Estimated Max Heart Rate: Tanaka Equation Derivation
Tanaka et al. (DOI 10.1016/S0735-1097(00)01054-8) derived HRmax = 208 - 0.7 x age from a meta-analysis of 351 studies involving 18,712 adults and cross-validated it in 514 healthy adults aged 18-81. The paper did not publish P5, P25, P50, P75, and P95 tables for age bands.
- Point estimate: FitnessNorms evaluates the equation once at the representative age shown below. It is not an average across all ages in the bracket.
- Approximate spread:
Q(p) = 208 - 0.7 x age + 10 x z(p), wherez(p)is the standard normal quantile. The fixed 10 bpm standard deviation is a transparent approximation within the paper's reported age-specific range of 7-11 bpm. - Rounding: calculated values are rounded to the nearest whole bpm, with half values rounded upward.
- Sex: the source found no significant difference in the regression by sex, so the same derived values are displayed for men and women.
| Display bracket | Representative age | Equation point (bpm) |
|---|---|---|
| 18-19 | 19 | 195 |
| 20-29 | 25 | 191 |
| 30-39 | 35 | 184 |
| 40-49 | 45 | 177 |
| 50-59 | 55 | 170 |
| 60-69 | 65 | 163 |
| 70-79 | 75 | 156 |
| 80-81 | 81 | 151 |
The labels describe the derived distribution, not exercise performance or a clinical target. Estimates stop at age 81, the upper end of the validation sample, rather than extending an 80+ bracket beyond the evidence. The source population was healthy, nonmedicated, and nonsmoking; medications and health conditions can materially change exercise heart-rate response. Full source details are on the reference page.