Maximum Heart Rate from Age (220 − Age)

The famous 220-minus-age rule was never derived from physiology. In 1971 William Haskell and Samuel Fox plotted maximum heart rates from about three dozen published studies, eyeballed a line through the scatter, and remarked in passing that it looked like 220 minus age. Haskell later said, with some amusement, that he never expected the throwaway line to end up printed on every treadmill on earth.

It survives because it is close enough on average and impossible to forget. The catch is the scatter around that average: the standard deviation is roughly 10 to 12 beats per minute, so among a hundred forty-year-olds with a predicted maximum of 180, plenty will genuinely top out near 160 and plenty near 200. Later fits such as Tanaka's $208 - 0.7a$ track measured data a little better, particularly for older adults, and none of them fixes the spread.

Treat the result as the middle of a wide band, not as your number. A measured maximum from a supervised test is the only way to know it, and beta blockers and other medications shift it substantially.