The seven equations
Each takes the weight lifted (w) and the reps completed (r) and returns an estimated one-rep max. All were fitted by regression on lifters performing submaximal sets, mostly between the 1970s and the 1990s.
| Formula | Equation | 225 lb × 5 | 225 lb × 10 |
|---|---|---|---|
| Brzycki (1993) | w × 36 ÷ (37 − r) | 253 lb | 300 lb |
| O'Conner (1989) | w × (1 + r ÷ 40) | 253 lb | 281 lb |
| Lander (1985) | 100w ÷ (101.3 − 2.67123r) | 256 lb | 302 lb |
| Wathan (1994) | 100w ÷ (48.8 + 53.8e−0.075r) | 262 lb | 307 lb |
| Epley (1985) | w × (1 + r ÷ 30) | 263 lb | 300 lb |
| Lombardi (1989) | w × r0.10 | 264 lb | 283 lb |
| Mayhew (1992) | 100w ÷ (52.2 + 41.9e−0.055r) | 268 lb | 309 lb |
At five reps the seven span 253 to 268 lb — a 15 lb spread, about 6%. At ten reps the same set spans 281 to 309 lb, a 28 lb spread, about 9%. The estimates do not merely get less accurate as reps rise; they stop agreeing with each other about what they are estimating.
Where they diverge, and why
Brzycki is linear and the most conservative at low reps. Its denominator, 37 − r, is also its limit: at 37 reps it divides by zero, and long before that it is producing nonsense. Epley is linear the other way and runs progressively higher as reps climb. The two cross at around ten reps, which is why coaches who have used both say they are “about the same” and mean it only for their own rep range.
Wathan and Mayhew are exponential fits and were derived largely on bench press data. They tend to sit in the middle of the pack and hold up better at higher reps than the linear pair. Lombardi is a power curve and flattens most aggressively — it is the lowest of the seven at ten reps and one of the highest at two.
The deeper reason they disagree: the relationship between reps and percentage of max is not the same for everyone. At three reps nearly everyone sits somewhere near 93% of their max. At twelve, the real figure might be 65% or 75% depending on muscle-fibre make-up, conditioning and how honest a definition of failure you are using. The formulas are fitting an average that fewer and fewer people match.
Percentage-of-max table
The inverse view — what percentage of your one-rep max you should be able to lift for a given number of reps. This is the median of the seven formulas, and it is the table to use for programming.
| Reps | % of 1RM | From a 300 lb max |
|---|---|---|
| 1 | 100% | 300 lb |
| 2 | 96% | 288 lb |
| 3 | 93% | 279 lb |
| 4 | 90% | 270 lb |
| 5 | 86% | 258 lb |
| 6 | 84% | 252 lb |
| 7 | 82% | 246 lb |
| 8 | 79% | 237 lb |
| 9 | 77% | 231 lb |
| 10 | 75% | 225 lb |
Round to what you can actually load. The precision these equations imply does not survive contact with a plate rack, and a 2.5 lb difference in a working set is not the variable that decides whether the programme works.
Which one to use
Ours reports the median of all seven, because no published comparison has established a clear winner across lifts, populations and rep ranges, and a median is robust to any single equation being a poor fit for you. If you want to pick one anyway:
- Two to five reps: it barely matters. All seven agree within a few percent. Use whichever your coach uses.
- Six to ten reps: Wathan or Mayhew, especially for bench press, which is the data they were fitted on.
- Above ten reps: none of them. Do a heavier set instead — a set of five tells you far more about your max than a set of fifteen ever will.
One more thing that matters more than the choice of equation: the set has to have been genuinely close to failure with technique you would be happy to show a coach. Five reps that moved fast and five that were a grind produce the same input and very different truths.