One-Rep Max Estimates and Training Loads
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 one of four published curves. This guide explains the four curves behind the One Rep Max Calculator, why they return four different answers, why those answers sit close together at low repetition counts and scatter at high ones, and what the percentage table underneath the result is — and is not.
What a prediction equation is doing
Weight and repetitions trade off against each other: the heavier the bar, the fewer times it moves. That relationship carries information, and a submaximal set is a sample from it. A prediction equation summarises that whole relationship with one piece of algebra — a shape with fixed constants that turns a weight-and-reps pair into a single number.
That framing explains the thing people find most confusing about the tool. The four equations are not four instruments measuring the same quantity with different levels of care; they are four different algebraic shapes — a line, a hyperbola, a power law and a second line with a gentler slope — published separately by different authors. Where the shapes coincide, the estimate is well-constrained. Where they part company, the disagreement is not noise to be averaged away — it is the honest width of what a weight-and-reps pair can tell you.
The four equations, written out
The calculator computes all four side by side and reports the range rather than choosing a winner:
- Epley (1985): w × (1 + reps/30). Linear in repetitions — 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 just grow, it accelerates.
- Lombardi (1989): w × reps0.10. A power law with a deliberately small exponent, so it climbs quickly over the first few reps and then rises 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.
Two of the four are straight lines, one bends upward without limit, and one climbs ever more slowly without ever levelling off. Four different opinions about what happens far from the data are baked in before a single number is entered.
Worked example: 90 kg for four reps
Take a clean set of four repetitions with 90 kg. The engine that powers the calculator returns Epley 102 kg, Brzycki 98.2 kg, Lombardi 103.4 kg and O’Conner 99 kg — a band running from 98.2 to 103.4 kg, a spread of 5.2 kg. Four reps sits inside the range where these equations are on their firmest ground, and the band is correspondingly tight. Notice the ordering, too: at four reps Lombardi returns the highest figure and Brzycki the lowest.
The same weight for twelve reps
Now keep the weight and change nothing but the repetition count. At 90 kg for twelve reps the same engine returns Epley 126 kg, Brzycki 129.6 kg, Lombardi 115.4 kg and O’Conner 117 kg: a spread of 14.2 kg, far wider than the four-rep band. The ordering has also inverted. Brzycki, which was lowest at four reps, is now highest; Lombardi, which was highest, is now lowest. The curves crossed somewhere in between, which is precisely what you would expect from a hyperbola that accelerates and a power law that flattens.
Twelve is past the point where the engine marks the estimate as less reliable: the tool accepts 1–15 repetitions and flags anything above 10. Push to the top of that range and the pattern continues — 90 kg for fifteen reps yields 118–147.3 kg, a spread of 29.3 kg: a band that widens every time the prediction has further to travel.
Why accuracy falls away as repetitions rise
Part of the reason is empirical: validation studies find these equations most accurate for low-rep sets, roughly three to five repetitions, with error growing as repetitions increase. That finding is why the flag exists at all.
The other part of the reason is visible in the arithmetic above. Every equation is anchored at the set that was actually performed, and every repetition beyond that anchor is extrapolation. 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 telling you as much about which author's algebra you are using as about the lifter.
There is also a limit no curve fit can escape: the only inputs are a weight and a repetition count. Nothing else about the set — the exercise, the lifter, the equipment — is an argument the function accepts, so everything else is averaged into the constants and disappears.
Why one repetition returns the weight you entered
Enter 90 kg for a single repetition and all four formulas return 90 kg, with a spread of 0. This is not a coincidence of rounding; it is the one case where nothing is being predicted. A one-rep set is a measured single, so the correct output is the input.
Two of the equations get there on their own: 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 the lifter has demonstrably already lifted. The engine handles the case explicitly instead, and the identical output from all four is a useful sanity check: they agree exactly where there is nothing to disagree about.
The Brzycki asymptote at 37 repetitions
Brzycki divides by 37 − reps. At 37 repetitions that denominator is zero and the estimate diverges; beyond 37 it turns negative. The calculator never reaches this territory — 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 relaxed.
It is a curiosity rather than a hazard, but an instructive one: a curve fit has no obligation to behave sensibly outside the range it was fitted to. The same caution applies well before 37. The flag above 10 repetitions marks where the four descriptions start drifting apart, long before one of them breaks outright.
Training percentages: a convention, applied arithmetically
Strength programs conventionally prescribe working weights as a percentage of a one-rep max, so the calculator applies the customary percentages to the Epley figure. For the four-rep example above, that produces:
- 90% of 102 kg → 91.8 kg
- 85% of 102 kg → 86.7 kg
- 80% of 102 kg → 81.6 kg
- 75% of 102 kg → 76.5 kg
This table is a programming convention, not a validated prescription. The percentages are the customary vocabulary of strength programming and the arithmetic is trivial — neither of which makes a load correct for a particular exercise, lifter, or day.
The subtler point is that the table inherits the uncertainty of the estimate it was built on, and a single column of numbers hides that inheritance completely. Run the same 85% row against the bottom of the four-rep band instead of the Epley figure and it lands at 83.5 kg; run it against the top of the band and it lands at 87.9 kg. That is a 4.4 kg swing in a single row, produced by nothing but the choice of which end of the band to build on — and this is the tight, low-rep, well-behaved end of the estimate. At twelve reps the same row would spread far wider still.
Common misreadings
Treating the four numbers as four accuracies. They are one band; picking the flattering end or the conservative end discards the only genuinely informative thing the calculator produces.
Reading the decimals as precision. Results are displayed to one decimal place because that is the precision the estimates deserve; an extra digit would imply an accuracy these formulas do not have. A band 14.2 kg wide does not become sharper because each end of it is printed to a tenth.
Treating an estimate as a lift. Nothing on the page has been performed. The figure is a prediction about a set that has not happened, produced from one that did.
Chasing the flagged end of the range. An estimate that only improves when the repetition count climbs past 10 is largely reporting formula behaviour, since that is exactly where the four equations diverge fastest.
This pattern — several published formulas shown together because they disagree by design — also appears in the Ideal Weight Calculator. The wider problem of applying a population-fitted equation to one person is taken up in the guide on heart-rate zones, and the same convention-versus-prescription distinction runs through calorie targets.
Frequently asked questions
Which of the four formulas should I use?
The question assumes one of them is right and the others are wrong, and that is not how curve fits work. Each equation is a different algebraic shape, so the four answers describe one band rather than four competing measurements. The calculator reports the range for exactly that reason, and deliberately does not pick a winner. If a single number has to go into a spreadsheet, the thing that matters is using the same equation every time, so that changes over time reflect training rather than a change of formula.
Why does a set of three tell you more than a set of twelve?
Because the prediction distance is shorter. At one repetition the formulas do not extrapolate at all — the set is the answer. Every additional repetition moves the estimate further from that anchor along a curve whose shape was chosen by its author, and the four chosen shapes diverge as they travel. Validation research also finds prediction most accurate for low-rep sets, roughly three to five reps, with error growing as repetitions increase.
What does the flag above ten reps mean?
It is a labelling rule in the engine, not a judgement about the set. The tool accepts 1–15 repetitions and marks any estimate computed from more than 10 reps as less reliable, because that is where the published accuracy of these equations is weakest and where the four of them disagree most sharply. The number is still shown; it is shown with a caveat attached.
Why does the calculator refuse repetitions above fifteen?
Two reasons, one practical and one structural. Practically, accuracy degrades as reps rise, and past a certain point the estimate says more about the formula than the lifter. Structurally, the Brzycki equation divides by 37 − reps, which reaches zero at 37 repetitions; the 1–15 cap keeps that region unreachable, and a separate guard in the engine rejects 37 or more even if the cap were ever loosened.
Are the training percentages a plan?
No. They are a programming convention — the customary way strength programs express working weights — applied arithmetically to an estimate. The table does not know your exercise, your technique, your equipment or your recovery, and it inherits every bit of uncertainty from the one-rep-max figure it was calculated from.
Does the unit matter?
No. All four equations multiply the entered weight by a factor that depends only on the repetition count, so the arithmetic is identical in kilograms and pounds and the result comes back in whatever unit went in. The unit control on the calculator changes the label, not the mathematics.
Not medical advice: this guide provides general educational information about 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. Calculations run locally in your browser and are never transmitted. See the methodology page.