Why an exponential curve?

Muscular endurance falls off in a curve, not a line: going from 12 to 15 reps at a weight costs far less than going from 3 to 6. An exponential term models that flattening, so Wathan does not keep inflating the max as reps rise the way Epley and O'Conner do.

Is Wathan accurate at 1 to 5 reps?

Yes — it is within a percent or two of Epley and Brzycki there. You do not lose low-rep accuracy by choosing it, which is why some coaches use Wathan as their single default.

Where does the formula come from?

Wathan (1994) fitted it to lifting data spanning a broad rep range, aiming for one equation that worked from heavy singles to sets of 15 or more, rather than a low-rep-only tool like Brzycki.

It generalises well across the squat, bench and deadlift. For bench press specifically, Mayhew was derived from bench data and is a close alternative.

Can I trust a 1RM from a 20-rep set?

Treat it as a ballpark. Even the best formula is rough past 15 reps because you are measuring conditioning as much as strength. Use it to pick a starting weight, then re-estimate from a heavier set of 5 to 8 reps within a few weeks.

Wathan 1RM Calculator — One Rep Max (Exponential Fit)

Training loads from your estimated 1RM
% of 1RM	Load	Typical reps
100%	—	1
95%	—	2
90%	—	3–4
85%	—	5–6
80%	—	7–8
75%	—	9–10
70%	—	11–12

The Wathan formula

1RM = 100w ÷ (48.8 + 53.8 · e^(−0.075 · reps)), where w is the weight lifted and reps the number completed. Best suited to wide range, good at 10+ reps.

Worked example

Squat 100 kg for 10 reps. Wathan: (100 × 100) ÷ (48.8 + 53.8 × e^(−0.75)) = 10000 ÷ 74.21 = 134.7 kg. For 100 kg × 5: 10000 ÷ (48.8 + 53.8 × e^(−0.375)) = 10000 ÷ 85.75 ≈ 116.6 kg.

How it compares

At low reps Wathan tracks Epley closely (about 117 vs 117 at 5 reps). Its edge shows at 12 to 20 reps, where the linear formulas over-predict: at 15 reps Wathan gives roughly 150 kg from a 100 kg set where Epley gives 150 and O'Conner only 138. If your only data is a high-rep set, Wathan or Mayhew is the pick.

Which formula for which rep range

Formula	Best for
Brzycki	≤ 10 reps
Lombardi	any rep count, conservative
O'Conner	low reps; understates at high reps
Wathan	wide range, good at 10+ reps
Lander	≤ 10 reps
Mayhew	bench press, 10+ reps
Epley	1–10 reps

Rule of thumb: Brzycki, Lander and O'Conner for sets of 10 reps or fewer; Wathan and Mayhew when the set ran longer; Lombardi as a conservative all-rounder. The safest input is a hard set of 3 to 6 reps, where every formula nearly agrees.

The other 1RM formulas

Epley formula — the default, and the parent calculator.
Brzycki — 1RM = weight × 36 ÷ (37 − reps). The other standard; the most accurate of the set at low reps.
Lombardi — 1RM = weight × reps^0.10. A power curve rather than a straight line — stays sane at high reps.
O'Conner — 1RM = weight × (1 + 0.025 × reps). The gentlest estimate — 2.5% added per rep.
Lander — 1RM = 100w ÷ (101.3 − 2.67123 × reps). Close to Brzycki in shape; undefined near 38 reps.
Mayhew — 1RM = 100w ÷ (52.2 + 41.9 × e^(−0.055 × reps)). Derived from bench-press data; a solid pick for higher reps.

Using the number

Once you have a 1RM, programmes prescribe work as a percentage of it — use the table above the fold to plan a session. Feed your bodyweight and goal into the calorie calculator and macro calculator to support the training, and see progressive overload for adding weight over time.

Source: Wathan, 1994; see Wikipedia, "One-repetition maximum".

Last reviewed: September 2026. Figures and formulas are checked against their published sources; see the site's data notes.

Wathan One Rep Max Calculator

The Wathan formula

Worked example

How it compares

Which formula for which rep range

The other 1RM formulas

Using the number

Related calculators

Related guides

Frequently asked questions