How to estimate your one rep max

Why a rep-max estimate exists at all

Testing a true one-rep max is not difficult, but it is disruptive. It requires a full warm-up ramp of progressively heavier singles, competent spotting or safety bars, fresh legs and a clear head, and it leaves you too fatigued to do anything useful afterwards. Doing it every time you want to know what to put on the bar would mean a training year made mostly of tests. So the estimate does the work of a test on a day that was going to be a training day anyway.

The estimate rests on a stable observation: for most people, the heaviest load that can be lifted for a given number of repetitions is a fairly predictable fraction of the heaviest load that can be lifted once. Roughly, five repetitions corresponds to about 85% of maximum and ten to about 75%. Every published equation is a different smooth curve drawn through that relationship, and the differences between them are differences in curve shape rather than differences in principle.

It is worth being clear about the hierarchy. The measured single is the reference, and the estimate is an approximation of it. When a calculator and a test disagree, the test is right. That sounds obvious, but it is routinely inverted by lifters who describe an estimated figure as their max and then treat a failed attempt at that weight as a bad day rather than as evidence that the estimate was optimistic.

The published equations

Seven prediction equations appear repeatedly in the strength literature and in the software built on it. Three of them are simple linear adjustments, one is a power function, and three are exponential or hyperbolic curves fitted to test data. They come from a mix of journal papers and coaching textbooks, which is why several of them are cited through a later comparison study rather than through an original article with a digital object identifier.

Brzycki published his in 1993 in a physical education journal, deriving it from the observation that the relationship between percentage of maximum and repetitions is close to linear in the range most people train in. Mayhew and colleagues fitted an exponential curve in 1992 to bench press data from college men and women. Wathan, Epley, Lander, Lombardi and O'Conner originate in coaching literature of the 1980s and 1990s; LeSuer and colleagues reproduced all seven in a 1997 comparison against measured maxima in the bench press, squat and deadlift, which is the citable record for several of them.

The equations below use w for the weight lifted and r for the number of repetitions completed. Our one rep max calculator computes all seven and shows the spread, because presenting a single number from a single equation implies a precision that none of them has.

• Epley (1985): 1RM = w × (1 + r ÷ 30)
• Brzycki (1993): 1RM = w × 36 ÷ (37 − r)
• Lombardi (1989): 1RM = w × r^0.10
• O'Conner (1989): 1RM = w × (1 + 0.025 × r)
• Lander (1985): 1RM = 100 × w ÷ (101.3 − 2.67123 × r)
• Mayhew (1992): 1RM = 100 × w ÷ (52.2 + 41.9 × e^(−0.055 × r))
• Wathan (1994): 1RM = 100 × w ÷ (48.8 + 53.8 × e^(−0.075 × r))

How far apart the equations get

The table below takes a single set of 100 kg and runs it through all seven equations at different repetition counts. The numbers are computed directly from the formulas above, so you can reproduce every one of them with a calculator. The pattern is the interesting part: the equations are closest at five repetitions, where they span 6.5 kg, and they fan out in both directions from there.

At the low end the divergence comes from curve shape. Mayhew's exponential rises steeply from a single, so at two repetitions it sits four and a half kilograms above the next highest estimate; it was fitted on bench press sets taken to fatigue at submaximal loads and was never intended to describe a double. At the high end the divergence is worse and more consequential: at twelve repetitions the spread is 16.2 kg, or nearly 12% of the mean estimate, which is the difference between a programme that works and a programme you cannot complete.

The practical reading is that the spread is itself the error bar. If seven reasonable equations fitted on real lifters disagree by twelve per cent about your maximum, then no single one of them knows it to better than that. Quoting an estimated max to the nearest kilogram is false precision, and rounding it down to the nearest loadable increment is the honest response.

Why accuracy collapses beyond about five reps

Every one of these equations is a one-parameter model. It assumes that knowing the load and the rep count is enough to locate you on a single universal curve. The trouble is that the curve is not universal: how many repetitions a person can complete at, say, 80% of their maximum depends on their training history, their fibre type distribution, the exercise, and how comfortable they are with genuine effort. At low rep counts that variation has little room to express itself. At high rep counts it dominates.

Richens and Cleather demonstrated the point directly by comparing endurance-trained and strength-trained athletes. At a given percentage of one-rep max, the two groups completed materially different numbers of repetitions, which means a single conversion table cannot be right for both. A strength-trained lifter who manages eight repetitions at 80% and an endurance-trained one who manages fourteen will be handed the same estimated maximum by the same equation, and at most one of them can be correct.

There is a second, simpler reason. At high repetitions the set stops being a test of strength and starts being a test of local muscular endurance, cardiovascular tolerance and willingness to hurt. A set of fifteen ends when your breathing, your grip or your motivation gives out, none of which is what a one-rep max measures. That is why our calculator refuses rep counts above twelve outright and tells you to test again with a heavier weight rather than returning a number it cannot stand behind.

The corollary is cheerful enough: the fix costs one set. If you want a good estimate, do a set of three to five repetitions taken genuinely close to failure, rather than a set of twelve. The equations agree most closely there, the physiology is closest to what they were fitted on, and the set itself is short.

The lift you chose changes the error

Most of these equations were derived from bench press data, because the bench press is the easiest lift to test safely in a laboratory and the easiest to standardise. They are then applied, uncritically, to squats and deadlifts. That transfer is not free. Lower-body lifts generally allow more repetitions at the same percentage of maximum than upper-body lifts do, partly because of the larger muscle mass involved and partly because of how the load is distributed through the movement. An equation calibrated on bench press therefore tends to underestimate a squat or deadlift maximum from the same rep count.

LeSuer and colleagues tested exactly this in 1997, comparing all seven equations against measured maxima in the bench press, the squat and the deadlift in the same participants. The finding that matters is not which equation won but that the ranking changed between lifts: an equation that tracked the bench press well did not necessarily track the deadlift well, and no single equation was best across all three.

Deadlifts are the worst case for a different reason. They have no eccentric phase to speak of when done from a dead stop, grip often fails before the posterior chain does, and technique degrades quickly under fatigue, so the rep count in a high-rep deadlift set reflects a mixture of factors that have little to do with maximal force production. Estimating a deadlift maximum from a set of ten is close to meaningless.

Machine exercises and isolation movements are a separate problem again. The equations were fitted on free-weight compound lifts where stabilisation and coordination are part of the task. A leg extension or a cable row has a different load-repetition curve, and applying a bench press equation to it produces a number with no clear referent.

Using an estimate to set training loads honestly

The estimate's real job is not to produce a trophy number. It is to convert a programme written in percentages into kilograms on a bar. For that purpose a figure that is a few per cent off is entirely serviceable, because the percentage bands in a well-written programme are wide enough to absorb it and because the sets themselves provide continuous feedback.

Take the mean of the equations rather than the friendliest one, round down to the nearest loadable increment, and then let the training correct you. If a prescribed set of five at 85% moves faster than it should, the estimate was conservative and you can add weight next week. If it grinds to a halt at the third repetition, the estimate was optimistic. Two or three sessions of that feedback will locate your true working maximum more accurately than any equation.

The most useful cross-check is repetitions in reserve. If a programme calls for five repetitions at 85% and you finish the set feeling you had four more in the tank, the load is wrong regardless of what the arithmetic said. The American College of Sports Medicine's position stand on progression in resistance training is built on this kind of ongoing adjustment rather than on a fixed percentage carried through a whole block.

One caution about updating. Re-estimating from every hard set produces a number that wanders with your sleep, your food and your mood, and it is tempting to treat each upward wobble as progress. Recalculate at fixed points (the start of a block, or every four to six weeks) and use the same lift and a similar rep count each time, so that what you are comparing is your strength rather than your protocol.

When to test rather than estimate

Testing is worth the session when the number itself is the point. If you are competing in powerlifting, selecting openers, qualifying for a weight class standard, or reporting strength as a research or clinical outcome, an estimate carrying a several-per-cent error band is not good enough and a measured single is.

The reassuring news is that a measured single is genuinely reliable. Grgic and colleagues reviewed 32 studies covering 1,595 participants and found test-retest correlations ranging from 0.64 to 0.99 with a median of 0.97, and coefficients of variation from 0.5% to 12.1% with a median of 4.2%. Reliability was good regardless of training experience, whether familiarisation sessions were used, whether the exercise was single-joint or multi-joint, upper or lower body, and regardless of the participants' sex or age. In other words, the test works, and it works for ordinary people rather than only for experienced lifters.

It is also fair to say when not to test. If you are new to a lift and your technique is still changing week to week, a maximal single mostly measures your technique. If you are unwell, under-slept or mid-way through a heavy training block, the result will be an underestimate that you then carry forward for months. And if you train alone without safety bars, testing a bench press or a squat to genuine failure is not a reasonable risk to take for a number you could have approximated from a set of three.

A sensible middle path for most people is to work from estimates through a training block and to take one carefully conducted heavy single (not a true failure attempt, but the heaviest weight that moves cleanly) at the end of it. That gives you a real data point without the risk profile of a maximal effort, and it is usually within a couple of per cent of the number an equation would have guessed.

Frequently asked questions

Put it into practice

Run your own numbers through the one-rep max calculator, the FFMI calculator and the protein calculator. Related reading: Heart rate zones, BMI for athletes and METs and calories burned.

Sources

1. Brzycki M. Strength testing: predicting a one-rep max from reps-to-fatigue. J Phys Educ Recreat Dance 1993;64:88–90. doi.org/10.1080/07303084.1993.10606684
2. LeSuer DA, McCormick JH, Mayhew JL, Wasserstein RL, Arnold MD. The accuracy of prediction equations for estimating 1-RM performance in the bench press, squat, and deadlift. J Strength Cond Res 1997;11:211–13. doi.org/10.1519/00124278-199711000-00001
3. 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;6:200–6. doi.org/10.1519/00124278-199211000-00002
4. Reynolds JM, Gordon TJ, Robergs RA. Prediction of one repetition maximum strength from multiple repetition maximum testing and anthropometry. J Strength Cond Res 2006;20:584–92. doi.org/10.1519/R-15304.1
5. Richens B, Cleather DJ. The relationship between the number of repetitions performed at given intensities is different in endurance and strength trained athletes. Biol Sport 2014;31:157–61. doi.org/10.5604/20831862.1099047
6. Wood TM, Maddalozzo GF, Harter RA. Accuracy of seven equations for predicting 1-RM performance of apparently healthy, sedentary older adults. Meas Phys Educ Exerc Sci 2002;6:67–94. doi.org/10.1207/S15327841MPEE0602_1
7. Grgic J, Lazinica B, Schoenfeld BJ, Pedisic Z. Test-retest reliability of the one-repetition maximum (1RM) strength assessment: a systematic review. Sports Med Open 2020;6:31. doi.org/10.1186/s40798-020-00260-z
8. American College of Sports Medicine. Position stand: progression models in resistance training for healthy adults. Med Sci Sports Exerc 2009;41:687–708. doi.org/10.1249/MSS.0b013e3181915670