Maximum Heart Rate Formula: 220 − Age and Better Options

Maximum heart rate, HRmax, is the fastest the heart beats during all-out effort. Finding it directly takes a maximal-effort test, so exercise guides estimate it from age with a straight line. Which line depends on who was tested. This page sets the lines side by side, with the papers behind each one, the error each carries and what that error does to the heart-rate zones built on top. The subject is the math of the estimate. It is not a prescription, and anyone with a heart condition or on heart medication should take the numbers to a clinician. The health section has the neighboring formulas, and the resting metabolic rate formulas page covers another family of fitted lines.

What is the formula for maximum heart rate (MHR)?

The best-known formula is HRmax = 220 − age, usually credited to Fox⁶. Government exercise guidance pairs it with the zone table: a 40-year-old has a maximum of 180 beats a minute, a 50-year-old 170⁸. The table figures are averages, so the guide tells readers to use them as general guidelines⁸.

The shape of every competitor is the same: a straight line, HRmax = intercept − slope × age. The 220 formula has a slope of 1 beat per year. Most newer fits have slopes between 0.64 and 0.88¹²⁴. Which one you pick changes the answer more for a 60-year-old than a 20-year-old, because the lines meet near the young end and part later⁶.

Where 220 − age came from

The history is thinner than the formula’s fame. An exercise-physiology review traced it and found it was not developed from original research, but resulted from observation based on data from approximately 11 references⁷. Textbooks often present it without explanation or citation to original research⁷, and the earliest equation, Robinson’s, dates from 1938⁷. Its authors conclude the formula has no scientific merit for use in exercise physiology and related fields⁷.

That is a strong verdict, so read the fine print. The 220 line is a rule of thumb that happens to sit close to the data for some groups. The Fox line was obtained from a cohort of men with an average age of 55 years⁶, and a later review explains why it misses elsewhere: the cohort mainly included men under the age of 55⁶.

Is 220 minus age accurate?

Not for any particular person, and the direction of the error depends on age. Because achievable HRmax declines with age in both sexes, the Fox equation tends to overestimate in young adults and underestimate in older adults, notably after age 40⁶. It also tends to overestimate in females⁶. The Tanaka meta-analysis reached the same verdict for older adults: its authors found that the currently used equation underestimates HRmax in them¹.

The size of the miss is large. The Tanaka paper’s own standard error is around 11.4 beats a minute⁶, the Norwegian study’s is 10.8², and Robinson’s ranges from 7 to 12⁶. A 2002 review puts the error inherent in HRmax estimation at 7 to 11 beats a minute⁷. HRmax can vary by 20 to 30 beats a minute among individuals of the same age, depending on the equation used⁶.

Direct tests agree. When 99 treadmill tests were compared with nine equations, Bland-Altman plots revealed wide limits of agreement for all nine, suggesting poor agreement between measured and predicted HRmax⁵. The equations under- and overestimated at the low and high ends of measured HRmax, with the exception of the Fox equation⁵. That is why the authors found Fox the best option for a general population, while stating that all the equations showed poor agreement⁵.

What is the new formula for maximum heart rate?

There is not one. Several formulas agree with each other better than they agree with 220⁶:

• Tanaka (2001). A meta-analysis gave HRmax = 208 − 0.7 × age with r = −0.90, and a laboratory study of 514 healthy subjects gave 209 − 0.7 × age, which the authors called virtually identical¹. The line did not differ between men and women, and was not influenced by habitual physical activity¹.
• Gellish (2007). Following the same people for up to 25 years gave 207 − 0.7 × age³. That is appreciably different from 220 − age, and it confirms the recent cross-sectional findings³.
• Nes, HUNT study (2013). 3,320 healthy adults gave 211 − 0.64 × age, with no interaction by sex, activity, VO2max or BMI². Earlier equations underestimated HRmax in subjects older than 30².
• Gulati (2010), women. In 5,437 asymptomatic women the line was 206 − 0.88 × age, lower than 220 − age⁴. That formula was a more accurate predictor of all-cause mortality in the sample⁴.

A 2024 review calls Tanaka’s line a more accurate average estimate, especially for older adults, while noting a standard error of about 11.4⁶. No age-only line escapes the error. A more elaborate model that adds body mass, BMI, VO2max, body fat, sex and test mode has the lowest error of those reviewed⁶, but it needs inputs that few people have.

Max heart rate by age: the formulas side by side

Worked example (our arithmetic): predicted HRmax in beats a minute, each formula applied to each age¹²³⁴⁶

Three patterns stand out. At 20 the 220 line is the highest of the four general lines, by 2 to 7 beats, and by 70 it is the lowest, 8 to 16 beats below the others (our arithmetic). It crosses Tanaka’s line at age 40, where both give 180, which matches the review’s point that Fox errs high in the young and low after 40⁶. Third, the women-only Gulati line sits below the others at every age, by 6 to 22 beats, which fits the report that Fox overestimates in women⁶.

Worked example: a 50-year-old, six formulas

Worked example (our arithmetic)¹²³⁴⁶

The four general-population lines span 9 beats, from 170 to 179. Add the standard error of about 11 beats²⁶ and the honest statement is a band: roughly one person in three, treating the error as a normal curve, would fall more than 11 beats from the line, in either direction. That remark is our statistics, not a finding of the papers. So a person aged 50 with a predicted HRmax of 173 could plausibly have a true maximum anywhere from about 162 to 184.

Factors affecting maximum heart rate

Age is the main one. It accounts for 70 to 80% of HRmax variability across different age groups⁶. The pace of decline is gentler in women than in men⁶, and in the Tanaka meta-analysis the regression line was not different between men and women, nor influenced by habitual activity¹. The sources disagree on sex. Taking the newer, larger HUNT data, which found no interaction with sex, physical activity, VO2max or BMI, the practical position is that age explains most of the variation and the rest is individual².

Other factors the review lists:

• Fitness. One study found HRmax lower in athletes than in sedentary people⁶.
• Smoking. It likely attenuates the achievable HRmax⁶.
• Medication. Beta-blockers and ivabradine reduce HRmax by approximately 10 to 15 beats a minute⁶. A few high blood pressure medicines lower the maximum heart rate, and the target zone with it⁸.
• Effort. HRmax is the peak rate reached in a maximal-effort test, often a plateau despite rising workload⁶. A gold standard for true maximal effort is a respiratory exchange ratio above 1.10⁶.

Implications for exercise: zones built on the estimate

Zones are percentages of HRmax, so the error carries straight through. The federal heart-health guide sets the target zone at 50 to 75 percent of maximum, and for age 50 tabulates 85 to 127 beats a minute against a maximum of 170⁸. Guidance summarized in the recent review uses higher bands: 64 to 76% of age-predicted HRmax counts as moderate-intensity exercise, and 77 to 95% as vigorous⁶.

Worked example (our arithmetic): the same age-50 zones from two maxima⁶⁸

The two maxima differ by 3 beats (our arithmetic), and the zones shift by about that much. An error of 11 beats in the maximum shifts every zone by 5 to 10 beats. That is why the same guide ties effort to how it feels: while walking briskly or jogging, you should be able to keep up a conversation without trouble⁸.

Percentages of HRmax map onto oxygen use. The review gives 55%, 70%, 85% and 90% of age-predicted HRmax as corresponding to 40%, 60%, 80% and 90% of VO2max⁶. A related approach scales the zone to the heart rate reserve: HR = HRrest + (intended fraction) × (HRmax − HRrest), the Karvonen method⁷.

Worked example (our arithmetic): Karvonen with an assumed resting rate of 60, HRmax 170⁷

The 85% mark has its own problem. In exercise stress testing, 85% of age-predicted HRmax is used as an endpoint, but one review found its use as an indication of maximal intensity likely arbitrary⁶. In a group of 469 healthy adults, using 85% as a cutoff underestimated exercise capability⁶. Only about 50% of 238 patients who reached 85% of HRmax had a respiratory exchange ratio above 1.10⁶.

HRmax calculator: how accurate is it, and how to do it by hand

A calculator for this is one subtraction and one multiplication, so the useful skill is choosing the line, not typing numbers. Pick the formula for your group (the general lines for most adults, the Gulati line only for women), enter your age, and read the answer as the middle of a band about 11 beats wide each way²⁶. For a number you can rely on, measure it: individuals should use data from graded exercise tests to determine HRmax when applicable⁵.

Mistakes with the formulas

• Treating the result as a limit. HRmax estimates are averages⁸. Individuals can exceed them or never reach them⁶.
• Applying a women-only line to men. The Gulati fit came from asymptomatic women⁴.
• Using a healthy-adult line on patients. Tanaka’s subjects were healthy and free of coronary artery disease, which could limit applicability to patients⁶.
• Forgetting medication. A drug that lowers the maximum also lowers every zone⁸.
• False precision. A formula that is wrong by 11 beats does not justify a decimal place⁶. The tables above keep decimals only to show the arithmetic.

What next

The same pattern, a fitted line with a named population and a standard error, runs through the total daily energy expenditure page, where the line predicts calories instead of beats. The slope of each formula here is a derivative in disguise: the slope of a straight line, as laid out on the derivative rules cheat sheet.