1RM calculator: 10 formulas and the spread between them

Counted by Bodi · Last counted 4 August 2026 · 5 sources

Calculate your 1RM

This calculator needs JavaScript. Switch it off and the formulas further down the page are still there, in full, with their sources. They are meant to be done by hand. That is deliberate.

Weight

The whole bar, or whatever the machine says. Not just the plates you hung on it.

Kilograms, please, not pounds. Eight of the ten formulas here are a multiplication of your weight and could not care less what unit it is in. The ninth and tenth could: the Nuzzo table works in percentages and survives anything, but the 2026 equation had its coefficients calibrated in kilograms, and says so itself.⁵

Repetitions

The number that was actually in there. Every formula below assumes you took that set to the point where an eleventh was never happening. If you had two left in the tank, every line in the table is aiming low, and not by a rounding error.

Two to ten is the range they were built for. Mayhew et al. say as much, and then went and measured it. Across their full range Brzycki was out by 26.7 per cent with a spread of 101.7 percentage points. Same formula, same 103 women, but only the sets of ten or fewer: minus 2.0 per cent with 10.5.³

reps

Which lift did you do?

This field changes exactly one row of the table, and it is the row the other nine are missing. The eight classic formulas never ask which lift you did. They were also, very nearly all of them, derived on a bench press.

What that costs you. Nuzzo et al. lined up 952 tests on 7,289 people from 269 studies and went looking for what the repetitions-to-load relationship actually depends on. Not sex. Not age. Not whether you have trained before. The lift, though. And so emphatically that it needed tables of its own. At 90 per cent of maximum the average human gets 4.11 repetitions on the bench press and 8.69 on the leg press.¹ Better than double, at the identical fraction of maximum.

Bench press. Smith machine included. This is the lift the research is really about: 42 per cent of every test in the analysis.¹
Leg press. Mind the top of that table: at 95 per cent of maximum the average already sits at 7.04 repetitions.¹ Manage five and you were above 95 per cent, which is where the table stops. That row then stays empty.
Something else. Squat, row, overhead press, curl. No table of their own could be built for those, so this is the general one. The authors write that it is the right one for everything other than the bench press and the leg press.¹

What this field cannot do. It knows which lift you did. It has no idea who you are. Richens and Cleather put eight weightlifters and eight distance runners on the same leg press at 70 per cent of their own maximum. The runners got 39.9. The weightlifters got 17.9.⁴ Same lift, same fraction, better than double.

Your 1RM according to the formulas

kilograms, rounded to whole kilograms

Formula	Estimated maximum
Epley (1985)
Brzycki (1993)
Lander (1985)
Lombardi (1989), exponent 0.10
Lombardi (1989), exponent 0.13
Mayhew et al. (1992)
O'Conner et al. (1989)
Wathen (1994)
Nuzzo et al. (2024), for your lift
Marzagão (2026), not yet reviewed

Two helpings of Lombardi, and that is not a mistake. His 1989 book is out of print. Jiménez and De Paz print the formula with exponent 0.10,² Mayhew et al. with 0.13.³

The band your 1RM probably falls in

This is the band between two people doing the same set. Nuzzo et al. give, per load, not only an average but also how much people differ from one another: one standard deviation is 2.51 repetitions at 80 per cent of maximum and 4.37 at 60 per cent.¹ We have converted that spread back into kilograms. Running it backwards is our arithmetic, not a claim of theirs.

All ten formulas are written out below, with their sources. Check the arithmetic yourself.

Short answer

What is your one rep max?: The heaviest weight you can get up exactly once. One repetition maximum. There is a way to measure it, and it involves walking over to the bar and lifting it. Everything else is estimation.
How do you calculate your 1RM?: Your weight times a factor pulled out of the repetition count. That is all the classic formulas do, and at 80 kg for eight repetitions they land between 96 and 105 kg.²³
Which 1RM formula is best?: A smaller question than how many repetitions you type in. Across the full range Lander was 22.9 per cent out in 103 women, and on sets of ten or fewer, minus 1.1 per cent.³
How accurate is a 1RM calculation?: To roughly the nearest ten kilograms. Two people benching 80 kg for eight land between 94 and 103 kg, going by the spread in Nuzzo et al.¹ Hence a band up there, and not one confident number.

How we count on the rest of this site

What is your one rep max?

1RM stands for one repetition maximum: the heaviest weight you can get up exactly once. One repetition. There is no second one.

Nothing about it needs calculating. You can lift it and find out. What that costs you is a warm-up, somebody watching, and a day on which everything happens to line up, and those three rarely coincide. Hence formulas.

An estimate does something else entirely. It takes a set you were doing anyway, and works backwards to the one repetition you never performed.

1RM calculator: what it actually does

Two numbers in, one number out: the weight on the bar, and the repetitions that were genuinely in there.

Over the top of that goes a factor, and that is precisely where the whole argument lives. At 80 kg for eight repetitions Epley says 101 kg, and O’Conner 96.² Same set. Five kilograms apart.

The arithmetic is trivial. The trouble is the factor, and the repetition count you hand it.

The ten formulas, so you can redo them yourself

Below, w is the weight and r is the repetitions, and every one of them fits on a pocket calculator. A formula you cannot redo is a formula you have to take on trust.

Formula	Arithmetic	80 kg, 8 repetitions
Epley (1985)	w × (1 + r/30)	101 kg
Brzycki (1993)	100w / (102.78 − 2.78r)	99 kg
Lander (1985)	100w / (101.3 − 2.67123r)	100 kg
Lombardi (1989), exponent 0.10	w × r^0.10	98 kg
Lombardi (1989), exponent 0.13	w × r^0.13	105 kg
Mayhew et al. (1992)	100w / (52.2 + 41.9 × e^(−0.055r))	101 kg
O’Conner et al. (1989)	w × (1 + 0.025r)	96 kg
Wathen (1994)	100w / (48.8 + 53.8 × e^(−0.075r))	102 kg
Nuzzo et al. (2024)	look it up in a table, per lift	96 kg
Marzagão (2026)	w × (1 + (r − 1)^0.85 / (−2.55 + 4.58 × ln w))	104 kg

The ten results run from 96 to 105 kg. Unrounded, the top and bottom classic results are 8.8 kg apart, which is 9.2 per cent of the lower one.

The Nuzzo row uses the general table, and choosing the bench press makes it 98 kg while the leg press gives 87.¹

Epley (1985) and Brzycki (1993)

Neither of them came out of a study. Epley is a poundage chart from a training book for athletes at the University of Nebraska, and somebody fitted a formula to it afterwards.⁵ Brzycki turned up in a practitioner piece in a magazine for physical education teachers, with no sample and no method.⁵

We have read neither original. Brzycki’s article returned HTTP 403 on 4 August 2026, meaning no access, and Epley’s book is out of print.

Lander (1985), Lombardi (1989) and O’Conner et al. (1989)

Of these three we know the shape and nothing else. Jiménez and De Paz print them in their table 1, taken over from a 1997 comparison by LeSuer et al.² That paper returned HTTP 403 as well.

Lombardi appears twice in the table, at 0.10 and at 0.13, and on eight repetitions those exponents are 6.4 per cent apart.²³

Mayhew et al. (1992) and Wathen (1994)

Mayhew et al. (1992) is the one classic formula with a sample of its own underneath it: 435 students on a bench press, 184 men and 251 women.⁵

Wathen has nothing of the sort. The table in Mayhew et al. (2008) carries a footnote saying the formula was itself worked out from a chart.³ As was Epley’s.

Nuzzo et al. (2024): a table instead of a formula

This row is not a formula but a lookup, and it is the only one on the list that asks which lift you did.¹

Watch what we are doing here. Nuzzo et al. run from load to repetitions: at 80 per cent of your maximum the average person completes 9.75 repetitions.¹ We run that backwards and divide your weight by the percentage your count lands on. That inversion is our arithmetic and not their claim.

Marzagão (2026): the weight joins in

This is the only one of the ten in which the weight itself helps decide what a repetition is worth.⁵ It was fitted on 303,494 sets from 14,966 users of a training app, across 388 lifts.⁵

Against the four classic formulas in the comparison, it came out 17 to 22 per cent more consistent, and that held for every one of the 183 lifts with enough data.⁵ Every single one.

And now the other half of it. Those 303,494 sets contain not one measured maximum, so nothing here has been checked against reality. The criterion is internal consistency, and a formula can be perfectly consistent and consistently wrong.⁵

Marzagão’s paper has also not been peer reviewed. The author appears on it with an email address at the company whose data it is.⁵

Which 1RM formula is best?

There is no answer to that, and the formulas are not entirely to blame. The range you use them over matters more than the choice between one and the next.

Mayhew et al. (2008) held fourteen formulas against a measured maximum in 103 women, before and after twelve weeks of strength training.³ Two of them are in the table above.

Formula	Across the full range	Ten repetitions or fewer
Brzycki	26.7 per cent out, spread 101.7 percentage points	minus 2.0 per cent, spread 10.5
Lander	22.9 per cent out, spread 70.7	minus 1.1 per cent, spread 10.5

Same formulas, same women, different range. A spread of 101.7 percentage points is not a rounding problem.

The authors add a note of their own: most of those fourteen formulas report neither a sample nor a derivation.³ And only five of the fourteen indicate having had any women in their material.³

How many repetitions can you enter?

Anything between two and ten is safe ground. Outside that a number still appears, and that is the whole difficulty.

One repetition: you already have your maximum

Enter one repetition and there is only one defensible answer, which is the weight you have just lifted. A set of one is a maximum.

Formula	80 kg, 1 repetition
Brzycki (1993)	80 kg
Lombardi (1989), exponent 0.10	80 kg
Lombardi (1989), exponent 0.13	80 kg
Wathen (1994)	81.04 kg
Lander (1985)	81.11 kg
O’Conner et al. (1989)	82 kg
Epley (1985)	82.67 kg
Mayhew et al. (1992)	87.09 kg

Five of the eight classic rows decline to give you your own weight back. Mayhew et al. (1992) sits 8.9 per cent above a load you have demonstrably just lifted.

Marzagão (2026) does return 80 kg, because r minus 1 is then zero.⁵ Nuzzo et al. return nothing at all, because their table stops at 95 per cent of maximum and one repetition is above it.¹

Above ten they wander off

The lighter the weight and the higher the repetitions, the further apart the formulas drift. At 12 kg and fifteen repetitions the classic ones land around 19 to 20 kg, and the 2026 one at roughly 25.⁵

On a bench press of 100 kg for five, they differ by less than 2 kg, so the disagreement is not spread evenly.⁵

Did that set really go to the end?

Every formula above assumes there was no eleventh repetition available. That is an assumption about you, not about the arithmetic.

Marzagão cites research in which people stop early while believing they are at the end.⁵ One to two repetitions for the experienced, four to five for the less experienced.⁵

So the number you type in is itself an estimate. It then enters the formula dressed as a measurement.

Why does it matter which lift you did?

Because the difference arrives in kilograms. Enter 80 kg and eight repetitions and the Nuzzo table gives 98 kg for a bench press and 87 for a leg press.¹ That is 12.9 per cent, on identical input.

Not one of the eight classic formulas has a field for the lift, so they put the same number down for both.

What the textbook says, and what was measured

The table that has stood for years in a widely assigned textbook names a single repetition count per percentage. Nuzzo et al. put it beside their own results.¹

Fraction of maximum	Textbook	Nuzzo et al., general table
90 per cent	4	4.94
80 per cent	8	9.75
70 per cent	11	14.80

The textbook undercounts, then, and it does so most at light loads.¹ At 70 per cent the average is 14.80 repetitions, not eleven.

What the lift does not capture

Richens and Cleather put eight weightlifters and eight distance runners on the same leg press.⁴ At 80 per cent of their own maximum the runners managed 19.8 repetitions and the weightlifters 11.8, and that difference held up in the test. At 90 per cent it was 10.8 against 7.0, and that one did not.⁴

So the gap widens as the load gets lighter. Sixteen people and one lift, mind, so this is not an estimate for the rest of the population.

The authors name a second explanation they cannot rule out.⁴ The runners were unused to heavy loads, and may have set their own maximum too low.

How accurate is a 1RM calculation?

Two of the studies here put a measured maximum next to an estimate, and both did it on a bench press.

Jiménez and De Paz measured 28 women aged 30 to 40 with no strength training behind them.² The real maximum sat 6.43 per cent below the estimate from Mayhew et al. (1992) and 14.19 per cent below Wathen’s. After eight weeks of training that was 7.93 and 16.98 per cent.²

Both formulas aim high, and slightly higher after training. That applies to those two formulas and those 28 women, and about the other five this study says nothing.²

Now set two numbers beside each other. At 80 kg and eight repetitions the classic formulas disagree with one another by 8.8 kg. Two people doing that same set land between 94 and 103 kg, going by the spread in Nuzzo et al.¹

You can take the disagreement between eight formulas, all of them published, all of them cited, all of them older than three decades, and set it against the plain fact that two people are two people. The two gaps are the same size.

What this figure is not

It is not a measurement. It is the output of formulas fitted on groups, and of a table we turned around.¹ If you want to know your maximum, there is exactly one way to find out, and it involves lifting it.

It is also not training advice.

Sources

Open a source and you see exactly what was used from that study, which sentence on this page it supports, and what it explicitly does not support.

1Nuzzo 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 Medicine 2024;54(2):303-321. DOI 10.1007/s40279-023-01937-7. Open access.meta-regression of published research · full text read; 1.4 MB PDF retrieved from Springer. The three tables sit inside figures 2, 3 and 4 as images and are therefore absent from the PDF text layer; they were read off pages 308, 309 and 310 rendered at 200 dpi · read 2026-08-04

Design: Meta-regression, not an experiment of its own. Means were modelled with natural cubic splines on the log of the repetition count, the spread with a linear model on the log of the standard deviations; both were then exponentiated back to whole repetitions. For 77 of the studies the numbers were read off graphs with WebPlotDigitizer. The authors state themselves that their search was thorough but not necessarily systematic or exhaustive.
Studied in: 269 studies, 452 groups, 952 tests in 7,289 people; the analyses themselves used 425 groups, 898 tests and 6,970 people. Of the groups, 66 per cent were men, 97 per cent healthy, 92 per cent under 59 years old (median group mean 23 years) and 60 per cent resistance trained. Median group size 13, range 3 to 112. Oldest study 1961, most recent 2023. Most tested lifts: bench press 189 (42 per cent), leg press 65 (14), squat 52 (12), knee extension 48 (11) and chest press 42 (9).
Compared with: The table that has stood for years in a widely assigned textbook, which names a single repetition count per percentage and no spread at all. And internally: men against women, young against old, trained against untrained, and five lifts against each other.
Dose and duration: Not applicable as a dose. The load is the exposure here: 15 to 95 per cent of a person's own maximum, in steps of 5 per cent. Only ordinary repetitions with a lifting and a lowering phase; the 1.3 per cent of tests with lowering only and the 1.1 per cent with lifting only were left out.
What was measured: The mean number of repetitions a person completes at a given percentage of their own maximum, plus the standard deviation of that between people. Both with a 95 per cent confidence interval, tabulated from 15 to 95 per cent in steps of 5.
What was found: Of everything examined, exactly one thing mattered, and it was the lift. Sex, age and training status did not, so no separate tables were made for them. Bench press and leg press did diverge and each got one. At 90 per cent of maximum the average person completes 4.11 repetitions on the bench press and 8.69 on the leg press; at 80 per cent, 8.82 against 13.05. The general table gives 4.94 repetitions at 90 per cent, 9.75 at 80 and 14.80 at 70. The textbook says 4, 8 and 11 at those same three points, so it undercounts the repetitions, and it does so most at light loads. The spread between people grows as the load gets lighter: a standard deviation of 2.51 repetitions at 80 per cent and 4.37 at 60.
Supports on this page: The three tables with which this calculator takes the lift into account, and the finding that the lift is the only factor that matters enough to. It also carries the band between two people doing the same set, because the standard deviation per load is in it.
Explicitly does not support: This is not an equation for estimating a maximum, and the authors do not present it as one. They go from load to repetitions; we run that backwards and divide the weight by the percentage we land on. That inversion is our arithmetic, not their claim, and the same goes for the band we derive from their standard deviation. Beyond that: the leg press table carries wide intervals, at 95 per cent it runs from 1.67 to 29.75 repetitions, so the point estimate there rests on little. For lifts other than the bench press and leg press there is no table of their own, only the general one. Above 95 and below 15 per cent there is nothing at all. The study says nothing about a nutrient, nothing about a supplement and nothing about what anyone should eat or do.
Interests and funding: Two of the four authors were previously employed by a manufacturer of resistance training equipment, and the article states so itself. The other two declare none. Open access paid by a university consortium; the second author held a doctoral scholarship from the Australian government.

https://doi.org/10.1007/s40279-023-01937-7

2Jimenez A, De Paz JA. Application of the 1RM estimation formulas from the RM in bench press in a group of physically active middle-aged women. Journal of Human Sport and Exercise 2008;III(1):10-22. Universidad de Alicante. Open access.controlled measurement with a training intervention · full text read, PDF retrieved via redalyc.org and extracted with pdftotext · read 2026-08-04

Design: Six familiarisation sessions to learn the technique, then two measurement sessions of which the first was again familiarisation and the second counted. Maximum and repetition count were measured under the ASEP protocol with a velocity transducer attached. Then eight weeks of training in three groups, classic linear, non-linear and a control group, three sessions a week, and the same measurement again.
Studied in: 28 physically active women aged 30 to 40, mean 35.32 years with a standard deviation of 3.04, recruited at a sports centre in Madrid. All 28 had been active in one of the centre's programmes for at least six months, and none of the 28 had prior resistance training experience.
Compared with: The measured bench press maximum against the estimate from the equations of Mayhew et al. (1992) and Wathen (1994), before and after the eight weeks.
Dose and duration: Not applicable. This is not a dosing study.
What was measured: The percentage difference between the estimated and the measured bench press maximum, plus means and standard deviations per group, reported in pounds.
What was found: Table 1 of this paper prints in full the seven equations LeSuer et al. set against one another in 1997: Brzycki, Epley, Lander, Lombardi, Mayhew et al., O'Conner et al. and Wathen. That is the table this calculator runs on. Their own measurement: at the first test the real maximum sat below both estimates, 6.43 per cent below Mayhew's and 14.19 per cent below Wathen's. After eight weeks of training that was 7.93 and 16.98 per cent. Both equations therefore aim high, and slightly higher after training.
Supports on this page: The exact form of seven of the eight classic equations on this page, and the direction of the error: too high, not too low.
Explicitly does not support: Bench press only, 28 middle-aged women without resistance training experience only, and of the seven equations only two were held against a measured maximum. The percentages above therefore apply to those two and to this group, not to the other five. The table of seven equations is moreover taken over from LeSuer et al. (1997), and we have not read that paper ourselves; it returned HTTP 403 on 2026-08-04. This paper prints Lombardi's exponent as 0.10 where source 3 makes it 0.13, and neither is the 1989 original. The study says nothing about a nutrient and nothing about a supplement.
Interests and funding: University research, carried out at the European University of Madrid and the University of Leon, with the measurements taken at a sports medicine centre of the Madrid region. No commercial funder named.

https://www.redalyc.org/pdf/3010/301023501002.pdf

3Mayhew JL, Johnson BD, LaMonte MJ, Lauber D, Kemmler W. Accuracy of prediction equations for determining one repetition maximum bench press in women before and after resistance training. Journal of Strength and Conditioning Research 2008;22(5):1570-1577. DOI 10.1519/JSC.0b013e31817b02ad.controlled measurement with a training intervention · full text read in a PDF copy hosted at unm.edu and extracted with pdftotext; the DOI itself returned HTTP 403 on 2026-08-04 · read 2026-08-04

Design: Each participant's bench press maximum was measured, and alongside it the number of repetitions she completed at a randomly assigned percentage between 60 and 90 per cent of that maximum. Then twelve weeks of progressive resistance training, and the same measurement again at exactly the same percentage as before. Fourteen published equations were run against those measurements. The reliability of the repetition test had previously been established at 0.97.
Studied in: 103 female students from a required course. The mean assigned percentage was 75.6 with a standard deviation of 10.3, and it stayed the same after training. The measured maximum rose from 28.7 kg to 36.4 kg. For the sub-analysis restricted to ten repetitions or fewer, 46 remained before training and 45 after.
Compared with: Fourteen equations against the measured maximum, first across the full range and then again for only those participants who completed ten repetitions or fewer.
Dose and duration: Not applicable. This is not a dosing study.
What was measured: The difference in kilograms between the estimated and the measured maximum, that same difference as a percentage, and the degree of agreement between the two.
What was found: Table 2 prints all fourteen equations in full, and that is the second place we have seen them set down. More important is what table 3 shows next to table 4. Across the full range Brzycki was out by 26.7 per cent with a spread of 101.7 percentage points, and Lander by 22.9 per cent with 70.7. Restrict those same equations to ten repetitions or fewer and Brzycki becomes minus 2.0 per cent with 10.5, and Lander minus 1.1 with 10.5. Same equation, same women, different range. The authors note themselves that most of these equations report neither a sample nor a derivation, and that only five of the fourteen indicate having had women in their material.
Supports on this page: That the two equations with a linearly shrinking denominator hold up to around ten repetitions and fall apart above it. It also carries the second printing of the equation set, and the exponent 0.13 for Lombardi.
Explicitly does not support: Women only, bench press only, and this one twelve-week programme only. It says nothing about other lifts, and therefore nothing about whether the same equations behave the same way on a squat or a leg press. The measured maxima are low, from 28.7 to 36.4 kg on average, so this measurement says little about heavy loads. The study says nothing about a nutrient and nothing about a supplement.
Interests and funding: University research at four American institutions and two institutes of the University of Erlangen. Published in the journal of the American strength and conditioning association. The text we read names no commercial funder.

https://www.unm.edu/~rrobergs/478PredictionAccuracy.pdf

4Richens B, Cleather DJ. The relationship between the number of repetitions performed at given intensities is different in endurance and strength trained athletes. Biology of Sport 2014;31(2):157-161. DOI 10.5604/20831862.1099047. Open access.comparative measurement between two groups of athletes · full text read, PDF retrieved from termedia.pl and extracted with pdftotext · read 2026-08-04

Design: Each participant's leg press maximum was established first. Then each of them completed as many repetitions as they had in them at 90, 80 and 70 per cent of that own maximum, after warm-up sets at thirty, twenty and ten per cent below the load to be used, with two minutes rest between. Differences tested with a repeated measures analysis of variance.
Studied in: Eight weightlifters and eight distance runners, from the School of Sport, Health and Applied Sciences at St Mary's University in Twickenham. The weightlifters averaged 4.1 years of resistance training experience with a standard deviation of 1.0 and a maximum of 335.6 kg (SD 48.6). The runners had zero years of experience and a maximum of 188.4 kg (SD 13.8).
Compared with: The two groups against each other, and both against the tables that textbooks give for repetitions per percentage.
Dose and duration: Not applicable. This is not a dosing study.
What was measured: The number of repetitions each group completed at 90, 80 and 70 per cent of their own maximum.
What was found: At 70 per cent of their own maximum the runners completed 39.9 repetitions with a standard deviation of 17.6, and the weightlifters 17.9 with 2.8. At 80 per cent that was 19.8 (SD 6.4) against 11.8 (SD 2.7). Both of those differences are significant. At 90 per cent it was 10.8 (SD 3.9) against 7.0 (SD 2.1), and that one was not. The gap between the two groups therefore widens as the load gets lighter. The authors put their results in a figure alongside the usual tables and write that those tables had little predictive value for these athletes.
Supports on this page: That two people at exactly the same fraction of their own maximum can complete more than twice the number of repetitions. A repetition count is therefore a weak handle on a maximum, even when you do nothing else wrong.
Explicitly does not support: Sixteen people, one lift, and two deliberately extreme groups. This is not an estimate of how large the difference is in the general population. The authors name a second explanation themselves that they cannot rule out: the runners were unaccustomed to heavy loads and may therefore have set their maximum too low, which makes every percentage of it too light. The study tests no estimation equation at all and says nothing about a nutrient or a supplement.
Interests and funding: University research at St Mary's University in the United Kingdom, published in a Polish open access journal. No funder named.

https://doi.org/10.5604/20831862.1099047

5Marzagao T. A Weight-Dependent 1RM Prediction Equation Optimized on 303,494 Near-Failure Sets Across 388 Exercises. Preprint, arXiv 2603.17495, ook geplaatst op SportRxiv als preprint 768. Niet beoordeeld door vakgenoten.preprint, not peer reviewed · full text read, 2.1 MB PDF retrieved from arXiv and extracted with pdftotext · read 2026-08-04

Design: Not an experiment but an analysis of training logs from a commercial app, over a 5 per cent sample of its users. The coefficients were found with a two-stage grid search. The criterion is not deviation from a measured maximum, because the data contain none, but internal consistency: the degree to which different weight and repetition combinations from the same person, the same lift and the same time window land on the same estimated maximum. Five-fold cross-validation at user level.
Studied in: 303,494 sets taken close to the point where it stops working, from 14,966 users, across 388 lifts and 16 muscle groups. The raw extract was larger: 37,736,594 sets from 65,757 users across 505 lifts. Mean weight per lift ran from 7.9 kg to 80.3 kg, with an average across all lifts of 35.8 kg.
Compared with: The four classic equations that appear most often in review articles: Brzycki, Wathen, Epley and Mayhew et al.
Dose and duration: Not applicable. This is not a dosing study.
What was measured: The reduction in the standard deviation of the log of the estimated maximum within a cluster of sets from the same person, lift and period. Consistency, that is, and explicitly not accuracy.
What was found: The proposed equation lets the conversion factor move with the weight instead of fixing it, and arrives at 1RM = w x (1 + (r - 1)^0.85 / (-2.55 + 4.58 x ln w)), with the weight in kilograms. Consistency improved by 17 to 22 per cent against all four classic equations, and it did so for all 183 lifts with enough data, without exception. By category: 19.3 per cent better than Brzycki, 19.4 than Wathen, 19.7 than Epley and 23.9 than Mayhew. For isolation lifts the gain was larger than for compound ones. The differences between the equations sit mainly at light weights and high repetition counts: at 12 kg and 15 repetitions the classic equations land around 19 to 20 kg and this one at roughly 25. On a 100 kg bench press at 5 repetitions they differ by less than 2 kg.
Supports on this page: An estimate in which the weight itself helps decide what a repetition is worth, and the observation that the classic equations disagree with one another most at light weights and high repetition counts. It also carries, from the literature review in part 1, the provenance of three equations: that Epley's came not from a study but from a poundage chart in a training manual for University of Nebraska athletes, that Brzycki's appeared in a practitioner article for physical education teachers with no sample or method stated, and that Mayhew et al. (1992) does rest on a sample of its own: 435 students, 184 men and 251 women, on the bench press.
Explicitly does not support: This is the weakest source on this list, for three reasons. It has not been peer reviewed. The data contain not one measured maximum, so nothing has been checked against reality: an equation can be perfectly consistent and consistently wrong, and this study cannot tell the difference. And the author appears in the paper with an email address at the company whose data it is. On top of that, a set was only flagged as intended to go to the point where it stops working, with no check that the point was reached; the paper itself cites research in which people stop one to five repetitions early. The coefficients are calibrated in kilograms, and the paper notes that for pounds the intercept has to shift. And the three provenance accounts above sit in its literature review, not in its own material: the author has not inspected Epley's 1985 poundage chart or Brzycki's 1993 article either, or at any rate writes nothing about having done so. It is a second-hand statement, exactly as it is with us.
Interests and funding: The author is listed with an email address at Fitbod, Inc., the company whose training logs these are. That is the heaviest declaration of interest on this list, and it is stated openly.

https://arxiv.org/abs/2603.17495