One Rep Max Calculator: Seven Published Formulas Computed Together, and How Far Apart They Get as the Repetitions Rise

Seven published one-repetition-maximum formulas from one set of inputs — Epley, Brzycki, Lombardi, O’Conner, Wathen, Mayhew and Lander — with the spread between them printed as an output rather than hidden behind whichever one a page happens to have chosen. That spread is about 5.6% of the lowest estimate at seven repetitions, 7.8% at ten, 24.9% at fifteen and 57% at twenty, so the number of repetitions you did decides how much the choice of formula matters. This page exists so that nobody has to attempt a true one-repetition maximum to get a figure, and it says plainly what each formula does at the edges where it stops working.

These are estimates from published formulas, not measurements of you, and they assume you are well enough to train. Build up gradually, do not attempt a maximum effort alone or without sound technique, and stop and get advice if you have chest pain, unusual breathlessness, dizziness or palpitations.

Seven functional forms, where each one breaks, and the one place two of them coincide

All seven formulas as a multiple of the weight lifted, and the spread between them

What the formulas say against what has actually been measured, at four repetition counts

Published accuracy of six of these formulas against measured one-rep maxima

Where each figure on this page comes from, and what was deliberately left out

Why seven formulas with one input each cannot agree, and why the answer is a band rather than a number

A one-repetition maximum is a lift. This page does not produce one; it produces an estimate of one, and the whole reason to use an estimate is to avoid performing the lift. That is worth saying first because it sets the standard the estimate has to meet: it does not need to be exact, it needs to be good enough to programme training from, and it needs to come with an honest width. The width is the point of this page. Seven published formulas, each with exactly two inputs — the weight and the repetitions — disagree with each other by 5.6% of the lowest at seven repetitions and by 24.9% at fifteen. Printing one of them alone would hide the fact that six others would have said something else.

They disagree because they are different functional forms fitted to roughly the same intuition, and the forms behave differently at the edges. Epley and O’Conner are straight lines, so they rise forever: Epley says a set of thirty means a maximum exactly twice the weight lifted. Brzycki and Lander divide by a falling line, so each has a pole — Brzycki’s denominator reaches zero at 36.97 repetitions and Lander’s at 37.92 — and both run to infinity and then go negative. Wathen and Mayhew are exponentials approaching a ceiling, 2.049 and 1.916 times the lifted weight, which makes them the best-behaved at high repetition counts. Lombardi is a power law, r to the power 0.10, and grows most slowly of all. In the repetition range anyone sensibly uses these tools — about three to eight — the differences between those shapes barely show, which is why all seven have survived. Push them out to fifteen repetitions and the shapes take over from the data: Brzycki gives 1.637 times the weight, Lombardi 1.311, and the two are no longer estimating the same thing.

Two of the seven are arithmetically wrong at one repetition, which is a useful diagnostic. If you lift a weight once and fail the second attempt, your one-repetition maximum is that weight. Lombardi and Brzycki return exactly it. Lander returns 1.4% more, Wathen 1.3% more, O’Conner 2.5% more, Epley 3.3% more, and Mayhew 8.9% more — claiming your maximum is nearly a tenth above a weight you have already proved is close to your limit. None of those authors intended their formula to be used at one repetition, and the failure tells you something about the fit: a curve that is not anchored at the point where the answer is known is being extrapolated at both ends, not interpolated. It is also why this page refuses a repetition count of one rather than answering it. At one repetition there is nothing to estimate, and a calculator that returns your own input dressed as a result is worse than one that declines.

Each formula also has its own error against real maximal lifts, and the error is about three kilograms. The clearest head-to-head comparison available gave, in 31 young men on the barbell bench press, standard errors of estimate of 2.7 kg for O’Conner’s, 2.9 for Epley’s, 3.0 for Baechle and Groves’s, 3.1 for Brzycki’s and Lander’s and 3.2 for Adams’s, with r² from 0.94 to 0.96. Both halves of that need reading. The r² values are near-meaningless as evidence of accuracy, because the dominant term in every formula is the weight lifted, which is most of the answer already — a correlation above 0.9 is effectively guaranteed and the preprint literature makes exactly this complaint. The standard errors are the real content, and three kilograms on a single lifter is larger than the increment most people train in. The ranking, on 31 men and one exercise, should not be read as a ranking at all: half a kilogram separates best from worst.

The deeper problem is that the repetitions-to-percentage relationship is genuinely loose between people, and no formula with one input can fix that. A meta-regression of 266 studies covering about 7,270 individuals found that the mean number of repetitions achievable at 90%, 80% and 70% of one-repetition maximum was around 5, 9 and 15 — and that the between-person standard deviation was about 1.5, 2.5 and 3.4 repetitions respectively. At 80% of maximum, in other words, the middle two thirds of people manage somewhere between about six and twelve repetitions. Invert that and the implication for this page is direct: two people who both do nine repetitions with the same weight may be at quite different fractions of their maxima, and any formula will give them the same answer. This is also where the formulas as a group reveal a bias. At five repetitions every one of the seven sits above the published average multiplier of 1.111, by between 1.3% and 7.1%. At fifteen they straddle the published 1.429, with Brzycki and Lander far above it. The page prints that comparison rather than applying it as a correction, because replacing seven visible disagreeing formulas with one population mean would swap a visible uncertainty for an invisible one.

What to do with the output. Use the percentage table, not the headline. For programming purposes the useful question is almost never “what is my maximum” but “what should be on the bar today”, and the percentage rows answer that directly from whichever formula you chose. Three habits make the estimate behave. Do the set you convert at five repetitions or fewer, where the seven formulas agree to within about 6%. Take it genuinely close to failure, because a set with three repetitions left in reserve is a different set and treating it as the one you recorded understates the estimate by roughly a tenth. And re-estimate from a recent set rather than carrying an old figure forward, because the estimate is a snapshot of a day. If you want to compare the estimate against something, compare it against your own figure from the same exercise a few weeks ago, computed the same way, which cancels most of the systematic error.

Safety, which on this page is specific rather than ornamental. The honest position is narrower than the usual warning. A maximal attempt is not inherently dangerous — a clinical guide to performing one-repetition-maximum assessment states that it is a safe means of strength assessment in older adults when performed correctly and with appropriate pre-screening, and no injury rate for supervised testing could be sourced for this page at all. What makes it risky is doing it badly: without a thorough warm-up, without sound technique at submaximal loads first, without a spotter or safety pins, alone, or with a breath held through the lift. A maximal lift also raises blood pressure sharply, which is a reason for specific caution if you have uncontrolled high blood pressure, an aneurysm, a hernia, recent eye surgery or retinal disease, or a recent fracture or joint replacement; the clinical guide that lists those conditions asks for specialist review before testing rather than forbidding it. So: the reason to use this page is convenience and the avoidance of an unnecessary risky attempt, not because a maximal lift is forbidden. If you do test one, warm up properly, work up in small steps, have someone with you, and stop if your technique changes. Stop and get advice for chest pain, dizziness, or breathlessness out of proportion to the effort. The endurance-side counterparts on this site are the VO₂ max page, which has the same shape of problem — three published field estimates disagreeing by 19% — and the target heart rate zones page. For the protein and energy side of training, the protein requirement page and the energy requirement page are the clinical counterparts.

Frequently asked questions

Related calculators

References

1. Epley B. Poundage chart. In: Boyd Epley Workout. Lincoln, NE: Body Enterprises, 1985 — the source of 1RM = w(1 + r/30), the most widely implemented of the seven and this page’s default. Recorded plainly: this is a poundage chart in a resistance training manual, not a peer-reviewed study, and it reports no derivation sample and no error term. The equation is used here because it is what readers will meet everywhere else, and its provenance is stated on the page for the same reason.
2. Brzycki M. Strength testing — predicting a one-rep max from reps-to-fatigue. JOPERD 1993;64(1):88–90. Source of 1RM = w / (1.0278 − 0.0278r). The only one of the seven whose author stated a validity range: the article says the method is accurate for fewer than ten repetitions and that beyond ten the test becomes less accurate both for evaluating anaerobic endurance and for estimating a one-rep max. It also gives the rule of thumb that individuals can typically perform about ten repetitions at roughly 75% of their maximum, and notes that genetic factors create individual variation around that. On risk, the article identifies stress on muscles, bones and connective tissue, injury when that stress exceeds structural limits, blood pressure elevated beyond submaximal levels, heightened concern for adolescents and older adults, and the fact that maximal lifting is a highly specialised skill requiring considerable technique — which is the substance of this page’s safety section rather than generic caution. The article presents lookup tables from 45 to 310 lb and no reps-to-percentage conversion table beyond the 75% figure; none of its tables is reproduced here.
3. Lombardi VP. Beginning Weight Training: the safe and effective way. Dubuque, IA: Wm. C. Brown, 1989 — source of 1RM = w × r^0.10. A textbook, with no derivation sample or error reported. Structurally the most distinctive of the seven: the only form besides Brzycki’s that returns exactly the lifted weight at one repetition, and the slowest-growing, which makes it the lowest of the seven from about eight repetitions upward.
4. O’Conner B, Simmons J, O’Shea P. Weight Training Today. St Paul, MN: West Publishing, 1989 — source of 1RM = w(1 + 0.025r), a flat 2.5% per repetition and the simplest of the seven. From a textbook rather than a study. In the Lacio comparison below it had the lowest standard error of the six tested, 2.7 kg with r² = 0.96 — on 31 men, which is why the page does not promote it on that basis.
5. Wathen D. Load assignment. In: Baechle TR, ed. Essentials of Strength Training and Conditioning. 1994 — source of 1RM = 100w / (48.8 + 53.8 e^−0.075r). A textbook chapter. One of the two exponential forms on this page and therefore one of the two that approaches a ceiling (100/48.8 = 2.049 times the lifted weight) instead of diverging, which makes it among the better-behaved at high repetition counts.
6. Mayhew JL, Ball TE, Arnold MD, Bowen JC. Relative muscular endurance performance as a predictor of bench press strength in college men and women. J Appl Sport Sci Res 1992;6(4):200–6. Source of 1RM = 100w / (52.2 + 41.9 e^−0.055r). The only one of the seven derived from a substantial sample: 435 college students, 184 men and 251 women, on the bench press. Its defect is at the low end — it returns 1.0886 times the lifted weight at one repetition, 8.9% above a weight already lifted once — which is a visible consequence of fitting an exponential without anchoring it at r = 1.
7. Lander J. Maximums based on reps. NSCA Journal 1985;6(6):60–1 — source of 1RM = 100w / (101.3 − 2.67123r), equivalently w / (1.013 − 0.0267123r). A professional association newsletter. Shares Brzycki’s structural problem: the denominator reaches zero at r = 101.3/2.67123 = 37.92 repetitions, beyond which it returns negative values. The coefficients were cross-checked between two independent sources that write the equation in the two different forms above and agree exactly.
8. Lacio ML, Damasceno VO, Vianna JM, Lima JRP, Reis VM, Brito JP, Fernandes Filho J. Precisão das equações preditivas de 1-RM em praticantes não competitivos de treino de força. Motricidade 2010;6(3):31–7. Source of the per-formula accuracy table on this page: 31 male non-competitive strength trainees at fitness centres, mean age 21.8 ± 4.0 years, barbell bench press, each performing both a maximal and submaximal strength tests. Coefficients of determination 0.94 to 0.96 and standard errors of estimate 2.7 to 3.2 kg across six equations — O’Conner 0.96 / 2.7 kg, Epley 0.95 / 2.9, Baechle and Groves 0.95 / 3.0, Brzycki 0.94 / 3.1, Lander 0.95 / 3.1, Adams 0.94 / 3.2. This paper also writes Brzycki as %1RM = 102.78 − 2.78r and Lander as %1RM = 101.3 − 2.67123r, which are algebraically identical to the forms used here and served as the independent check on both. WHAT COULD NOT BE ESTABLISHED: no comparable per-formula standard error could be sourced for Lombardi, Wathen or Mayhew, so the accuracy table is six rows rather than seven and the page says so. CAVEAT stated on the page: n = 31 on one exercise cannot rank six equations separated by half a kilogram.
9. Nuzzo JL, Pinto MD, Nosaka K, Steele J. Maximal number of repetitions at percentages of the one repetition maximum: a meta-regression and moderator analysis of sex, age, training status, and exercise. Sports Med 2024. Source of the measured comparison on this page: 266 studies, about 7,270 individuals across 450 groups, 952 repetitions-to-failure tests of which 898 entered the final analyses covering 6,970 individuals. Mean repetitions achieved were approximately 24 at 60% of one-rep max (95% CI 18.0 to 31.8), 15 at 70% (11.9 to 19.0), 9 at 80% (7.7 to 10.5) and 5 at 90% (4.3 to 5.8), modelled with natural cubic splines with knots at 60% and 80%. The between-individual standard deviations were approximately 4.36 repetitions at 60%, 3.4 at 70%, 2.51 at 80% and 1.5 at 90%, from a separate linear model on the log-transformed standard deviations. Those standard deviations are the most important figures on this page: they say the repetitions-to-percentage mapping is intrinsically loose for an individual, which is a limit no prediction formula with one input can get past. Four mean values and four standard deviations are cited; no table from the paper is reproduced.
10. Agency for Clinical Innovation (NSW Health). Guide: performing 1 repetition maximum strength assessment. Source of this page’s safety section, and the reason that section is narrower than the usual warning. The guide states that 1RM testing is a safe means of strength assessment in older adults when performed correctly and when appropriate pre-screening is conducted; it requires clear instruction and demonstration of the correct breathing pattern before advancing the load; and it lists conditions warranting specialist review before testing, including hernia, prolapse, haemorrhoids, previous retinal detachment, diabetic retinopathy, recent cataract removal, aneurysms (particularly abdominal aortic), uncontrolled hypertension with a systolic pressure above 200 mmHg, fractures or joint replacements within three months, bony metastases, muscle or tendon tears, and severe joint degeneration. WHAT COULD NOT BE ESTABLISHED: the guide contains no injury rates, no adverse-event statistics and no citations to safety studies, and no injury rate for supervised one-rep-max testing could be sourced from anywhere reachable for this page. The page therefore says that a maximal attempt is a technique-dependent, blood-pressure-raising task done badly by many people, and does NOT claim it is how people get hurt, because that claim could not be supported with a number.
11. A 2026 preprint analysing 303,494 near-failure sets from 14,966 users across 388 exercises, drawn from 37.7 million logged sets, is cited on this page for two of its observations rather than for its own equation. First, that all the classical equations produce correlations above about 0.90 with actual one-rep max, which can obscure meaningful absolute errors — the point this page makes about the r² column in its accuracy table. Second, that prediction accuracy degrades above approximately ten repetitions, and that all the equations tested significantly underestimated the deadlift. It is also the source of the characterisation that Epley, Brzycki, Lombardi, Lander and O’Conner originated in practitioner manuals, textbook chapters or small unpublished datasets rather than peer-reviewed studies, which this page repeats and attributes. STATUS: a preprint, not peer reviewed, and its own proposed equation is not implemented here for exactly that reason.
12. LICENSING POSITION taken for this page, recorded because it determined what the page contains. All seven formulas are arithmetic identities in two variables, stated in journal articles, textbooks and manuals: a two-coefficient relation is not a protected expression and the coefficients are reproduced exactly as published because changing them would be worse than quoting them. Brzycki’s 1993 article contains lookup tables from 45 to 310 lb and NONE of them is reproduced, paraphrased or approximated here; the page computes from the equation instead. The r² and standard error figures are measurements, reproduced with attribution from an open-access journal. The four means and four standard deviations from the Nuzzo meta-regression are figures cited from a paper, not a table lifted from it. No commercial strength-standard table, percentile chart or training programme is reproduced, and no strength rating is assigned at all. No guidance from the UK national institute is used, because its open content licence is United Kingdom-only and forbids display beside advertising, and this site carries advertising; no World Health Organization material is used or reached through a republisher, because WHO publications are licensed non-commercially. The NSW clinical guide is cited for its stated positions and its contraindication list is summarised as a list of conditions rather than reproduced as the guide’s recommendation text.
13. Derivations and checks performed for this page rather than taken from a source, recorded so they can be checked. All computed independently and then reproduced in this page’s own engine. (1) The spread across the seven formulas, as a percentage of the lowest, is NOT monotonic in repetitions: 8.86% at 1, 8.34% at 2, 7.65% at 3, 6.80% at 4, 5.79% at 5, 5.63% at 6, 5.56% at 7 (the minimum), 6.39% at 8, 7.14% at 9, 7.80% at 10, 9.40% at 11, 12.64% at 12, 16.23% at 13, 20.27% at 14, 24.88% at 15, 57.09% at 20 and 267.23% at 30. (2) Epley and Brzycki coincide at exactly 10 repetitions in Brzycki’s exact fractional form 36/(37 − r), both giving 4/3; with the published rounded coefficients they differ by 0.027% there. Below 10 Epley is the higher, above 10 the lower. (3) At 1 repetition the seven give 1.0000 (Brzycki), 1.0000 (Lombardi), 1.0130 (Wathen), 1.0139 (Lander), 1.0250 (O’Conner), 1.0333 (Epley) and 1.0886 (Mayhew) times the lifted weight — only two are arithmetically correct. (4) Brzycki’s pole is at r = 1.0278/0.0278 = 36.9712 and Lander’s at r = 101.3/2.67123 = 37.9226; both are negative beyond. Wathen and Mayhew have horizontal asymptotes at 100/48.8 = 2.0492 and 100/52.2 = 1.9157. (5) Lombardi is the lowest of the seven from 8 repetitions upward and O’Conner below that; Brzycki is the highest from 11 upward and Mayhew below that, so both ends of the band change identity with the repetition count. (6) Against the meta-regression means, at 5 repetitions all seven exceed the implied 1.1111 multiplier, by 1.25% (O’Conner) to 7.11% (Mayhew); at 9 repetitions all seven except Lombardi and O’Conner exceed the implied 1.2500; at 15 the seven straddle the implied 1.4286. (7) Every figure in this page’s worked example, in its two computed tables and in the secondary rows was produced by the same engine that answers the calculator.

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