Where “220 − age” actually came from
The most famous formula in fitness has a remarkably thin origin story. In 1970–71, physicians Samuel Fox, William Haskell and colleagues, writing about exercise and heart disease, plotted data from roughly eleven earlier studies — small, mostly male, none designed to measure maximal heart rate across ages — and drew an approximate line through the cloud: about 220 minus age. It was offered as a convenient rule of thumb, not a validated equation. Haskell himself later expressed surprise at how the back-of-envelope line ended up printed on gym equipment worldwide. It stuck because it is easy arithmetic, not because it fits people well.
The four formulas compared
| Formula | Basis | Best for |
|---|---|---|
| Fox | ~11 small studies, line drawn by eye | Historical interest; device defaults |
| Tanaka | Meta-analysis of 351 studies, ~18,700 people | General default for adults |
| Gulati | 5,437 women (St. James Women Take Heart) | Women, especially in clinical stress-test contexts |
| Nes | 3,320 healthy Norwegian adults (HUNT study) | Healthy, active adults; reads highest of the four |
Why Tanaka replaced Fox
In 2001 Tanaka, Monahan and Seals pooled essentially all published max-HR data — 351 studies — plus their own lab measurements, and found the true age slope is shallower than 1 bpm per year: about 0.7. The consequence is systematic: 220 − age reads too high for people in their twenties and too low from middle age onward — by around 7 bpm at 60 and more beyond. Since heart rate zones are percentages of this number, an error at the top propagates into every training target built on it. The age chart in the calculator shows the fan-out directly.
The honesty section: ±10–12 bpm
Here is what formula marketing leaves out: even the best equation only predicts the average person of your age. The standard deviation around that average is roughly 10–12 bpm, which means about one person in three sits more than 10 bpm from the formula — and one in twenty sits more than 20 bpm away. Two healthy 35-year-olds can have genuine maxima of 170 and 200 bpm. Max HR is mostly genetic, barely trainable, and says nothing about fitness; it is simply your ceiling, and formulas locate it only approximately. If you train by heart rate zones, this is the single best argument for measuring rather than estimating.
How to field-test your real max
A maximal test is, by definition, exhausting — do it only if you are healthy and already fit, and get medical clearance first if you are over 40, sedentary, or have any cardiac risk factors or symptoms. Use a chest strap if possible; wrist sensors often miss the peak.
- Warm up thoroughly — 15 minutes easy, with a few short pickups.
- On a steady hill (or treadmill at 2–4% incline), run 2–3 minutes hard, jog down, and repeat — each effort harder than the last.
- On the final effort, go to your limit, driving the last 30 seconds all-out. The highest number you see — typically in those closing seconds — is a close approximation of your max.
- Cool down long, and do not schedule anything hard for a couple of days.
A hard race finish at 5K, or the last interval of a genuinely maximal session, often reveals the same number without a dedicated test — check your history for the highest value you trust.
What to do with the number
Max HR is an input, not an outcome — its whole job is to anchor training intensities. Feed it into the heart rate zone calculator to build your five training zones, or the target heart rate calculator for Karvonen targets that also account for your resting heart rate. And remember it declines with age no matter what you do — revisit the estimate (or retest) every couple of years.