What the formulas do
A one-rep max (1RM) is the heaviest weight you can lift once. Testing it directly is tiring and, for beginners, risky, so most people estimate it from a set taken close to failure: the weight lifted and the number of reps. Every estimation formula is a curve that says how much heavier a single rep can be than a set of r reps. The curves were fitted to real lifters, but to few of them: a 2026 review of the literature notes that the classical equations came from small samples, typically young trained men on the bench press, or from practitioner manuals and textbook chapters rather than large studies. That origin explains most of what follows.
The seven classical formulas
w is the weight lifted, r the reps completed to failure. Three use a straight line, four a curve; the Brzycki formula is also written as w ÷ (1.0278 − 0.0278 r).
| Formula | Year | Estimated 1RM |
|---|---|---|
| Epley | 1985 | w × (1 + r ÷ 30) |
| Brzycki | 1993 | w × 36 ÷ (37 − r) |
| Lander | 1985 | w ÷ (1.013 − 0.0267123 r) |
| Lombardi | 1989 | w × r^0.10 |
| O'Conner | 1989 | w × (1 + 0.025 r) |
| Mayhew | 1992 | w ÷ (0.522 + 0.419 e^(−0.055 r)) |
| Wathen | 1994 | w ÷ (0.488 + 0.538 e^(−0.075 r)) |
The same set through every formula
The table takes 100 kg lifted for the number of reps in the first column and shows what each formula makes of it. The last column is the spread between the lowest and the highest estimate.
| Reps at 100 kg | Epley | Brzycki | Lander | Lombardi | O'Conner | Mayhew | Wathen | Spread |
|---|---|---|---|---|---|---|---|---|
| 2 | 106.7 | 102.9 | 104.2 | 107.2 | 105.0 | 111.4 | 105.1 | 8.6 kg |
| 3 | 110.0 | 105.9 | 107.2 | 111.6 | 107.5 | 114.0 | 109.0 | 8.1 kg |
| 5 | 116.7 | 112.5 | 113.7 | 117.5 | 112.5 | 119.0 | 116.6 | 6.5 kg |
| 6 | 120.0 | 116.1 | 117.3 | 119.6 | 115.0 | 121.5 | 120.3 | 6.5 kg |
| 8 | 126.7 | 124.1 | 125.1 | 123.1 | 120.0 | 126.3 | 127.7 | 7.7 kg |
| 10 | 133.3 | 133.3 | 134.1 | 125.9 | 125.0 | 130.9 | 134.7 | 9.7 kg |
| 12 | 140.0 | 144.0 | 144.4 | 128.2 | 130.0 | 135.4 | 141.5 | 16.2 kg |
| 15 | 150.0 | 163.6 | 163.3 | 131.1 | 137.5 | 141.7 | 150.9 | 32.5 kg |
| 20 | 166.7 | 211.8 | 208.9 | 134.9 | 150.0 | 151.2 | 164.5 | 76.8 kg |
Three things stand out. Up to about five reps the formulas agree within a couple of kilograms on a 100 kg set, so the choice of formula barely matters. Epley and Brzycki give the same answer at exactly 10 reps (133.3 kg here) and sit on opposite sides of each other elsewhere: Brzycki is lower below 10 reps and climbs steeply above, because its denominator heads towards zero at 37 reps. Past 10 reps the spread widens to 76.8 kg at 20 reps, which is why no sensible calculator should accept a 20-rep set as a 1RM test. The one rep max calculator shows Epley, Brzycki and Lombardi next to each other so the spread is visible rather than hidden behind one number.
Which rep count to test with
The studies agree that the formula matters less than the set you feed it. Reynolds, Gordon and Robergs (2006) had 70 people aged 18 to 69 perform 1, 5, 10 and 20 rep maximums on the bench press and leg press. The 5RM predicted the 1RM best, with an R² of 0.993 for the bench press and 0.974 for the leg press, accuracy fell as the reps went up, and the authors advise using no more than 10 repetitions in a linear equation. Adding body measurements, age or sex did not improve the prediction beyond the lifted load itself. Mayhew and colleagues (2008), summarised in the same review, likewise found the equations more accurate when fewer than 10 reps were used.
So the test set is a heavy one: a weight you can lift three to six times with good form, stopping at the last clean rep. A set of 15 tells you about endurance, not about your max, and the formulas know it, which is why they disagree there.
The lift changes the answer
LeSuer and colleagues (1997) tested seven equations on 67 untrained college students across the bench press, squat and deadlift. Correlations between predicted and actual 1RM were uniformly high, above 0.95, yet absolute accuracy differed by exercise, and every equation underestimated the deadlift. The review of the literature draws the general lesson: lower-body compound lifts, the deadlift most of all, are predicted less well than the bench press the formulas were built on.
The reason is that the number of reps a person manages at a given percentage of their max is not a constant. It depends on the exercise and on the lifter. Richens and Cleather (2014) had eight competitive weightlifters and eight endurance runners do leg-press reps at 70, 80 and 90 percent of their 1RM: the runners managed 39.9 reps at 70 percent against 17.9 for the weightlifters, and 19.8 against 11.8 at 80 percent, with the gap narrowing at 90 percent. The same 70 percent set means a different thing for each group, and one formula cannot serve both. Wikipedia's summary of the field puts the practical margin at 10 percent or more between an estimate and a tested max in some cases.
Reps to percent of 1RM, by formula
Turn the formulas around and they become the loading tables in training programs: the percentage of your max that a given rep count corresponds to. Epley and Brzycki, the two most common, give these:
| Reps | Epley: % of 1RM | Brzycki: % of 1RM |
|---|---|---|
| 1 | 96.8% | 100.0% |
| 2 | 93.8% | 97.2% |
| 3 | 90.9% | 94.4% |
| 4 | 88.2% | 91.7% |
| 5 | 85.7% | 88.9% |
| 6 | 83.3% | 86.1% |
| 8 | 78.9% | 80.6% |
| 10 | 75.0% | 75.0% |
| 12 | 71.4% | 69.4% |
| 15 | 66.7% | 61.1% |
Note that Epley gives 100 percent only at zero reps, so its single-rep figure is 96.8 percent, a reminder that it is a fitted curve, not a law. For programming, pick one table and stay with it, then adjust from how the sets feel rather than switching formulas when the number looks wrong. The plate calculator turns the resulting target into plates per side for the bar you have.
Which one to use
- Test with 3 to 6 reps. The formulas agree there and the studies say that is where they are accurate.
- Use Epley or Brzycki for everyday work. They are the most widely used, agree at 10 reps, and bracket the others in the middle range. Report which one you used.
- Expect the deadlift and squat to be underestimated and the bench press to be the best case, because that is what the formulas were fitted to.
- Do not estimate from a 15- or 20-rep set. The spread between formulas there is larger than the error you were trying to avoid by not testing.
- Re-test rather than re-calculate. A formula cannot know your training background; a heavier set a few weeks later can.
Frequently asked questions
Why do two calculators give different one-rep maxes for the same set?
Because they use different formulas. Seven classical equations are in common use, and for a set of 100 kg × 5 they agree within about two kilograms, but the same 100 kg × 15 gives anything from 131 to 150 kg depending on the formula. Any calculator is only as good as the formula and the rep count it was fed; the formula name is worth knowing.
Which formula is the most accurate?
None is best everywhere. Validation studies find high correlations for all of them with meaningful differences in absolute error by exercise; in LeSuer and colleagues' 1997 test on the bench press, squat and deadlift, every equation underestimated the deadlift. What matters more than the formula is the rep count: Reynolds and colleagues (2006) found the 5-rep max predicted the 1RM best and advise no more than 10 reps. Our calculator shows Epley, Brzycki and Lombardi side by side so you can see the spread.
How many reps should I use for the test set?
As few as you can do safely with good form, ideally 3 to 6 and no more than 10. Reynolds and colleagues found 5RM data gave the highest prediction accuracy (R² of 0.993 for the bench press), with accuracy falling at higher rep counts, and the formulas themselves diverge after about 10 reps.
Is the estimate the same for squat, bench and deadlift?
No. The classical equations were derived mostly from young trained men on the bench press, and the number of reps a lifter manages at a given percentage of 1RM differs by exercise and by training background. Treat the estimate as a bench-press-shaped guess and expect lower-body lifts, especially the deadlift, to be estimated less well.
Should I use the estimate to set training percentages?
Use it as a starting point and adjust from how the sets feel. Richens and Cleather (2014) found endurance runners managed 39.9 reps at 70 percent of their leg-press 1RM against 17.9 for weightlifters, so a percentage table that fits one lifter can be badly off for another. The plate calculator turns whatever target you settle on into plates per side.
Sources
- Wikipedia: One-repetition maximum (the Epley, Brzycki, Lander, Lombardi, O'Conner, Mayhew and Wathen formulas; Epley and Brzycki agree at 10 reps and diverge after; estimates may vary by 10 percent or more from a tested 1RM)
- Brzycki (1993): Strength testing, predicting a one-rep max from reps-to-fatigue. Journal of Physical Education, Recreation and Dance 64(1)
- Reynolds, Gordon and Robergs (2006): Prediction of one repetition maximum strength from multiple repetition maximum testing and anthropometry. Journal of Strength and Conditioning Research 20(3): the 5RM predicted best, R² 0.993 bench press and 0.974 leg press; no more than 10 repetitions for linear equations
- Richens and Cleather (2014): The relationship between the number of repetitions performed at given intensities is different in endurance and strength trained athletes. Biology of Sport 31(2): 39.9 vs 17.9 reps at 70 percent of 1RM
- LeSuer, McCormick, Mayhew, Wasserstein and Arnold (1997): The accuracy of prediction equations for estimating 1-RM performance in the bench press, squat, and deadlift. Journal of Strength and Conditioning Research 11(4)
- Marzagao (2026, preprint): A weight-dependent 1RM prediction equation optimized on 303,494 near-failure sets across 388 exercises (summarises the validation literature: classical equations derived from small bench-press samples, all equations underestimated the deadlift in LeSuer et al., accuracy falls above about 10 reps)