One-rep max (Brzycki)

The formula

• 1RM = 36 · w / (37 − r)

w is the weight lifted, r the repetitions completed and 1RM the estimated maximum in the same unit as the weight. The denominator shrinks by one for every repetition, so each extra rep raises the estimate a little more than the one before; the source, Brzycki (1993), is cited under the formula.

Holds when the set is short, up to about ten repetitions, and taken near failure. Brzycki fitted the line to sets in that range, and the formula is undefined at 37 repetitions and nonsense long before.

A worked example

80 kg for 5 repetitions: 1RM = 36 · 80 / (37 − 5) = 2,880 / 32 = 90 kg. The same weight for 10 repetitions: 2,880 / 27 = 106.7 kg.

Brzycki and Epley

Epley’s formula, w · (1 + r / 30), gives 93.3 kg for the same 80 × 5. The two meet at exactly 10 repetitions, where both give the weight times 4/3, and differ on either side: Brzycki reads lower below ten and higher above. The one-rep max calculator shows both and a percentage table from their mean.

Working backwards

For a set of r at a known max, the load is 1RM · (37 − r) / 36. A lifter with a 1RM of 100 who wants a set of 8 loads 100 · 29 / 36 = 81 kg; the card above gives the weight or the repetitions from the other two.

Common mistakes

• Reading the 36 and 37 as repetitions to aim for. They are the constants of a straight line fitted to short sets.
• Using a long set. Past ten repetitions the estimate climbs faster than any lifter.
• Treating the estimate as a test result. It is a planning figure, and a real maximal attempt is a different thing with its own precautions.

Frequently asked questions