Worked example: age 35
| Equation | Published as | Result |
|---|---|---|
| Tanaka | 208 − 0.7 × 35 | 184 bpm |
| Fox | 220 − 35 | 185 bpm |
| Gellish | 207 − 0.7 × 35 | 183 bpm |
| Nes | 211 − 0.64 × 35 | 189 bpm |
| Åstrand | 216.6 − 0.84 × 35 | 187 bpm |
Six beats between the highest and the lowest. That is the disagreement between the equations, and it is the smaller of the two numbers on this page.
The number that matters more: ±10 beats
Every one of these five equations is a line fitted through a cloud of people, and the cloud is wide. The residual standard deviation around each of them is about 10 to 12 beats a minute.
Put concretely: at 35, the headline estimate is 184 bpm, and roughly two thirds of 35-year-olds fall somewhere between 174 and 194. About one in three falls outside even that. Some 35-year-olds have a genuine maximum of 165 and some of 200, and neither is unusual or a sign of anything.
So the honest reading of any age equation is: this is where the middle of the population sits, and your own figure could easily be ten beats either side of it. The gap between Tanaka and Nes is six beats; the gap between you and the average person your age could easily be twenty. Choosing carefully between the five equations is fussing over the smaller error while ignoring the larger one.
Why Tanaka is the headline, and why 220 − age is not
Tanaka, Monahan & Seals (2001) came out of a meta-analysis of 351 studies covering nearly 19,000 people, plus a prospective validation on a further 514. It is the best-evidenced of the five, and it is what most exercise physiology now uses.
220 − age is the famous one, and it has no primary derivation at all. Fox and colleagues offered it in 1971 as a rough summary line drawn through data from about ten earlier studies; it was never presented as a fitted regression and it came with no error term. It then acquired authority purely by repetition, which is how it ended up printed on gym equipment worldwide.
The practical difference: 220 − age is reasonably close to Tanaka in the mid-thirties and drifts apart at the ends. It overestimates young adults and underestimates older ones — at 20 it is 6 beats high against Tanaka, at 70 it is 9 beats low. If you are over about fifty and setting training zones from 220 − age, every zone is being set several beats too low.
Gellish (2007) came from longitudinal data on over 900 people tracked across repeated tests, and lands one beat below Tanaka. Nes (2013) came from the Norwegian HUNT study, a large healthy adult population, and runs a little higher. Åstrand (1952) is the oldest of the five and has the steepest age slope after Fox, so it sits high in young adults and low in older ones.
Measuring yours instead of estimating it
The only figure that is actually yours is one you have seen on a monitor during an effort hard enough to reach it — typically at the end of a hard race, or the last repetition of a maximal interval session. Even that is a floor rather than a ceiling: it tells you your maximum is at least that, because it is genuinely difficult to reach a true maximum voluntarily.
If you have a figure like that, use it everywhere in place of an estimate. It is worth more than any choice between the five equations on this page, and it feeds directly into the zone calculator, which is where a maximum heart rate is actually used for anything.
What this page deliberately does not do
It does not interpret your heart rate. It does not tell you whether a maximum is high or low for your age, because the spread makes that meaningless; it does not read anything into a resting rate; and it does not produce a “fat burning zone”, a health target or a risk figure of any kind.
That is not caution for its own sake. A maximum heart rate is an input to a training plan, and turning it into a statement about a person requires clinical context that a web form does not have and cannot get.
Limitations, stated plainly
All five equations use age and nothing else. None of them knows your sex, your weight, your training history, your genetics, your altitude, the temperature, how much caffeine you have had, or whether you are on medication that affects heart rate — and several of those move the real figure more than the difference between the equations does. Maximum heart rate is also barely affected by fitness: a very fit person and an untrained person of the same age typically have similar maximums, which is why a rising maximum is not a sign of improvement and a falling one is mostly just age.
These are population regressions applied to one person. They are a starting point for setting training zones and nothing more. This is a fitness estimate, not medical advice, and nothing on this page should be read as an assessment of anybody's heart.