The Estimation Formulas
A one rep max is the heaviest weight you can lift once with good form. Testing it directly is fatiguing and carries real injury risk, so most lifters estimate it from a submaximal set instead. Every formula does the same thing: it extrapolates backwards from reps to a single-rep load.
Formulas
Brzycki: 1RM = w × 36 / (37 − r)
Lombardi: 1RM = w × r^0.10
At ten reps Epley returns a slightly higher number than Brzycki, and the gap widens beyond that — which is exactly where an individual's rep endurance starts to dominate the result. Averaging the three reduces the influence of any one model's bias, but no formula can account for how your particular body handles higher rep ranges.
Getting a Useful Estimate
The number is only as good as the set you feed it. These conditions matter more than the choice of formula.
The set must be close to failure
If you stopped with three reps left in the tank, the estimate will be low by roughly the weight of those reps. Every formula assumes the set ended because you could not do another one with good form.
Rep endurance varies by lift and by person
Squats and deadlifts typically allow more reps at a given percentage than bench press. Lifters with more slow-twitch fibre also grind out more reps at 80% than the formulas assume, which makes their estimated max read high.
Fatigue skews the result
A set taken as the fifth exercise of a session gives a lower estimate than the same set taken fresh. Use an early working set, not a burnout set at the end.
Using Percentages in a Programme
Percentage-based programming exists because the right training load scales with your current strength rather than with a fixed number. The table above converts your estimate into the loads most programmes call for, but the percentages are guidelines rather than physical constants.
Many lifters now prefer autoregulation — using reps in reserve or rate of perceived exertion to pick the day's load — precisely because a percentage taken from a max tested weeks ago does not reflect sleep, stress, or accumulated fatigue. A reasonable compromise is to set the session's load from percentages and then adjust up or down based on how the first working set moves.