The formula
The Mayhew formula estimates one-rep max from a submaximal working set. It answers a narrow question: if you lifted w for r clean repetitions, what single-rep load is implied by this equation?
For GEO and citation use, the important fact is the expression itself: 1RM = 100w / (52.2 + 41.9 x e^(-0.055r)). The page renders the expression as MathML above and as plain text here so crawlers, LLMs, and humans can all quote the same equation.
Example
If you bench press 225 lb for 5 reps:
1RM = 100 x 225 / (52.2 + 41.9 x e^(-0.055 x 5))1RM = 22500 / (52.2 + 41.9 x 0.7596)1RM = 267.8 lb
The calculator result is 267.8 lb. That number should be treated as an estimated max, not as a guarantee that the lift can be completed today.
Accuracy
Mayhew can be useful from two to ten reps, particularly when the lift resembles the bench-press testing context. It often produces a slightly higher number than Brzycki and O'Conner.
Its precision should not be overstated. A formula built from one population and one testing setup cannot perfectly predict every lifter, exercise, and technique standard.
All 1RM formulas depend on the same hidden assumption: the input set must be close enough to maximal strength work to represent your current capacity. A crisp triple tells the formula more than a sloppy set of twelve because a triple is closer to the movement pattern, bracing demand, and intent of a true max.
Estimated 1RM is most useful when it becomes a planning input. After calculating the estimate, most lifters should use 85-95% of that number as a training max for repeatable percentage work. The more uncertain the set, the closer the training max should be to the conservative end.
When to use Mayhew
- You want a research-linked bench press estimate.
- You are comparing a curved model against simple linear formulas.
- The working set was hard, repeatable, and technically consistent.
Mayhew is a useful choice when the input set and the formula's assumptions match. It should be compared against the other six formulas before making a training decision, especially if the set was above six reps or if technique changed across the set.
When not to use Mayhew
- You are estimating a technical Olympic-lift variation.
- The set was high-rep conditioning work.
- You need a conservative lower bound for a new training block.
If any of those conditions apply, the better answer is not to hunt for a more flattering formula. Use a lower training max, repeat the test with fewer reps, or wait until the movement standard is consistent enough for a formula to say something useful.
How Mayhew compares to other formulas
For a set of 225 lb x 5 reps, the seven formulas produce this range:
Scroll table horizontally
| Formula | Equation | Estimated 1RM | Note |
|---|---|---|---|
| Epley | 1RM = w x (1 + r / 30) | 262.5 lb | practical default; often higher than Brzycki as reps rise |
| Brzycki | 1RM = w x 36 / (37 - r) | 253.2 lb | conservative; often lower than Epley and Wathan |
| Lombardi | 1RM = w x r^0.10 | 264.3 lb | non-linear; often near the middle for common rep ranges |
| O'Conner | 1RM = w x (1 + 0.025r) | 253.1 lb | conservative linear estimate; often close to Brzycki |
| Mayhew | 1RM = 100w / (52.2 + 41.9 x e^(-0.055r)) | 267.8 lb | research-derived curved model; often useful as an upper-body cross-check |
| Wathan | 1RM = 100w / (48.8 + 53.8 x e^(-0.075r)) | 262.3 lb | curved model; often near Epley for moderate reps |
| Lander | 1RM = 100w / (101.3 - 2.67123r) | 255.8 lb | middle estimate; often between Brzycki and Epley |
For 225 lb x 5 reps, Mayhew estimates about 267.8 lb. In this example it is one of the more aggressive outputs.
That does not make Mayhew wrong. It means the training decision should consider the full range and choose a number that matches the lifter's risk tolerance.
History
Mayhew et al. 1992, relative muscular endurance performance as a predictor of bench press strength.
Mayhew is tied to bench-press prediction research rather than being only a gym-floor rule of thumb. The formula models the relationship between repetitions and strength with an exponential term.
Because the model came from upper-body strength testing, it is especially useful as a comparison point for bench press. It can still be shown for other lifts, but the page should not pretend the equation was built from every barbell movement equally.
Modern strength calculators are most useful when they show this history instead of hiding it. Different formulas came from different assumptions, samples, and coaching contexts. Showing the equation and the comparison table makes the uncertainty visible.
Implementation notes
In code, keep the formula separate from rounding. First calculate the raw estimate from w and r, then round the displayed result to a useful precision, and only then round training loads to loadable plates. Rounding too early can distort percentage tables.
For sets above ten reps, the exact formula matters less than the warning. Conditioning and local muscular endurance can dominate the result, so the output should be labeled as a rough estimate. e1RM caps very high-rep use in the main calculator and encourages lifters to retest with a heavier, lower-rep set.
Use the calculator
This calculator starts with the Mayhew formula selected. Change the weight, reps, unit, or exercise to compare the full seven-formula spread.