How the formulas work
The arithmetic here is deliberately simple, so the honest value of this page is in knowing where each number comes from and how far to trust it. The Tanaka formula, 208 minus 0.7 times age, was published by Tanaka, Monahan, and Seals in 2001 after a meta-analysis that pooled hundreds of studies of measured maximum heart rate. The regression they fit tracks laboratory-measured values well across the whole adult age range, which is why it is the primary result above and the formula this site uses everywhere heart rate zones are calculated.
The Fox formula, 220 minus age, dates to a 1971 paper by Fox, Naughton, and Haskell. It was proposed as a rough rule of thumb drawn from a handful of earlier studies, and it was never fit to data with statistical rigor. It survived for fifty years because it is easy to do in your head, not because it is accurate.
Why 220 minus age keeps missing
Because the Fox line has the wrong slope, its error changes direction depending on how old you are. For younger runners it tends to overestimate: a 25-year-old gets 195 from Fox but 191 from Tanaka, and measured averages sit closer to the lower number. For older runners it underestimates, and the gap grows every year. A 60-year-old gets 160 from Fox and 166 from Tanaka, a 6 bpm difference that shifts every training zone built on top of it. The two lines cross near age 40, which is the one age where the old rule happens to agree with the better data. If you set zones from a max that is 6 bpm too low, your easy days get slower than they need to be and your threshold work lands below the stimulus you were aiming for.
Estimates versus your real max
Here is the caveat that matters more than the choice of formula: both equations carry an individual standard deviation of roughly 10 bpm. In plain terms, about a third of runners have a true max more than 10 bpm away from what any age formula predicts, in either direction. A formula is a population average, and you are not a population.
The only reliable number is a measured one: the highest value you have seen from a chest strap or clean optical reading at the end of a hard race, a set of all-out hill repeats, or a lab test. A practical field test looks like this: warm up thoroughly for 15 to 20 minutes, then run 2 to 3 repeats of about 2 minutes up a steady hill, each one harder than the last, finishing the final repeat at a full effort. The peak reading during or just after that last repeat is close to your true max. Treat this as a hard workout: only do it when you are healthy, rested, and used to intense running, and talk to a doctor first if you have any heart condition or are returning from a long layoff.
One more thing worth internalizing: training does not raise your max heart rate. It declines slowly with age no matter how fit you are, and that decline is normal, not a warning sign. Fitness shows up elsewhere, in a lower resting heart rate and faster paces at the same effort, which is why the Zone 2 calculator can also use your resting heart rate to personalize zones rather than leaning on max alone.
Worked example: the formulas at 40 and at 60
Take a 40-year-old runner. Tanaka gives 208 minus 28, which is 180 bpm. Fox gives 220 minus 40, also 180 bpm. At this age the formulas agree, because 40 is where the two lines cross. Now take a 60-year-old: Tanaka gives 208 minus 42, which rounds to 166 bpm, while Fox gives 160 bpm. That 6 bpm gap is the difference between a Zone 2 ceiling of about 116 versus 112 bpm, and it widens further for masters runners in their seventies. The older you are, the more it pays to drop the old rule.
Max heart rate by age: reference table
Every value below is computed with the same functions the calculator uses, rounded to the nearest beat per minute.
| Age | Tanaka max HR (bpm) | Fox max HR (bpm) |
|---|---|---|
| 20 | 194 | 200 |
| 25 | 191 | 195 |
| 30 | 187 | 190 |
| 35 | 184 | 185 |
| 40 | 180 | 180 |
| 45 | 177 | 175 |
| 50 | 173 | 170 |
| 55 | 170 | 165 |
| 60 | 166 | 160 |
| 65 | 163 | 155 |
| 70 | 159 | 150 |
Related tools and guides
A max heart rate is only useful once you build zones on it. The Zone 2 heart rate calculator turns your max into an easy-day ceiling using four methods, and the MAF calculator offers a conservative alternative that skips max heart rate entirely. The VO2 max calculator uses the same Tanaka estimate in its resting heart rate method. For deeper reading, see MAF vs Karvonen vs percent of max and why Zone 2 feels too slow.
Frequently asked questions
Which max heart rate formula is most accurate?
Tanaka (208 minus 0.7 times age) is the better choice. It came from a 2001 meta-analysis of hundreds of studies and tracks measured values more closely across the full age range, while 220 minus age was never fit to data with any rigor. That said, both formulas carry an individual standard deviation of roughly 10 bpm, so a measured max from a hard effort beats either one.
My watch has recorded a higher heart rate than the formula predicts. Which is right?
Trust the watch, assuming the reading came from a chest strap or a clean optical trace during a genuinely hard effort. A formula is a population average; a real reading from your own heart is data. If you have seen 192 at the end of a 5K, your max is at least 192, whatever the formula says. Spikes from strap dropouts or optical cadence lock are the exception, so sanity-check any single outlier reading.
Does training raise my max heart rate?
No. Max heart rate is set largely by age and genetics, and it declines slowly over the years regardless of how fit you are. Training changes almost everything else: resting heart rate drops, stroke volume rises, and you run faster at any given heart rate. But the ceiling itself does not move upward with fitness.
How do I measure my actual max heart rate?
The most practical field test is a set of hard hill repeats: after a long warmup, run 2 to 3 efforts of about 2 minutes up a steady hill, each harder than the last, with the final one all out to the top. The highest reading during or just after the last repeat is close to your true max. Only attempt this if you are healthy, well warmed up, and accustomed to hard running; check with a doctor first if you have any cardiac history.
Is a high max heart rate a sign of good fitness?
No. Max heart rate says nothing about fitness in either direction. Two equally fit runners of the same age can have maxes 20 bpm apart. It is simply a personal ceiling used to anchor training zones; the fitness signal lives in what pace you can hold at a given percentage of it.