One minute is exactly 60 seconds. The second is the SI base unit of time and the most precisely realised unit in the entire system, while the minute is a convention layered on top of it.
About the units
Since 1967 the second has been defined by the caesium atom: it is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of caesium-133. Before that it was a fraction of the mean solar day, which turned out to be unsuitable because the Earth's rotation is neither constant nor perfectly predictable. Atomic clocks now realise the second to better than one part in 10¹⁶, and optical clocks under development are better still. The minute inherits its sixty from Babylonian sexagesimal counting, the same source as the hour's sixty minutes and the circle's 360 degrees.
The exact factor
The factor is exactly 60. The complication is not the arithmetic but the leap second: because atomic time runs at a constant rate while the Earth's rotation slowly varies, UTC has occasionally inserted an extra second at the end of a day. Such a minute contains 61 seconds. Twenty-seven leap seconds were added between 1972 and 2016, and in 2022 it was agreed to stop the practice by 2035. Systems that assume every minute has exactly sixty seconds have failed during leap seconds, repeatedly and expensively.
Where you meet this conversion
Sports timing, cooking, music tempo and any calculation of rates. Heart rate is beats per minute while intervals between beats are measured in milliseconds, so cardiology moves across this boundary constantly. Engine speed in revolutions per minute converts to hertz — revolutions per second — by dividing by sixty, which is the relationship linking the frequency and rotation categories on this site. Network timeouts, animation timings and process durations are all specified in seconds while described in minutes.