Maximum heart rate: 220 − age vs Tanaka vs Gellish, with Karvonen zones

220 − age and Tanaka’s 208 − 0.7 × age cross at 40, both 180 bpm; Gellish’s 207 − 0.7 × age runs 1 bpm under Tanaka. At 20, 220 − age gives 200 against Tanaka’s 194, and at 70, 150 against 159. For a 70-year-old, the vigorous percent-of-maximum zone is 116 to 142 bpm by 220 − age and 123 to 151 by Tanaka.

Line chart of predicted maximum heart rate against age from 18 to 90 years. Tanaka, 208 − 0.7 × age, a solid line with circles, falls from 195.4 bpm at 18 to 145 bpm at 90. Gellish, 207 − 0.7 × age, a dotted line with triangles, runs 1 bpm under Tanaka at every age, 194.4 bpm at 18 and 144 bpm at 90. 220 − age, a dashed line with squares, falls from 202 bpm at 18 to 130 bpm at 90. It crosses Tanaka at 40 years and 180 bpm. Two hatched areas show Karvonen zones on Tanaka’s maximum for a resting rate of 60 bpm: moderate, diagonal hatch, 114 to 139 bpm at age 20 and 94 to 110 bpm at 90; vigorous, cross hatch, 141 to 179 bpm at age 20 and 111 to 135 bpm at 90. — Predicted maximum heart rate by 220 − age, Tanaka’s equation and Gellish’s, from the maximum table. The hatched zones beneath are the resting 60 bpm columns of the Karvonen table. Every plotted point is a row of the table. Image © ScienceQuest, CC BY 4.0: free to reuse with credit and a link to this page, as the image licence explains.

Maximum heart rate by age

Predicted maximum heart rate by 220 − age, by Tanaka’s 208 − 0.7 × age and by Gellish’s 207 − 0.7 × age, at 18 and every 5 years from 20 to 90, in beats per minute
Age (years)	220 − age	Tanaka, 208 − 0.7 × age	Gellish, 207 − 0.7 × age	220 − age above Tanaka
18	202	195.4	194.4	+6.6
20	200	194.0	193.0	+6.0
25	195	190.5	189.5	+4.5
30	190	187.0	186.0	+3.0
35	185	183.5	182.5	+1.5
40	180	180.0	179.0	0.0
45	175	176.5	175.5	−1.5
50	170	173.0	172.0	−3.0
55	165	169.5	168.5	−4.5
60	160	166.0	165.0	−6.0
65	155	162.5	161.5	−7.5
70	150	159.0	158.0	−9.0
75	145	155.5	154.5	−10.5
80	140	152.0	151.0	−12.0
85	135	148.5	147.5	−13.5
90	130	145.0	144.0	−15.0

Karvonen zones on Tanaka’s maximum

Moderate (40 to 59 percent of heart rate reserve) and vigorous (60 to 89 percent) zones by Karvonen’s method on Tanaka’s maximum, at resting rates of 60 and 75 bpm, in whole beats rounded inwards
Age (years)	Resting 60 bpm, % of reserve		Resting 75 bpm, % of reserve
Age (years)	Moderate, 40 to 59%	Vigorous, 60 to 89%	Moderate, 40 to 59%	Vigorous, 60 to 89%
20	114 to 139	141 to 179	123 to 145	147 to 180
30	111 to 134	137 to 173	120 to 141	143 to 174
40	108 to 130	132 to 166	117 to 136	138 to 168
50	106 to 126	128 to 160	115 to 132	134 to 162
60	103 to 122	124 to 154	112 to 128	130 to 155
70	100 to 118	120 to 148	109 to 124	126 to 149
80	97 to 114	116 to 141	106 to 120	122 to 143
90	94 to 110	111 to 135	103 to 116	117 to 137

A resting rate 15 bpm higher lifts the 40 percent edge by 9 bpm and the 89 percent edge by under 2, since Karvonen’s target is intensity × HRmax plus (1 − intensity) × HRrest. The bands are whole percents, so a beat or two between zones can fall in neither: 140 bpm at 20 years, resting 60, is 59.7 percent of reserve, which the calculator counts as moderate.

Percent-of-maximum zones under each formula

Moderate (64 to 76 percent of maximum) and vigorous (77 to 95 percent) zones on Tanaka’s maximum and on 220 − age, in whole beats rounded inwards
Age (years)	Tanaka, % of maximum		220 − age, % of maximum
Age (years)	Moderate, 64 to 76%	Vigorous, 77 to 95%	Moderate, 64 to 76%	Vigorous, 77 to 95%
20	125 to 147	150 to 184	128 to 152	154 to 190
30	120 to 142	144 to 177	122 to 144	147 to 180
40	116 to 136	139 to 171	116 to 136	139 to 171
50	111 to 131	134 to 164	109 to 129	131 to 161
60	107 to 126	128 to 157	103 to 121	124 to 152
70	102 to 120	123 to 151	96 to 114	116 to 142
80	98 to 115	118 to 144	90 to 106	108 to 133
90	93 to 110	112 to 137	84 to 98	101 to 123

The bands stop at 76 and start again at 77 percent, so a beat or two between them is in neither: at 70 on Tanaka, 121 bpm is 76.1 percent and 122 bpm is 76.7 percent of maximum. The calculator gives such a figure without naming a band.

Why the formulas disagree

Robergs and Landwehr traced 220 − age to a 1971 review by Fox, Naughton and Haskell, who set the line by eye through about 35 data points and fitted no regression. Their figure legend says the line runs “not far from many of the data points”. Robergs and Landwehr refitted those points and got 215.4 − 0.9147 × age, with r = 0.51 and a standard error of 21 bpm.

Tanaka’s group and Gellish’s reached the same slope by different routes. Tanaka, Monahan and Seals pooled group means from 351 studies; Gellish and colleagues followed 132 people through 908 exercise tests over 25 years. Their lines sit 1 bpm apart. 220 − age drops 1 bpm a year against their 0.7 bpm, so it parts from Tanaka by 3 bpm for every decade away from 40 and runs 15 bpm under at 90.

The 9 bpm gap at 70 is about the size of the error in any age-only estimate. Robergs and Landwehr report standard errors of 7 to 11 bpm across two decades of studies, so for one person a maximum measured on an exercise test is the better figure. At 70, resting at 60 bpm, Karvonen’s vigorous zone is 120 to 148 bpm on Tanaka’s maximum and 114 to 140 bpm on 220 − age.

The formulas

Tanaka, Monahan and Seals (2001) [1]: $\mathrm{HR_{max}} = 208 - 0.7 \times \text{age}$
Gellish and colleagues (2007) [2]: $\mathrm{HR_{max}} = 207 - 0.7 \times \text{age}$
The older rule [3]: $\mathrm{HR_{max}} = 220 - \text{age}$
Karvonen, heart rate reserve [5]: $\mathrm{THR} = \mathrm{HR_{rest}} + i \times (\mathrm{HR_{max}} - \mathrm{HR_{rest}})$
Percent of maximum [6]: $\mathrm{THR} = i \times \mathrm{HR_{max}}$

Where each formula holds

Each formula’s sample, the people it holds for, and where it does not apply
Formula	Fitted in	Holds for	Not for
Tanaka, 208 − 0.7 × age	Healthy adults: 18,712 people in 351 pooled studies, checked on 514 measured in one laboratory	The average maximum of healthy adults, the population the paper names; no sex or activity correction needed	One person’s true maximum, children, or people outside the healthy adults it was fitted to, such as those on beta blockers or with heart disease
Gellish, 207 − 0.7 × age	132 adults of both sexes and a broad range of ages and fitness, 908 maximal exercise tests at one university fitness centre from 1978 to 2003, fitted with linear mixed models	A longitudinal check on Tanaka: the same slope, 1 bpm lower	One person’s true maximum, children, or a maximum lowered by medication
220 − age	Not fitted: set by eye through about 35 points in a 1971 review (Fox, Naughton and Haskell); a regression on those points gives 215.4 − 0.9147 × age, r = 0.51 (Robergs and Landwehr 2002)	Reading older charts; within 3 bpm of Tanaka from 30 to 50	Older adults, where it runs low: 9 bpm under Tanaka at 70
Karvonen, heart rate reserve	A 1957 longitudinal training study (Karvonen, Kentala and Mustala); the bands are ACSM’s	A resting rate measured at rest, with the reserve bands	Percent-of-maximum bands: the two scales have different edges
Percent of maximum	ACSM classification of relative intensity (Garber 2011)	The percent-of-maximum bands only	Reserve bands, or a maximum lowered by medication

Calculators and simulators

A study tool, not a clinical one

This page exists for working out a training heart rate by the Karvonen method, and seeing why Tanaka’s 208 − 0.7 × age replaced 220 − age as the estimate of maximum heart rate. It is not clinical decision support and must not be used to treat anybody.

Some medicines change the heart rate response. Beta blockers, and rate-slowing calcium channel blockers such as verapamil and diltiazem, lower the resting rate, the maximum and the rise with exercise, so a zone from an age-predicted maximum can sit above anything the heart reaches on them.
With a heart condition, ask a clinician before a hard training plan. A pacemaker, an irregular rhythm such as atrial fibrillation or a transplanted heart each make heart rate an unreliable guide, and a maximum measured on an exercise test replaces the age-predicted one.

Three more cautions

Each formula has a population. The table of where each one holds gives the people each was fitted in, and each is least reliable outside them.
Know which equation your course or laboratory uses. The ones compared here give different numbers for the same patient, which is what the tables show.
Every cell is worked by the calculators’ own code. If a figure does not match what you were taught, check it against the formulas above, and tell us if we have it wrong. How the tools are checked is set out in the editorial policy.

Sources

Tanaka H, Monahan KD, Seals DR. Age-predicted maximal heart rate revisited. Journal of the American College of Cardiology 2001;37(1):153 to 156. doi:10.1016/S0735-1097(00)01054-8
Gellish RL, Goslin BR, Olson RE, McDonald A, Russi GD, Moudgil VK. Longitudinal modeling of the relationship between age and maximal heart rate. Medicine and Science in Sports and Exercise 2007;39(5):822 to 829. doi:10.1097/mss.0b013e31803349c6
Fox SM 3rd, Naughton JP, Haskell WL. Physical activity and the prevention of coronary heart disease. Annals of Clinical Research 1971;3(6):404 to 432. https://pubmed.ncbi.nlm.nih.gov/4945367/
Robergs RA, Landwehr R. The surprising history of the “HRmax=220-age” equation. Journal of Exercise Physiology Online 2002;5(2):1 to 10. https://www.asep.org/asep/asep/Robergs2.pdf
Karvonen MJ, Kentala E, Mustala O. The effects of training on heart rate; a longitudinal study. Annales Medicinae Experimentalis et Biologiae Fenniae 1957;35(3):307 to 315. https://pubmed.ncbi.nlm.nih.gov/13470504/
Garber CE, Blissmer B, Deschenes MR, et al. American College of Sports Medicine position stand: quantity and quality of exercise for developing and maintaining cardiorespiratory, musculoskeletal, and neuromotor fitness in apparently healthy adults: guidance for prescribing exercise. Medicine and Science in Sports and Exercise 2011;43(7):1334 to 1359. The band edges are the ones the site’s target heart rate calculator uses, which it takes from Table 6.1 of ACSM’s Guidelines for Exercise Testing and Prescription, 10th edition (2018). doi:10.1249/MSS.0b013e318213fefb