Maximum heart rate (max HR or HRmax) is the highest number of beats per minute your heart reaches during maximal effort. It is commonly used to estimate heart rate zones and describe exercise intensity.
There is no single accepted formula for estimating max HR. Every age-based equation is a statistical estimate derived from a population, not a physiological limit for an individual. Published studies commonly report prediction errors of about 10-12 bpm, with larger differences possible for some people.
Common Formulas
Fox Formula
The best-known formula is simple and remains common in general fitness guidance and exercise equipment. It first appeared in scientific writing in a 1970 review associated with William Haskell and Samuel Fox, but it was not derived from a single rigorous population study.
Its simplicity makes it useful as a rough reference, but it can underestimate or overestimate max HR considerably for an individual.
Tanaka Formula
Published by Hirofumi Tanaka and colleagues in 2001, this equation was developed from a meta-analysis of 351 studies involving 18,712 participants and cross-validated in a laboratory study of 514 healthy adults.
It is a well-supported general-purpose starting point for healthy adults, although its typical individual error remains around 10 bpm.
Gellish Formula
Ronald Gellish and colleagues published this equation in 2007 after analyzing repeated exercise-test measurements. Its estimates map to the Tanaka formula minus 1 bpm.
Nes Formula
This equation was developed from maximal exercise tests completed by 3,320 healthy adults in the Norwegian HUNT Fitness Study. It tends to produce somewhat higher estimates than the Tanaka and Gellish formulas, particularly in older adults.
Gulati Formula
Martha Gulati and colleagues developed this equation from exercise stress tests completed by 5,437 asymptomatic women. Published in 2010, it was designed to address the limited representation of women in earlier exercise-testing research.
Inbar Formula
Published by Omri Inbar and colleagues in 1994, this equation is another commonly cited alternative in exercise physiology and sports science. Its estimates are generally close to the Tanaka and Gellish formulas.
Comparison at Age 38
The formulas cluster around a similar range, but even small differences can shift calculated heart rate zone boundaries.
| Formula | Estimated max HR |
|---|---|
| Fox | 182 bpm |
| Gellish | 180 bpm |
| Gulati | 173 bpm |
| Inbar | 180 bpm |
| Nes | 187 bpm |
| Tanaka | 181 bpm |
Which Formula Should You Use?
For a healthy adult without a measured max HR, Tanaka is a practical general-purpose starting point. Nes is a well-supported alternative based on a large, healthy population, while Gulati may be useful when a women-specific equation is preferred.
Choosing between formulas matters less than recognizing their limits. The result is a population estimate, not a ceiling, target, or measure of fitness. Use the same formula consistently when comparing workouts, then replace it with reliable personal data when available.
Measured Max HR
A measured max HR is more useful than an age-based estimate. It can be determined during a supervised maximal exercise test, such as a laboratory treadmill or cycle test. Experienced, healthy athletes also use carefully planned field tests or maximal race efforts.
The highest value recorded by a wearable is an observed peak, not necessarily your true max HR. A verified reading shows that your max HR is at least that high, but sensor error and the absence of a genuinely maximal effort can make individual recordings misleading.
Maximal testing is strenuous. Seek qualified medical or exercise-professional guidance if you have cardiovascular symptoms or conditions, take medication that affects heart rate, or are unsure whether maximal exercise is appropriate for you.
Sources
- "Age-Predicted Maximal Heart Rate Revisited" by Tanaka, Monahan, and Seals
- "Longitudinal Modeling of the Relationship Between Age and Maximal Heart Rate" by Gellish et al.
- "Age-Predicted Maximal Heart Rate in Healthy Subjects" by Nes et al.
- "Heart Rate Response to Exercise Stress Testing in Asymptomatic Women" by Gulati et al.
- "Measured Maximal Heart Rates Compared to Commonly Used Age-Based Prediction Equations" by Sarzynski et al.
- "HR Max Prediction Based on Age, Body Composition, Fitness Level, Testing Modality and Sex" by Shookster et al.