1RM Calculator

Put 100kg × 8 reps into two different one-rep max calculators and you can get 124.1kg from one and 126.7kg from the other. Both are doing the arithmetic correctly. They are simply running different equations — Epley and Brzycki, the two formulas that sit behind almost every 1RM calculator on the internet, including the one on this site.

Most comparisons of the two say roughly the same thing: they are close at low reps and drift apart at high reps. That is the wrong way round. Worked out properly, the two formulas agree exactly at 10 reps and disagree mostat 3 to 4 reps — which is precisely the rep range every coach recommends for testing. This guide shows the arithmetic, gives the full comparison table, extends it to all seven published formulas, and works out what the disagreement actually costs you when you load a bar.

The two formulas

Both take a set taken to, or very near, technical failure and extrapolate upward to a single. They differ in the shape of that extrapolation.

Epley (1985):1RM = weight × (1 + reps / 30)

Epley is linear. Every additional rep adds a fixed 1/30th — 3.33% — of the weight lifted. Ten reps always means exactly one third more than the load on the bar.

Brzycki (1993):1RM = weight × 36 / (37 − reps)

Brzycki is hyperbolic. The denominator shrinks as reps rise, so each additional rep adds more than the last. It starts more conservative than Epley and accelerates past it. The formula breaks down entirely at 37 reps, where the denominator hits zero.

They agree at exactly 10 reps — and this is provable

This is not an approximation or a coincidence of rounding. Set the two formulas equal to each other and the weight cancels out:

1 + r/30 = 36 / (37 − r)

Multiply out: (30 + r)(37 − r) = 1080, which expands to 1110 + 7r − r² = 1080, and rearranges to r² − 7r − 30 = 0. That factorises cleanly as (r − 10)(r + 3) = 0. The only positive root is r = 10.

So at 10 reps both formulas return exactly 4/3 — 1.3333 × — the weight lifted, regardless of what that weight is. A 100kg set of 10 gives 133.3kg from both. A 60kg set of 10 gives 80.0kg from both. Below 10 reps Epley is always the higher estimate; above 10 reps Brzycki always is. There is exactly one crossover point and it is a whole number, which is why nobody notices it: the one rep count where the formulas are identical is a common enough test set that plenty of lifters have compared two calculators and concluded they agree.

The full comparison table

All figures computed from a 100kg working set. To read this for your own numbers, multiply by your weight and divide by 100.

Reps	Epley	Brzycki	Difference	Gap
1	103.3kg	100.0kg	+3.3kg	+3.33%
2	106.7kg	102.9kg	+3.8kg	+3.70%
3	110.0kg	105.9kg	+4.1kg	+3.89%
4	113.3kg	109.1kg	+4.2kg	+3.89%
5	116.7kg	112.5kg	+4.2kg	+3.70%
6	120.0kg	116.1kg	+3.9kg	+3.33%
7	123.3kg	120.0kg	+3.3kg	+2.78%
8	126.7kg	124.1kg	+2.5kg	+2.04%
9	130.0kg	128.6kg	+1.4kg	+1.11%
10	133.3kg	133.3kg	0.0kg	0.00%
11	136.7kg	138.5kg	−1.8kg	−1.30%
12	140.0kg	144.0kg	−4.0kg	−2.78%

Difference and gap are Epley minus Brzycki. Positive means Epley is the higher estimate.

The gap is widest exactly where you are told to test

Read down the gap column and the shape is a hump, not a ramp. The disagreement grows from 3.33% at one rep to a peak of 3.89% at 3 and 4 reps, then narrows steadily to nothing at 10 reps before reopening in the other direction. The two formulas are at their most divergent in the 3 to 6 rep window — the window recommended for testing precisely because that is where prediction is most reliable.

This is worth sitting with, because it produces an awkward result. Testing at low reps genuinely does give you a more accurate estimate of your true max. But it also puts you in the range where your answer depends most on which equation your calculator happens to run. Doing the more rigorous thing makes the formula choice matter more, not less.

The practical resolution is not to pick a side. It is to note that a 3.89% disagreement between formulas sits well inside the 5 to 10% error band that validation research finds between any predicted max and a tested one. If you are choosing between 110.0kg and 105.9kg, the honest answer is that your real max is somewhere in that region and neither number deserves a decimal place.

The one-rep problem

Look at the first row again. Given a 100kg single, Epley returns 103.3kg. It has told you that your one-rep max is 3.3% heavier than a rep you have already completed, from no information other than that rep.

Brzycki returns exactly 100.0kg, because 36/(37 − 1) = 36/36 = 1. It is self-consistent at the boundary; Epley is not. This is a structural flaw rather than an inaccuracy — Epley was fitted to multi-rep data and was never intended to be evaluated at r = 1 — but it matters if you feed a tested single into a calculator and get a number back that is higher than the lift you just made. Our calculator returns the weight unchanged at one rep for both formulas for exactly this reason.

Seven formulas, not two

Epley and Brzycki dominate because they are the easiest to compute by hand, but at least five other equations are in published use. Running the same 100kg set through all seven shows how much of the apparent precision of any single estimate is illusory.

Reps	Epley	Brzycki	Lombardi	O'Conner	Wathan	Lander	Mayhew	Spread
1	103.3	100.0	100.0	102.5	101.3	101.4	108.9	8.86%
3	110.0	105.9	111.6	107.5	109.0	107.2	114.0	7.66%
5	116.7	112.5	117.5	112.5	116.6	113.7	119.0	5.79%
6	120.0	116.1	119.6	115.0	120.3	117.3	121.5	5.63%
7	123.3	120.0	121.5	117.5	124.0	121.1	123.9	5.56%
8	126.7	124.1	123.1	120.0	127.7	125.1	126.3	6.39%
10	133.3	133.3	125.9	125.0	134.7	134.1	130.9	7.80%
12	140.0	144.0	128.2	130.0	141.5	144.4	135.4	12.64%

All values in kg from a 100kg set. Spread is the range from lowest to highest estimate, as a percentage of the lowest.

The seven-formula spread is 8.86% at one rep, bottoms out at 5.56% at seven reps, and widens to 12.64% by twelve. So the rep range where the published formulas most nearly agree with each other is 6 to 7 — slightly higher than the 3 to 5 usually recommended, and a reasonable compromise if you want a number that does not depend heavily on whose equation you used.

What the disagreement costs you on the bar

Percentages are abstract. Here is the same 100kg × 8 set converted into the 80% working load each formula implies, which is the number you would actually load:

Formula	Estimated 1RM	80% working load
Wathan	127.7kg	102.1kg
Epley	126.7kg	101.3kg
Mayhew	126.3kg	101.0kg
Lander	125.1kg	100.1kg
Brzycki	124.1kg	99.3kg
Lombardi	123.1kg	98.5kg
O'Conner	120.0kg	96.0kg

The full range is 96.0kg to 102.1kg — 6.1kg, or a 2.5kg plate either side of the bar. Between Epley and Brzycki alone it is 2.0kg, which on most bars is a single small plate per side. That is the real size of the decision: meaningful enough to be worth being consistent about, small enough that it is not what is limiting your progress.

Which should you use?

Testing at 1 to 3 reps:use Brzycki. It is self-consistent at a true single, and Epley's fixed 3.33%-per-rep increment overstates the extrapolation when there is barely any extrapolating to do.
Testing at 4 to 8 reps: either, or the average of both. This is where the two are converging and where both sit closest to tested maxes. Our calculator shows both plus their mean.
Testing at 10+ reps: Epley is the more conservative of the two here, and conservative is the right bias when the estimate is least trustworthy. Better still, do not programme from a 12-rep set at all.
Whichever you choose, stay with it. Progress is measured as a change over time, and switching formula mid-block introduces a 2 to 4% step that has nothing to do with training. A consistently applied slightly-wrong formula is more useful than an inconsistently applied slightly-better one.

Frequently asked questions

Is Epley or Brzycki more accurate?

Neither is reliably more accurate across all rep ranges. Below 10 reps Epley returns the higher estimate and Brzycki the more conservative one; above 10 reps that reverses. At exactly 10 reps they return the same number. Validation studies put both within roughly 5 to 10 per cent of a tested max when the set is 3 to 6 reps, which is a wider margin than the gap between the two formulas.

At what rep count do Epley and Brzycki agree?

Exactly 10 reps. Setting the two formulas equal gives the quadratic r squared minus 7r minus 30 = 0, whose only positive root is r = 10. At 10 reps both return 1.3333 times the weight lifted, whatever that weight is.

Why does Epley say my 1RM is higher than a single I actually lifted?

Because Epley is not self-consistent at one rep. Substituting reps = 1 gives weight times 1.0333, so it claims a max 3.3 per cent above a single you have already completed. Brzycki returns exactly the weight lifted at one rep. Our calculator special-cases one rep for this reason.

Does the choice of formula actually matter for training?

It matters about as much as one small plate. A 100kg set of 8 produces estimated maxes from 120.0kg to 127.7kg across the seven published formulas, so an 80 per cent training load lands anywhere between 96.0kg and 102.1kg. That is a 6.1kg spread on the bar from an arbitrary choice of equation.

Method, assumptions and sources

Every figure on this page was computed programmatically from the published equations rather than transcribed from another source, then rounded for display. The crossover at 10 reps is derived algebraically above and can be checked by hand.
Formulas used: Epley, 1RM = w(1 + r/30); Brzycki, w × 36/(37 − r); Lombardi, w × r^0.10; O'Conner, w(1 + 0.025r); Wathan, 100w / (48.8 + 53.8e^−0.075r); Lander, 100w / (101.3 − 2.67123r); Mayhew, 100w / (52.2 + 41.9e^−0.055r).
The 5 to 10% predicted-versus-tested error band is a summary of the general finding across validation studies of rep-max prediction, not a single published figure. Reported errors vary by lift, training status and how close the test set was taken to genuine failure.
All examples assume a set taken to technical failure with consistent form. Stopping short of failure understates every estimate on this page.
This is training information, not medical or coaching advice specific to you. Maximal testing carries injury risk; warm up thoroughly and use a spotter or safety pins.

Epley vs Brzycki Formula: Which 1RM Calculator Is More Accurate?