How Accurate Are 1RM Formulas? What the Validation Studies Actually Measured

If you have ever typed a set into a 1RM calculator and wondered how much to trust the number that came back, the useful answer is that which of the six equations you picked is the smallest of the things deciding it. The bigger ones are which exercise you tested, how many repetitions you took the set to, and how close to failure you actually got.

So this report puts the measurements side by side with a plain statement of what each one actually tested. The short version: the man who wrote one of the most implemented formulas printed a validity limit on it in 1993, the field's standard loading chart publishes one mapping for every exercise with no caveat attached, and the studies that look like they answer the same question have been measuring different things for decades.

Key figures

• Brzycki's original 1993 article in the Journal of Physical Education, Recreation and Dance states that his formula "is only valid for predicting a 1-RM when the number of reps-to-fatigue is less than 10", and the table printed alongside it stops at 10 repetitions.
• In Mayhew et al. (2008), 103 college women performed a mean of 12.5 repetitions to fatigue on the bench press, and the Brzycki equation returned a constant error of +7.2 kg with a standard deviation of 23.7 kg and an intraclass correlation of 0.24 against their measured 1RM.
• The NSCA Training Load Chart, copyright 2012, maps 8 repetitions to 80% of 1RM for every exercise, and cites a single two-page 1984 note in the NSCA Journal as its source.
• Nuzzo et al. (2024), pooling 898 analysed repetitions-to-failure tests from 6,970 individuals, estimated 13.1 repetitions (95% CI 9.8 to 17.5) at 80% of 1RM in the leg press against 8.8 (95% CI 7.7 to 10.1) in the bench press.
• Richens and Cleather (2014) recorded 39.9 plus or minus 17.6 leg press repetitions at 70% of 1RM in 8 endurance runners against 17.9 plus or minus 2.8 in 8 weightlifters, in the same study on the same machine.
• Reynolds, Gordon and Robergs (2006) fitted 5RM prediction equations in the same 70 adults and reported a standard error of the estimate of 2.98 kg for the chest press and 16.16 kg for the leg press.

The six equations barely disagree with each other

Start with the part that turns out not to matter much. The table below runs one set, 160 lb for 8 repetitions, through the six equations our calculator implements, alongside the NSCA chart's own worked answer for the identical set.

The highest and lowest of the six estimates are 10.7 lb apart, about 5.6% of the lowest. The six-formula average lands 1.2 lb below the chart's answer for the same set, and Brzycki lands 1.4 lb below it. For most training decisions that is noise.

It is also worth knowing that our calculator codes Brzycki as w multiplied by 36/(37 - r), which is the 1993 equation exactly, with the printed constants 1.0278 and 0.0278 being 37/36 and 1/36 rounded to four places. The two agree to better than 0.03% across the whole 1 to 10 rep range.

One genuine discrepancy sits in that table and we are flagging it rather than resolving it. Our calculator implements Lombardi as w multiplied by r to the power 0.1. The equation table in Mayhew et al. (2008) prints Lombardi as w multiplied by r to the power 0.13. We have not found a source that settles which exponent Lombardi published, so we are not silently changing either one.

What Brzycki actually wrote in 1993

Brzycki's equation is one of the six our calculator runs. Its origin is a three-page practitioner article in a physical education teaching journal, and it is worth reading, because the author put a limit on his own formula that most implementations do not enforce. Ours accepts up to 20 repetitions.

The article contains no participants, no data collection, no sample and no statistics. Its "Reference" heading carries a single item, and that item is not a source of data. Three further items sit under a separate "Resources" heading.

Writing in the Journal of Physical Education, Recreation and Dance in 1993, Brzycki describes the chain himself. A review by Sale and MacDougall (1981) "noted the unpublished observations of Anderson and Haring (1977) which indicated that there is a direct relationship between reps-to-fatigue and the percentage of maximal load", including the suggestion "that 10 repetitions can be performed with a weight that was equal to approximately 75 percent of a maximal load".

Then, in his own words: "based upon their observations, I calculated a mathematical equation for predicting a 1-RM based upon reps-to-fatigue." So the chain runs from unpublished 1977 observations, through a 1981 review that relayed them, to a linear approximation fitted to them by hand in 1993.

That description is Brzycki's. The full text of the 1981 review could not be obtained, so the Anderson and Haring link is reported here as he reports it, not as something independently confirmed.

What is beyond doubt, because it is printed in the article, is the limit. "It appears as if the relationship is not quite linear beyond about 10 reps. Therefore, this formula is only valid for predicting a 1-RM when the number of reps-to-fatigue is less than 10. If the reps exceed about 10, then the test becomes less accurate for evaluating anaerobic endurance as well as for estimating a 1-RM." The lookup table printed with the article runs from 1 to 10 repetitions and stops.

He flagged the individual variation problem too. Because of "genetic influences", he wrote, "some people are able to perform either less than or more than 10 reps-to-fatigue with 75 percent of a maximum load", and "because genetic traits may differ from one muscle to another, the relationship between anaerobic endurance and muscular strength for each major muscle in the body must be determined for more precise measurements."

Read against the three decades of validation work that followed, that last sentence is the whole finding. Brzycki named both the between-person spread and the between-exercise effect in 1993, and every study since has been measuring how large they are.

The chart the sport actually uses

Alongside the equations sits a lookup table. The NSCA Training Load Chart maps repetitions to a percentage of 1RM, and it is the document behind a great deal of programming: 1 rep at 100%, 2 at 95%, 3 at 93%, 4 at 90%, 5 at 87%, 6 at 85%, 7 at 83%, 8 at 80%, 9 at 77%, 10 at 75%, 12 at 70%. It stops there.

Three things about that document are worth stating precisely. Its entire cited provenance is one line: "Adapted from Landers, J. Maximum based on reps. NSCA J 6(6):60-61, 1984." It gives one mapping for every exercise, and both of its worked examples use the squat. And it carries no caveat anywhere on it about accuracy, about variation between individuals, or about differences between exercises.

That last point is the one that matters, because the research is unusually consistent that the exercise changes the number, and that one mapping cannot cover two of them.

Read the first row against the rest. The chart's 12 repetitions at 70% of 1RM sits below the lower bound of Nuzzo's 95% confidence interval for the bench press, 12.4 to 16.1, and below the leg press interval of 14.2 to 25.5. Its 8 repetitions at 80% sits below the leg press interval of 9.8 to 17.5, while landing inside the bench press interval of 7.7 to 10.1.

That is the cost of one mapping for every exercise. The chart is a programming guideline rather than an estimate of a population mean, so this is not strictly a like-for-like test. Read as a prediction of what a lifter will actually complete, it lands inside the pooled interval for the bench press at 80% and outside it for the leg press at both loads.

The cleanest row pair in the whole dataset is Tibana and colleagues (2011), because it is within-subject. The same nine untrained women, tested on both exercises in randomized counterbalanced order across separate visits at least 48 hours apart, completed 30.5 repetitions on the 45 degree leg press at 60% of their 1RM and 12.2 on the knee extension. At 90% it was 15.6 against 6.1. More than double, at every load, in the same people. No cross-study arithmetic is needed to see that "reps at a percentage of 1RM" is not a property of a lifter. It is a property of a lifter and an exercise together.

Nuzzo, Pinto, Nosaka and Steele (2024) reached the same conclusion from the largest pool of repetitions-to-failure data in this source set, 898 analysed tests from 6,970 individuals across studies published between 1961 and 2023. Their finding is worth quoting because of what it rules out as much as what it establishes: "Sex, age, and training status did not clearly moderate the REPS ~ %1RM relationship", but "more repetitions were evident in the leg press than bench press across the loading spectrum, thus separate REPS ~ %1RM tables were developed for these two exercises."

Shimano and colleagues (2006) found the same shape in free weights rather than machines, reporting that more repetitions were performed in the back squat than in the bench press or arm curl at 60% of 1RM, and that "the number of repetitions performed at a given percent of 1RM is influenced by the amount of muscle mass used during the exercise". They also found training status made almost no difference, with one exception at 90% in the bench press.

How far apart individuals sit, inside one group

Exercise is the first axis. The second is that even a tightly defined group of lifters does not share a repetition count.

Cooke and colleagues (2019) took 58 well-trained lifters with a mean training age of 5.5 years and had them go to failure at 70% of 1RM in the back squat. The mean was 14 plus or minus 4 repetitions. The range was 6 to 26. That is a more than fourfold difference between individuals at one load, on one exercise, in one homogeneous group. Body mass, body fat percentage and femur length all correlated inversely with repetitions performed, but the model R was 0.200, so most of that spread stayed unexplained.

Rodriguez-Rosell and colleagues (2020) put a number on the same spread from a different direction, reporting a coefficient of variation of 15 to 22% for repetitions completed in the bench press and 26 to 34% in the back squat. Note that the squat's spread is consistently wider than the bench press's in that study, which is the exercise effect showing up again as variability rather than as a mean.

That criticism is where Nuzzo and colleagues (2024) start. Describing the loading table printed for years in a commonly assigned strength training textbook, the same prescriptive lineage as the NSCA chart above, they write: "The current REPS ~ %1RM table provides only point estimates for the number of repetitions that individuals might be expected to complete at a given relative load. The table does not incorporate the uncertainty of such estimates, nor does it indicate the expected variation between individuals."

Their own meta-regression reports that spread rather than suppressing it. They estimate a standard deviation about the point estimate of 2.51 repetitions at 80% of 1RM and 4.36 repetitions at 60%, so the heterogeneity grows as the load lightens, which points the same way as the rep-range findings below.

What the error actually is, study by study

Repetition counts are the input. The output is a predicted 1RM, and the studies that measured its error did not all define error the same way. The column that matters most in the table below is the third one.

Take the Brzycki row first, because it looks damning and is not quite what it seems. In Mayhew and colleagues (2008), the equation predicted a mean of 35.9 kg against an actual bench press 1RM of 28.7 kg in 103 college women, with an intraclass correlation of 0.24.

The test protocol is the context. Participants performed repetitions to fatigue at a randomly assigned 60 to 90% of their 1RM, and the mean number completed before training was 12.5, with a range from 2 to 20. That is above the limit Brzycki printed in 1993, and the authors say so themselves in their own terms: equations "significantly overestimate 1RM bench press when the repetition range is large", a tendency "apparent for some of the equations in the current study, especially the linear ones", and "the accuracy of these predictions appears to be enhanced if fewer than 10 RTF are used".

So the headline finding of that paper is not that the equations are broken. It is that only 3 of the 14 tested produced predictions significantly different from a measured 1RM: Berger, Brzycki and Lander. Brzycki was the one of those three whose own author had printed a rep-range warning, and the failures do not share a direction, since Berger underestimated by 7.1 plus or minus 3.9 kg rather than overestimating.

Two other teams found the same relationship independently. Whisenant and colleagues (2003) tested 69 collegiate football players at a fixed 225 lb load and reported that validity was higher when fewer repetitions were completed. Reynolds, Gordon and Robergs (2006) concluded from 70 adults aged 18 to 69 that "no more than 10 repetitions should be used in linear equations to estimate 1RM" for the chest press and leg press.

Two of those teams put the boundary at the same number, 10, in two different populations, and it is the number the formula's author drew in the first place. Whisenant reports the direction without naming a threshold.

Precision is exercise-specific too

The second chart sets out the two studies in this set that reported a standard error of the estimate for more than one lift in the same subjects. They are drawn as separate groups on purpose, because their equations, populations and error definitions differ and no number should be carried across the gap between them.

Reynolds, Gordon and Robergs fitted 5RM equations in the same 70 subjects for both lifts. The leg press equation reached an R2 of 0.974, which looks excellent, and carried a standard error of the estimate of 16.16 kg. The chest press equation reached 0.993 with an error of 2.98 kg. Same study, same subjects, same method, and the absolute error differs more than fivefold between two exercises. Part of that gap is scale, since leg press maxima are far heavier than chest press maxima, but the leg press error stays large in the units a lifter actually loads the bar in. That is the clearest demonstration in the whole set that a high correlation coefficient can sit on top of an absolute error big enough to matter.

Kravitz and colleagues (2003) found the same ordering in 18 elite high-school powerlifters and added a wrinkle worth knowing: the best test load was itself lift-specific. For the squat and bench press, sets at 70% of 1RM produced the best prediction equations. For the deadlift it was 80%.

Li and colleagues (2026) add a recent deadlift-specific confirmation from the velocity side, finding intensity estimates valid to within 4.05% absolute error around 80 and 90% of 1RM but 6.31% or worse from 40 to 70%. Heavy and few is the accurate end. Light and many is not.

The input assumption nobody checks

Every repetitions-to-failure equation assumes the set you typed in actually went to failure. Armes and colleagues (2020) tested that assumption directly on knee extensions, comparing repetitions completed when participants stopped at their own self-determined maximum against repetitions completed when they were taken to momentary failure.

Meta-analysed across their two experiments, "the number of repetitions performed during the MF condition was 2.0 greater than during the sdRM condition", with a 95% confidence interval from 0.0 to 4.0. Everyone in both experiments had at least a year of resistance training behind them. The authors are blunt about it: even trying to get as close as possible without reaching failure, "resistance training experienced participants (>1 year) are still not adequately accurate".

Two things follow. If you stop two repetitions early, you feed a short count into the equation and get an estimate that is too low, which is the opposite direction to the overestimation that comes from testing at high rep counts. And these two error sources do not cancel in any predictable way, because one scales with your rep range and the other with how well you read your own effort. The caveat on this figure is that it comes from knee extensions only, with the load set as a percentage of 1RM in one experiment and of a daily isometric maximum in the other, so do not carry the 2 repetitions over to a barbell squat as a fixed correction.

Where the sources genuinely disagree

Three disagreements in this source set are worth stating outright rather than smoothing over, because each one changes what you should conclude. The secondary figures in the table below are all from Mike Zourdos's write-up at Stronger by Science, read against the primary papers themselves.

Training status against training background. Nuzzo and colleagues found that training status did not clearly moderate the repetitions-to-percentage relationship. Richens and Cleather (2014) found 8 endurance runners completing 39.9 plus or minus 17.6 leg press repetitions at 70% of 1RM against 17.9 plus or minus 2.8 for 8 weightlifters, and concluded that "traditional guidelines may underestimate the potential number of repetitions that can be completed at a given percentage of 1RM, particularly for endurance trained athletes".

These look like opposite findings and they are not. Nuzzo's moderator is training status, trained against untrained. Richens and Cleather's is training modality, with both groups trained and the comparison running between two kinds of training.

Averaging them, or picking a winner, would destroy the actual finding: what you have been training for moves this number even when whether you train does not.

Secondary sources drifting from primaries. Several figures about Nuzzo's meta-regression circulate in forms the paper does not support, and tracing them was worth the effort. The table below is why every number in this report was read out of the paper it came from.

The exercise mix is the one that is now settled. The published paper's SportRxiv preprint states plainly that "the bench press (42%) and leg press (14%) were the most commonly studied exercises", and a 2026 arXiv preprint by Marzagao, not peer reviewed and written by an author affiliated with the fitness app Fitbod, summarises the split the same way. Mike Zourdos's write-up at Stronger by Science is a genuinely useful reading of the paper and is worth reading for its interpretation, but its study count and exercise split do not match the paper, so neither is used here.

Mean difference against absolute error. Sigvaldsen and colleagues (2023) compared three prediction methods against a measured 1RM in 28 recreationally active adults. On the bench press, the repetitions-to-failure method had the smallest mean difference of the three, at 0.0 kg, against 0.1 kg for the isometric method and 5.0 kg for load-velocity.

It would be easy and wrong to report that as the reps method winning. The authors recommend the load-velocity method instead, because its mean absolute error, standard error and coefficient of variation were better, and they state that the methods "cannot be used interchangeably".

A mean difference near zero tells you the errors balanced out across the group. It says nothing about how big any one of them was.

That distinction has a practical edge. Marston and colleagues (2022), reviewing 25 load-velocity studies covering 842 participants, found a predicted 1RM coefficient of variation of 5.2 to 5.7% against 2.1 to 2.4% for a directly measured one, and concluded that predictions of this kind "are unlikely to be able to detect small changes in maximal strength (e.g., less than 5 to 7%)". If your training block added 4% to your bench press, a load-velocity estimate of the kind that review covers could not reliably see it.

What to do with all this

The practical instructions fall out of the measurements without much interpretation needed.

Test in the range the equations were built for. Brzycki wrote fewer than 10; Mayhew and colleagues concluded fewer than 10 helps; Reynolds and colleagues concluded no more than 10. A set of 3 to 6 hard repetitions sits comfortably inside all three limits.

Estimate on the lift you care about, and do not carry the number sideways. The leg press and the knee extension differed by more than double in the same nine women. The bench press and the leg press differ across the entire loading spectrum in the largest pooled dataset available. A chart built for one exercise will mislead you on another, and the NSCA chart does not say which exercise it was built for.

Treat your own repetition count as data, not as an error. If you get 20 reps where a chart says 12, you are probably not doing it wrong. Cooke and colleagues found a 6 to 26 range at one load in 58 trained lifters, and Richens and Cleather found endurance-trained athletes roughly doubling the count of weightlifters on the same machine. Write down what you actually get and use that as your own baseline, which is the same logic behind logging sets in a workout volume tracker rather than recalculating a theoretical max every week.

Do not expect an estimate to resolve small changes. Between a coefficient of variation of 5.2 to 5.7% on a load-velocity predicted 1RM and the roughly 2 repetitions of uncertainty in judging failure, a few percent of real strength change disappears into the noise. If a decision genuinely depends on resolving that, the measurement you want is an actual 1RM attempt, not a better formula.

And if you just want the number, run your set through our 1RM and strength standards calculator at 3 to 6 reps, take the six-formula average, and treat it as a training anchor rather than a measurement. The same caution applies to any percentage-of-maximum prescription, including the pace-based ones in our running training zone calculator, where a single percentage stands in for a range that individuals occupy differently.

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