Max heart rate: 220 − age vs 208 − 0.7 × age

Where 220 − age came from

220 − age is so common that it can look like a law of physiology. It isn't. Tanaka and colleagues traced the original reports proposing it to reviews by Fox and Haskell in the 1970s.

According to their account, the equation was determined arbitrarily from a total of 10 studies. It was a convenient rule of thumb, not a regression fitted to a large, checked sample. Its main strength is that anyone can work it out in their head, with no calculator at all.

How 208 − 0.7 × age was built

Tanaka, Monahan and Seals published their paper in the Journal of the American College of Cardiology in 2001. They used two approaches and compared the results.

• A meta-analysis of 351 studies covering 492 groups and 18,712 subjects. Groups had to be healthy, nonmedicated and nonsmoking adults, with maximal effort checked by objective criteria.
• A laboratory study of 514 healthy adults aged 18 to 81, each tested on a continuous, incremental treadmill protocol.
• The meta-analysis gave 208 − 0.7 × age. The laboratory study gave 209 − 0.7 × age, almost the same line.
• The regression line did not differ between men and women, and habitual activity did not significantly change it.

Where they agree and where they split

Because the slopes differ, the two lines cross. Setting 220 − age equal to 208 − 0.7 × age gives 12 = 0.3 × age, so age = 40. At 40, both formulas give 180 bpm.

Below 40, 220 − age gives the higher number. Tanaka's paper states that the traditional equation overestimates maximum heart rate in young adults. Above 40, it gives the lower number, and the paper concludes that it underestimates maximum heart rate in older adults. By age 70 the gap is about 10 bpm.

Why the gap matters for zones

Every zone is a percentage of the maximum, or of the maximum minus rest. A 6-bpm difference in the maximum at age 60 moves the 70% mark by about 4 bpm with percent of max. The shift is smaller for low zones and larger near the top.

For a 25-year-old the direction flips. The traditional formula sets the ceiling 4.5 bpm higher than Tanaka's, so every zone edge sits a little higher too.

How far off can an age formula be?

Any formula that uses only age predicts the average for that age. Real people scatter around it. In Tanaka's laboratory data, the standard deviations were 7 to 11 bpm, and the discussion uses about 10 bpm as a round figure.

That scatter is far bigger than the gap between the two formulas at most ages. Two healthy 40-year-olds can have true maximums 20 beats apart while both formulas say 180.

Later studies also found that 208 − 0.7 × age does not fit every group equally. Machado and colleagues (2018) summarize reports where it overestimated maximum heart rate in sedentary adults and in active young adults, and underestimated it by 4.2 bpm in military personnel and by 6.2 bpm in a sample of 3,320 healthy people. They note that most age-only equations carry errors of 7 to 11 bpm.

These formulas were fitted on healthy adults. Medicines such as beta-blockers and heart conditions change heart rate, and the formulas are not made for that case.