Max heart rate formulas compared: Fox, Tanaka and Gulati

Where each equation came from

They are not three versions of the same work. Fox, Naughton and Haskell published 220 minus age in 1971, and Robergs and Landwehr traced it in 2002 to a line drawn by observation through raw and averaged data compiled from roughly eleven sources - there is no published regression behind it, and its authors did not claim one. Tanaka 2001 pooled 351 studies covering 18,712 subjects and cross-validated the resulting regression in 514 more. Gulati 2010 derived its equation in 5,437 asymptomatic women in the St James Women Take Heart Project. One convention, two regressions.

Where they cross, and where they part

Fox and Tanaka give the identical answer at exactly age 40: 220 - 40 and 208 - 0.7 x 40 are both 180 bpm. Below 40 Fox reads higher - 200 against 194 at age 20 - and above 40 it reads lower, by 9 bpm at 70 and 12 bpm at 80. That crossover is why "220 minus age is too high" and "220 minus age is too low" are both things you will read, and why both can be right depending on the age being discussed. Gulati is below both at every adult age, since the algebra puts its crossing point with Fox beyond 116 years.

What the disagreement costs downstream

Nobody trains at their maximum, so the practical effect is on the zones built from it. At 60, zone 2 at 60 to 70 percent of maximum is 100 to 116 bpm from Tanaka, 96 to 112 from Fox, and 92 to 107 from Gulati. That is a 9 bpm shift in the upper edge, from nothing but the equation the calculator happened to pick. Any tool that prints one maximum without naming the equation has made that choice on your behalf and then hidden it.

The band all three share

Robergs and Landwehr report a standard error of estimate of 7 to 11 bpm across the prediction literature; Gulati 2010 reports about 9 bpm for its own equation. This site renders every predicted maximum inside a 10 bpm band, which is wider than the disagreement between the equations at most ages. Read together, those two facts say something specific: arguing about which equation to use matters less than remembering that all three are describing a population average, and that only a supervised maximal test measures your own.

Official sources

• Tanaka, Monahan & Seals, Age-predicted maximal heart rate revisited, J Am Coll Cardiol 2001
• Gulati et al., Circulation 2010 — St James Women Take Heart Project
• Robergs & Landwehr, The surprising history of the HRmax = 220 - age equation, JEPonline 2002
• Garber et al., ACSM Position Stand, Med Sci Sports Exerc 2011 — the published intensity classification

Frequently asked questions