24 x 60 x 60), or 1/86400, of a day.

The current and formal definition in the International System of Units (SI) is more precise:

The second [...] is defined by taking the fixed numerical value of the caesium frequency, ??Cs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s?1.

This current definition was adopted in 1967 when it became feasible to define the second based on fundamental properties of nature with caesium clocks. Because the speed of Earth's rotation varies and is slowing ever so slightly, a leap second is added at irregular intervals to civil time to keep clocks in sync with Earth's rotation.