1RM Formulas Compared

Six equations dominate one-rep-max estimation, and they disagree by design. Understanding how each is built explains why your estimate shifts depending on which one you trust — and why averaging them, as many calculators do, is usually the sanest choice.

Epley

The Epley equation, 1RM = weight × (1 + reps ÷ 30), is the most widely quoted. Its charm is linearity: every extra rep adds a fixed slice of estimated max. That simplicity makes it easy to reason about, but it also means Epley keeps climbing steadily even into high-rep territory where real strength gains flatten. As a result Epley tends to read a touch high once you pass roughly eight reps. At low reps it is essentially interchangeable with Brzycki.

Brzycki

Brzycki, 1RM = weight × 36 ÷ (37 − reps), is Epley's most common rival. Instead of a straight line it uses a hyperbola, so the estimate curves rather than marching upward forever. In the practical one-to-ten range Brzycki sits slightly below Epley, and many lifters find it matches their gym experience for triples and fives. Its weakness is the denominator: as reps approach thirty-seven the equation blows up, so it is meaningless for very high-rep sets and should never be fed a set near failure at twenty-plus reps.

Wathan

Wathan takes a different shape entirely, using an exponential decay: 1RM = 100 × weight ÷ (48.8 + 53.8 × e^(−0.075 × reps)). It was fitted to a broad data set and is often praised for staying sensible across a wide rep range rather than exploding or drifting. Because it was regressed against many subjects, it behaves like a smoothed consensus and frequently lands near the middle of the pack, which is exactly why it is a good anchor when the linear and hyperbolic formulas pull apart.

Lander

Lander, 1RM = 100 × weight ÷ (101.3 − 2.67123 × reps), is another regression-based equation and reads very close to Brzycki through the low and middle rep ranges. Like Brzycki it has a denominator that eventually breaks down, so it is reliable for the everyday one-to-ten window but not for endurance sets. Its near-agreement with Brzycki is useful: when two independently derived formulas converge, you can be more confident in that region of the estimate.

Lombardi

Lombardi is the outlier in form, using a power curve: 1RM = weight × reps^0.10. Because the exponent is small, the multiplier grows slowly, so Lombardi is conservative at low reps and only gradually catches up. Some lifters find it under-reads their true single from a heavy triple. It rarely produces the extreme values that the denominator-based formulas can, which makes it a stabilising voice in an average even if it is seldom anyone's single favourite.

O'Conner

O'Conner, 1RM = weight × (1 + reps ÷ 40), is essentially a gentler cousin of Epley. Swapping the 30 in Epley's denominator for 40 flattens the slope, so O'Conner consistently returns the lowest estimates of the linear family. If Epley marks the optimistic edge of a plausible range, O'Conner often marks the cautious edge, and the gap between them is a quick visual gauge of how much rep count is influencing your number.

Why they diverge — and what to do about it

The spread between formulas is not noise; it reflects the fact that each was fitted to different people performing different lifts. A trainee with high muscular endurance genuinely out-reps their true max, so endurance-biased lifters see inflated estimates from the steeper equations. The practical response is not to hunt for the "one true formula" but to read the disagreement as an uncertainty band. When all six cluster tightly — which happens at low reps — you can trust the number. When they fan out, which happens as reps climb, that fanning is a signal to lower the reps on your test set rather than to pick whichever formula flatters you.

The case for averaging

Because no equation is universally best and each carries a known directional bias, averaging several tends to cancel individual quirks and land near the truth for a typical lifter. That is why a good calculator reports every estimate and then the mean, rather than hiding behind one equation. You keep the transparency of seeing the range while getting a single, defensible number to program against. If you want to bias your own estimate conservative, lean on O'Conner and Lombardi; if you suspect you under-test true singles, Epley and Wathan will read higher.

To see all six side by side for your own lift, run your working set through the one-rep max calculator, and read the practical guide for how to turn the resulting number into training loads.