One Rep Max Calculator

Four formulas, one honest range

A one-rep-max calculator measures nothing. It takes a set that was actually completed — a weight and a number of clean repetitions — and reads a maximum off a published curve. Four of those curves are classic, and this page computes all four rather than choosing between them:

Epley (1985): w × (1 + reps/30) — linear in repetitions, so each extra rep adds the same fixed increment to the multiplier.
Brzycki (1993): w × 36 ÷ (37 − reps) — a hyperbola. The denominator shrinks as repetitions rise, so the estimate does not merely grow, it accelerates.
Lombardi (1989): w × reps^0.10 — a power law with a small exponent, climbing quickly over the first few reps and then ever more slowly.
O’Conner et al. (1989): w × (1 + reps/40) — the same linear shape as Epley with a gentler slope, 40 in the denominator instead of 30.

For 100 kg lifted 5 times the engine returns Epley 116.7 kg, Brzycki 112.5 kg, Lombardi 117.5 kg and O’Conner 112.5 kg — a band running from 112.5 to 117.5 kg, a spread of 5 kg. Those are not four competing measurements, and the exercise is not to work out which one is telling the truth. They are four different algebraic shapes published separately, so the four answers describe one band. The width of that band is the honest width of what a weight-and-reps pair can tell you, which is why the calculator reports the range and deliberately does not name a winner.

The companion guide — one-rep max estimates and training loads — is the longer read: the four curves taken one at a time, the arithmetic of why they cross, and what the percentage table underneath a result is and is not.

What the repetition count does to the band

Hold the weight still and change only the number of repetitions, and the band opens up. At 100 kg for 3 reps the four estimates run 105.9–111.6 kg, a spread of 5.7 kg. At 12 reps the same weight gives 128.2–144 kg, a spread of 15.8 kg. At the top of what the tool accepts, 15 reps, it is 131.1–163.6 kg — 32.5 kg wide.

The ordering moves too. At 3 reps the four line up Lombardi, Epley, O’Conner, Brzycki, highest first; at 12 reps the same list reads Brzycki, Epley, O’Conner, Lombardi. The curves crossed somewhere in between, which is what a hyperbola that accelerates and a power law that flattens eventually do to each other. Nothing about the set changed between those two rows except the distance the formulas had to travel from it.

Where the equations are on firm ground

Validation research finds prediction most accurate for low-rep sets — roughly three to five repetitions — with error growing as repetitions increase. The engine encodes that finding twice: it accepts whole-number repetitions from 1 to 15, and it flags any estimate computed from more than 10 repetitions as less reliable. A flagged figure is still shown, with the caveat attached, because the alternative is not a more careful number — it is the same arithmetic done somewhere that says nothing about its own limits.

The structural reason sits alongside the empirical one. Every equation is anchored at the set that was entered, and every repetition beyond that anchor is extrapolation along a curve whose shape was chosen by its author. Near the anchor the four shapes have barely had room to diverge; far from it, the choice of shape dominates the answer. A high-rep estimate is therefore reporting as much about which author’s algebra is in use as about the set it came from.

There is also a ceiling no curve fit can lift: the only inputs are a weight and a repetition count. The exercise, the equipment, the tempo, the day — none of them is an argument these functions accept, so all of it was averaged into the constants when the curves were fitted and none of it comes back out. Weight from 1 to 1,000 and whole-number repetitions from 1 to 15 is the whole of what the tool is given, and anything outside those ranges is refused with an explanation rather than answered with a wrong number.

The one repetition where nothing is predicted

Enter 100 kg for a single repetition and all four formulas return 100 kg, with a spread of 0. That is not a rounding artefact. A one-rep set is a measured single, so the only correct output is the input.

Two of the equations arrive there by themselves: Brzycki’s multiplier at one repetition is 36 ÷ (37 − 1), which is exactly 1, and Lombardi raises 1 to a power, which is also 1. Epley and O’Conner, being linear in repetitions, would each add a small increment to a weight that has demonstrably already been lifted, so the engine handles the single explicitly instead. Four identical outputs make a useful sanity check: the formulas agree exactly where there is nothing to disagree about.

The 37 in Brzycki’s denominator

Brzycki divides by 37 − reps. At 37 repetitions that denominator is zero and the estimate diverges; past 37 it turns negative. The calculator never goes near it — the accepted range stops at 15 repetitions, and the engine rejects 37 or more outright, so the asymptote stays structurally unreachable even if the cap were ever loosened.

It is a curiosity rather than a hazard, but an instructive one: a curve fit carries no obligation to behave sensibly outside the range it was fitted to. The same caution applies long before 37. The flag above 10 repetitions marks where the four descriptions start drifting apart, not where one of them finally breaks.

Training percentages: a convention, applied arithmetically

Strength programs conventionally express working weights as a percentage of a one-rep max, so the calculator applies the customary percentages to the Epley figure. For the 100 kg × 5 example above, that produces:

90% of 116.7 kg → 105 kg
85% of 116.7 kg → 99.2 kg
80% of 116.7 kg → 93.3 kg
75% of 116.7 kg → 87.5 kg

That table is a programming convention, not a validated prescription. The percentages are the customary vocabulary of strength programming and the arithmetic is a single multiplication — neither of which makes a load correct for a particular exercise, lifter, or day.

It also inherits every bit of the uncertainty above it, and a tidy column of numbers hides that inheritance completely. Run the 85% row against the bottom of the 5-rep band instead of against the Epley figure and it lands at 95.6 kg; run it against the top and it lands at 99.8 kg — a 4.2 kg swing in one row, produced by nothing but the choice of which end of the band to build on. And that is the tight, low-rep, well-behaved end of the estimate: the same row computed from the 12-rep band swings 13.4 kg.

What this tool does, and what it leaves alone

A prediction equation exists precisely so that a maximum can be estimated from a submaximal set rather than tested. Everything on this page is computed from a set that was already completed; nothing here has been performed, and each figure is a prediction about a lift that has not happened. Results are printed to one decimal place because that is the precision these estimates deserve — a band 15.8 kg wide does not get sharper because each end of it carries a tenth.

The arithmetic is also unit-agnostic. All four equations multiply the entered weight by a factor that depends only on the repetition count, so the same 5-rep set entered as 225 lb returns Epley 262.5 lb and a band of 253.1–264.3 lb. The unit control on the form changes the label above the result, not the mathematics underneath it.

Everything runs in your browser: nothing you enter is transmitted or stored, and every worked example on this page is produced by the same functions the calculator calls, evaluated at build time. If the copy and the code ever disagreed, the site would fail to build rather than publish the difference.

Frequently asked questions

Why do the four formulas disagree?

Because they are four different algebraic shapes rather than four instruments measuring the same quantity with different levels of care: a line, a hyperbola, a power law, and a second line with a gentler slope, published separately. The four answers therefore describe one band rather than four competing measurements. At 100 kg for 5 reps the engine's band is 5 kg wide; at 12 reps it is 15.8 kg wide. Reporting the range is more honest than picking a winner.

How accurate are the estimates?

Validation research finds prediction most accurate from low-rep sets — roughly three to five repetitions — with error growing as repetitions rise. That is why the calculator accepts 1–15 repetitions and flags anything above 10 as less reliable. The useful output is the band rather than any one figure inside it: its width is the arithmetic's own statement of how far a weight-and-reps pair can be taken.

Does this replace testing a true single?

A prediction equation exists precisely so that a maximum can be estimated from a submaximal set rather than tested — that is the whole purpose of the algebra. What comes back is a prediction about a lift that has not happened, computed from one that did, and it stays a prediction however many decimal places it is printed to. Whether to attempt a maximal single is a training decision no formula can inform; it belongs with a qualified professional who can see the whole context.

What does the calculator refuse, and what does it only flag?

Refusing an entry and flagging a result are separate things here. Three checks can refuse outright: the repetition field must hold a whole number — a decimal is rejected with its own message rather than rounded, because rounding an input would quietly change the set the estimate was computed from — the count must fall between 1 and 15, and the weight between 1 and 1,000. A fourth, structural guard rejects 37 repetitions or more, which keeps Brzycki's asymptote unreachable even if the cap were ever loosened. A refused entry returns the reason under the field instead of a number. Anything above 10 repetitions is not refused — it is accepted with a flag.

What does the result box show, and what does "Copy result" copy?

The box leads with the band — the lowest of the four estimates to the highest — and only then lists Epley, Brzycki, Lombardi and O’Conner individually, so the range is read before any single figure. The spread between the formulas is printed as its own line rather than left to be worked out, and above 10 repetitions a caution line is added to the same box. The training-percentage rows follow underneath. "Copy result" copies the band as one line of plain text, and the button stays disabled until there is a result to copy.

Not medical advice: this calculator provides general educational estimates from published population formulas. It cannot account for your individual health context and must not be used to diagnose or treat any condition — consult a qualified healthcare professional. Values are processed locally in your browser and never transmitted. See the methodology page.

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