The formula
The Epley 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 = w x (1 + r / 30). 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 = 225 x (1 + 5 / 30)1RM = 225 x 1.16671RM = 262.5 lb
The calculator result is 262.5 lb. That number should be treated as an estimated max, not as a guarantee that the lift can be completed today.
Accuracy
Epley is usually strongest for hard sets from two to eight reps. It stays easy to audit because the adjustment is visible: a five-rep set is multiplied by 1.1667, and an eight-rep set is multiplied by 1.2667.
The linear assumption becomes less defensible above ten reps because endurance, breathing, pacing, and technique fatigue explain more of the result than max strength does.
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 Epley
- You need a fast, transparent estimate for a normal barbell lift.
- The set was hard, clean, and between two and eight reps.
- You plan to compare the result against more conservative formulas before choosing a training max.
Epley 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 Epley
- The set was above ten reps or clearly limited by conditioning.
- You are returning from a layoff and need a deliberately conservative block.
- The lift has a large technical failure point, such as strict overhead press or power clean.
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 Epley 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, Epley estimates 262.5 lb. That is a useful top-end number for planning, but many lifters would still choose a 90-95% training max before building volume.
If Epley is the highest number in the group, treat it as an optimistic estimate rather than an instruction to load that weight immediately.
History
Boyd Epley's strength-coaching equation, widely cited through later 1RM comparison papers.
The Epley equation became one of the default rules of thumb in American strength rooms because it is simple enough to check without a spreadsheet. Every extra rep adds about 3.33% of the working weight to the estimated max.
That simple linear structure is the reason many calculators choose Epley as the default. It gives useful numbers from hard triples, fives, and eights, but it can read too high for lifters who are especially good at rep work.
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 Epley formula selected. Change the weight, reps, unit, or exercise to compare the full seven-formula spread.