# Estimating Your Maximum Heart Rate

Loosely speaking, an individual’s maximum heart rate (MHR) is the highest heart rate (measured in beats per minute) that can be sustained during prolonged exercise. Lucky for us, researchers have gotten many brave individuals to exercise at their MHRs in the name of science. These experiments have yielded equations that estimate MHR based on just age. You may already be familiar with the most popular formula:

$\text{MHR} = 220 - a,$

where a is your age (in years). This is a linear function of age. But it turns out the following quadratic function of a has a smaller error (see the Limitations section below for the reference):

$\text{MHR}=192-0.007a^2.$

Try it out for yourself with the calculator below—input your own age into the green cell and the calculator will calculate your theoretical maximum heart rate using both equations.

## Limitations

The quadratic MHR formula came from the study “Longitudinal Modeling of the Relationship between Age and Maximal Heart Rate,” by Gellish, R.L. et al., published in Medicine & Science in Sports & Exercise, 39, no. 5 (2007), pgs. 822-829. The study was based on roughly 900 exercise tests of about 130 people (mostly male) conducted over a 25-year span of time. (More information on other characteristics of the participant pool (e.g., race and fasting vs. not) are included in the study.) The researchers derived two formulas for MHR: the quadratic one cited above, and another linear one different from the 220 – age one discussed above. Their analysis concluded that the quadratic model had lower errors than their linear model (which in turn had lower errors than the 220 – age model), but ultimately recommended their alternate linear model, 207 – 0.7a, due to it being easier to use than the quadratic model.

The researchers also mentioned that, based on their data, the 220 – age model “overestimates MHR in young adults and underestimates it in older people.” This can be seen graphically; Figure 1.2 in The Calculus of Happiness analyzes the two MHR functions’ graphs to illustrate that, and the ensuing discussion works through the details of the exact age ranges for which the 220 – age model over- and underestimates MHR relative to the quadratic model.