A one-rep max, or 1RM, is the heaviest load a person can lift once. Published equations estimate it from a lighter load lifted for several reps to failure, the point where one more rep cannot be completed. We ran seven of them on the same set. Up to ten reps their estimates stay within a tenth of the weight lifted. By fifteen reps they spread to about a third of it, on our calculations. Wikipedia's article on the one-repetition maximum charts ten or more of these equations and notes that they "greatly diverge after about 10 reps". One study of 103 college women's bench press found the equations more accurate when sets stayed under ten reps (Mayhew and colleagues, 2008).
Estimates sit closest together around six reps
Each equation gives the maximum as a multiple of the load, so any unit works. We ran all seven for 1 to 20 reps on a load of 100, with Brzycki in the 36/(37 − r) form Wikipedia uses. The gap between highest and lowest estimate, as a share of the weight lifted, is narrowest around six reps, at 6.5%.
| Equation | Ratio of 1RM to load, r reps | 6 reps | 10 reps | 15 reps |
|---|---|---|---|---|
| Epley | 1 + r/30 | 120.0 | 133.3 | 150.0 |
| Brzycki | 36/(37 − r) | 116.1 | 133.3 | 163.6 |
| Lander | 100/(101.3 − 2.67123r) | 117.3 | 134.1 | 163.3 |
| Lombardi | r^0.10 | 119.6 | 125.9 | 131.1 |
| Mayhew | 1/(0.522 + 0.419e^(−0.055r)) | 121.5 | 130.9 | 141.7 |
| O'Conner | 1 + 0.025r | 115.0 | 125.0 | 137.5 |
| Wathen | 1/(0.488 + 0.538e^(−0.075r)) | 120.3 | 134.7 | 150.9 |
Estimates per 100 lifted, our calculation. At ten reps the spread is 9.7%. At a single rep the band widens again. The Mayhew equation, credited to a 1992 paper, puts the maximum 8.9% above the load, while the other six lie in a band 3.3% wide. Brzycki and Lander stay within 1.39 points of each other up to 12 reps, and Epley and Wathen within 2.20 up to 20. Wikipedia notes that Epley and Brzycki agree exactly at ten reps, true of this form.
These seven are a selection, and the 2008 study by Mayhew and colleagues compared 14. The McGlothin equation on some lists, 100w/(101.3 − 2.67123r), is Lander's term for term.
Reciprocal formulas climb towards infinity as reps approach 37
Brzycki and Lander divide the load by a number that shrinks as reps rise, reaching zero at 37 reps for Brzycki and near 37.9 for Lander. At that point, called a pole, the estimate becomes infinite. The climb starts long before: by 20 reps Brzycki gives 211.8 per 100 lifted, and from 11 reps one of the pair gives the highest estimate of the seven. Mayhew and colleagues print Brzycki as 1/(1.0278 − 0.0278r), which moves the 15-rep spread from 32.5% to 32.6%.
Lombardi's power law gives the lowest estimates at high reps
Lombardi multiplies the load by the reps to the power 0.10, a curve rising ever more slowly. It is the lowest of the seven from 11 reps on, and by 20 reps the gap between it and Brzycki is 76.8% of the weight lifted. The two exponentials level off instead, towards about 1.92 times the load for Mayhew and 2.05 for Wathen, on our arithmetic.
Poundage charts and textbook tables frame most of the equations
Mayhew and colleagues found that "most of the prediction equations gave no evidence of the population used to develop the equations or how they were derived statistically." Their reference list traces Lombardi and O'Conner to training books of 1989. The Wathen equation, they note, was "calculated from chart provided" in a 1994 textbook chapter: someone fitted it to Wathen's chart, and the paper does not say who.
Epley's equation has two attributions: Mayhew and colleagues list its form under Welday, Scholastic Coach, 1988. Lacio and colleagues (2010) credit Epley, and a 2026 preprint says it came "from a poundage chart". Brzycki's equation appeared in a physical education journal in 1993 and Lander's in the NSCA's journal in 1984, often cited as 1985. We did not open either, so cannot say what, if anything, they were fitted to.
Individual lifters miss by far more than the group averages do
Lacio and colleagues tested six equations on 31 recreational lifters, all men, from bench-press sets of 4 to 10 reps. The measured maximum averaged 76.23 kg and the equations' averages ran from 73.05 to 77.38 kg, with no significant difference between them. On our check, three of those averages, as ratios to Epley's, match the formulas at the sample's mean of 7.29 reps within a quarter of a percentage point.
In the 2008 study, on the 46 women whose sets ran to ten reps or fewer, every equation's average error fell between −3.7% and +1.6% of the tested maximum. With standard deviations of 9.1 to 10.6%, individual misses of around a tenth were ordinary. Over the full rep range before training, the paper reports Brzycki at +26.7 ± 101.7%. The pole cannot explain a figure that large. No set ran past 20 reps, where Brzycki gives about double the load. The paper offers no explanation. It concludes: "The accuracy of these predictions appears to be enhanced if fewer than 10 RTF are used," RTF meaning reps to fatigue.
Textbook percentage tables undercount reps at 70% of the maximum
Run backwards, an equation gives the reps a share of the maximum allows. Nuzzo and colleagues (2024) reprint a strength textbook table that allows 11 reps at 70% of 1RM, and Brzycki and Lander reproduce it closely at that row and the heavier ones. Nuzzo's pooled bench-press estimate runs about three reps higher: 14.1 reps at 70%, with a 95% confidence interval of 12.4 to 16.1. Of the seven, only Brzycki and Lander predict fewer reps than that range allows. Wathen lands right on its lower edge, and Epley, at 12.9 reps, falls inside it, as does Mayhew. O'Conner and Lombardi overshoot it, Lombardi by a wide margin.
Our one-rep max calculator averages five of them, without Mayhew and Wathen. Until 15 October 2026 its percentage table took weights from that average and reps from Brzycki alone, so a set of 100 for 5 reps produced a row reading "90% × 5 reps" at 103. It said each formula was fitted to particular lifters and lifts, and its title named only Epley and Brzycki. The revised table lists rep counts from 1 to 12, working out each weight from the same average run backwards. The entered set's row now shows the weight entered.
Leg press sets run to more reps than bench press at every load
Nuzzo's analysis pooled 952 reps-to-failure tests from 7,289 people in 269 studies into a meta-regression, a single line fitted through many studies' results. At 70% of 1RM it puts the leg press at 19.0 reps. The authors write that "more repetitions were evident in the leg press than bench press across the loading spectrum." The equations above take only load and reps, with no term for the exercise, and both validation studies here used the bench press alone.
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