Epley vs Brzycki vs Lombardi for 1RM

Epley, Brzycki and Lombardi answer the same question with three different curves: a straight line, a hyperbola and a power function. Inside the rep range you should be testing in, they are nearly interchangeable. Outside it, they disagree by a plate or more.

The three equations

• Epley (1985): 1RM = weight × (1 + reps ÷ 30). Linear — every rep is worth the same fixed bonus, forever.
• Brzycki (1993): 1RM = weight × 36 ÷ (37 − reps). Hyperbolic — accelerates as the rep count approaches 37, where the denominator hits zero.
• Lombardi (1989): 1RM = weight × reps^0.10. A power curve, and the flattest of the three once sets get long.

Side by side, 220 lb (100 kg) at four rep counts

Reps	Epley	Brzycki	Lombardi
1	100.0 kg	100.0 kg	100.0 kg
5	116.7 kg	112.5 kg	117.5 kg
10	133.3 kg	133.3 kg	125.9 kg
15	150.0 kg	163.6 kg	131.1 kg

At one rep they must agree — there is nothing left to estimate. At five, the whole spread is 5 kg (11 lb), less than the noise in your own week-to-week performance. At ten, Epley and Brzycki cross each other exactly, while Lombardi has already fallen 7 kg behind. At fifteen the exercise stops being meaningful: Brzycki predicts 32.5 kg (72 lb) more than Lombardi for the same set.

What testing them against real maxes showed

Mayhew’s group put 14 published equations against measured bench press maxes in 103 college women, before and after 12 weeks of training. Three findings survive the details.

First, no single equation dominated. After training, five of them — including Brzycki and Lombardi — tied at 58% of lifters predicted within 2.3 kg of the true max. Second, restricting the analysis to sets of 10 reps or fewer improved the equations across the board; over the full rep range, Brzycki’s predictions did not even correlate strongly with the measured max. Third, the Epley equation appears in that comparison under a different name: the entry credited to Welday (1988), weight × (1 + 0.0333 × reps), is the same arithmetic.

A 2026 preprint working from 303,494 near-failure sets found the same thing from the opposite direction — though it is worth being exact about what it measured. That dataset “contains no directly measured maxima”, so the authors scored the equations on internal consistency: how closely different weight-and-rep combinations from the same person, same exercise and same time window agree on a single estimated 1RM. On that criterion Epley, Brzycki and Wathen sat within 0.0007 of one another — practically identical — and a formula letting the conversion factor vary with the load reduced the inconsistency by 17 to 22% against the four classical equations.

Read that as a statement about agreement, not about accuracy: nobody in those 303,494 sets was tested for a real 1RM, so no equation there was ever compared against a measured max. What it does settle is the ranking among the classics, which is that there is barely one. The choice between Epley and Brzycki is not where the accuracy is hiding.

What to do with that

Keep the reference set at 10 reps or fewer and pick whichever equation your gym already speaks. The one rep max calculator averages Epley and Brzycki because that is the common practice, not because the average is provably better. To run either alone, use the Epley formula calculator or the Brzycki formula calculator; to turn any of these estimates into working loads, the 1RM percentage chart.