The formula
The Lander 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 / (101.3 - 2.67123r). 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 / (101.3 - 2.67123 x 5)1RM = 22500 / 87.943851RM = 255.8 lb
The calculator result is 255.8 lb. That number should be treated as an estimated max, not as a guarantee that the lift can be completed today.
Accuracy
Lander is best treated as one formula in a cluster rather than the single correct answer. It is useful from low to moderate reps when the set quality is high.
The denominator structure can become sensitive at high reps. The more reps you enter, the less the result should be treated as a max-strength fact.
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 Lander
- You want a denominator model with a middle-of-pack estimate.
- The set was a clean two-to-eight-rep barbell effort.
- You are comparing seven common formulas side by side.
Lander 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 Lander
- The set was above ten reps.
- You need the simplest formula to explain to a new lifter.
- The input movement standard changed across the set.
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 Lander 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, Lander estimates about 255.8 lb. That is close to the conservative cluster but slightly above Brzycki and O'Conner.
Lander is most useful when the question is not which formula wins, but whether several independent equations converge on the same practical training range.
History
Lander's 1985 equation, often listed in comparative 1RM formula tables.
Lander is another denominator-based formula. It looks more complex than Brzycki because the coefficients are decimals, but the idea is similar: the denominator falls as reps increase, and the projected max rises.
For many common inputs, Lander sits between conservative formulas such as Brzycki and more liberal formulas such as Epley. That makes it useful as a middle reference point.
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 Lander formula selected. Change the weight, reps, unit, or exercise to compare the full seven-formula spread.