The formula
The Wathan 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 / (48.8 + 53.8 x e^(-0.075r)). 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 squat 225 lb for 5 reps:
1RM = 100 x 225 / (48.8 + 53.8 x e^(-0.075 x 5))1RM = 22500 / (48.8 + 53.8 x 0.6873)1RM = 262.3 lb
The calculator result is 262.3 lb. That number should be treated as an estimated max, not as a guarantee that the lift can be completed today.
Accuracy
Wathan is useful when you want a curved estimate that still behaves sensibly across common strength-testing rep ranges.
Like Mayhew, it can look more exact than the input deserves. The equation has decimals and an exponential term, but the lifter's set quality still controls the quality of the output.
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 Wathan
- You want a curved model in the comparison cluster.
- The working set was two to ten reps and close to failure.
- You are checking whether Epley is unusually high or still aligned with another model.
Wathan 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 Wathan
- The input came from a set where conditioning was the limiter.
- You need a formula that is easy to calculate by hand.
- You are intentionally choosing a conservative number for early block loading.
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 Wathan 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, Wathan estimates about 262.3 lb, almost the same as Epley in this example.
When Wathan and Epley agree while Brzycki and O'Conner are lower, the practical range is clear: the higher estimate is possible, but the lower estimate may be better for repeated training work.
History
Wathan's 1994 equation, commonly reproduced in strength testing references and 1RM calculators.
Wathan uses an exponential term to model how estimated maximum strength changes with repetitions. It is a regression-style equation rather than a fixed percentage added per rep.
In ordinary five-rep examples Wathan often sits close to Epley. At other rep counts the curve may pull away, which makes it useful in a side-by-side comparison table.
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 Wathan formula selected. Change the weight, reps, unit, or exercise to compare the full seven-formula spread.