The best known formula for maximum heart rate is 220 minus your age. The Tanaka equation, published later and fitted to a larger set of studies, is 208 minus 0.7 times your age. They do not agree, and the direction of the disagreement changes with age.
- At 20: 200 beats per minute against 194, a gap of 6
- At 30: 190 against 187, a gap of 3
- At 50: 170 against 173, a gap of 3 the other way
The two lines cross in the early forties. Below that, the old formula reads higher; above it, lower.
Why 220 minus age persists
It is memorable, and it was never presented as precise. It came out of a rough fit to limited data and stuck because it can be done in your head. Tanaka's version fits the underlying data better, particularly at the ends of the range, which is exactly where the simple version drifts.
The variation that dwarfs both
The more important number is not the gap between formulas but the spread around either of them. Actual maximum heart rate at a given age varies between individuals by roughly ten beats per minute in each direction, and no equation using only age can capture that.
Put differently: the formulas disagree by three to six beats, and the person in front of you may sit twenty beats from the prediction. Choosing between the two equations is a smaller decision than most training articles imply.
What this means for zones
Training zones defined as percentages of maximum inherit all of that uncertainty. A zone described as 70 to 80 per cent of maximum is really a band around an estimate that itself has a band around it.
Two practical alternatives are more robust. Rate of perceived exertion needs no formula at all. A measured maximum from a supervised test replaces the estimate with your own figure, which is worth doing for structured training but is genuinely strenuous and not something to attempt casually.
Reading a heart rate number sensibly
Heart rate is affected by caffeine, heat, sleep, illness, hydration and stress, which is why the same effort can produce noticeably different readings on different days. A session that feels hard at a lower heart rate than usual is information, not a malfunction.
The maximum heart rate calculator shows both formulas together so the size of the disagreement is visible, and the target heart rate calculator converts a chosen maximum into training zones. If a heart rate reading is unusual at rest or comes with symptoms, that is a question for a doctor rather than a calculator.