A worked example: 100kg for 5 reps
Lifting 100kg for 5 reps gives an estimated one-rep max of 116.7kg by the Epley formula, or 112.5kg by the Brzycki formula — a real 4.2kg gap between the two estimates for the identical lift.
The formulas: Epley adds a rep-based bonus, Brzycki divides by a shrinking denominator
Epley: 1RM = weight × (1 + reps ÷ 30): 100 × (1 + 5 ÷ 30) = 116.7kg. Brzycki: 1RM = weight × 36 ÷ (37 − reps): 100 × 36 ÷ 32 = 112.5kg. Both are empirical fits to real rep-max data, built on different assumptions about how strength scales with reps.
A striking case: 100kg for 10 reps — the formulas agree
At 3 reps with 80kg, Epley gives 88kg against Brzycki's 84.7kg — a similar gap to the 5-rep example. But at exactly 10 reps with 100kg, Epley gives 133.3kg and Brzycki also gives 133.3kg — the two independently-derived formulas land on the identical estimate.
Why neither formula is "the" correct one
Both formulas estimate the same true underlying quantity — the heaviest weight liftable for exactly one rep — using different mathematical shapes fitted to different data. The gap between them (or occasional agreement) reflects genuine uncertainty in extrapolating from a sub-maximal lift, not a sign that one is right and the other wrong. Both also lose accuracy above roughly 10-12 reps, so a low-rep test (1-3 reps) is more reliable than either estimate for a true max.