Estimated 1RM explained: turning a logged set into a max

A set of 100 kg for five at RPE 8 is worth 123.3 kg for one rep, computed with the app's model. Log the same five reps with no RPE and the estimate falls to 115.9 kg. The 7.4 kg between those two numbers is the two reps the lifter had left and did not show. An estimated 1RM is that conversion and nothing more: a set's weight, reps and effort read off one curve of percentages. This guide shows the curve, runs the same set through the Epley and Brzycki formulas, and marks the point where the estimate stops deserving trust.

What is an estimated 1RM?

An estimated 1RM is the heaviest single a lifter could probably manage today, worked out from a set they actually did rather than a set they tested. Nobody wants to pull a true max every week to find out whether a program is working, and nobody has to. Every working set already contains the information, provided the log records three things: the weight, the reps, and how hard it was.

The third item is the one most logs leave out. RPE, rating of perceived exertion, is a 1 to 10 scale where 10 means no reps were left, 9 means one was left, 8 means two, and so on. That scale, with the rating tied to reps in reserve, is the one Zourdos and colleagues tested on 29 squatters [1]. Bar speed fell as the rating rose, with a correlation of minus 0.88 in experienced lifters and minus 0.77 in novices, which is to say the rating tracks something real about how close to the limit a set was [1]. That is the property the conversion depends on.

In Top Sets the estimate is recalculated on every working set, so the number on a lift moves with training instead of waiting for a test day. The same code runs the one-rep max calculator, where any set can be checked by hand.

How the chart turns reps and RPE into a percentage

The model is one published chart of percentages, the reps by RPE table popularised by Reactive Training Systems and studied by Zourdos and colleagues, read along a single line. Add the reps a lifter did to the reps they had in reserve, which is 10 minus the RPE, and the sum is the only thing the chart needs. Five reps at RPE 8 is five plus two, so the lookup is seven. Seven on the chart is 81.1 per cent of a max, and 100 kg divided by 0.811 is 123.3 kg.

That one rule gives the chart a useful symmetry. Five at RPE 8, six at RPE 9 and seven at RPE 10 all add up to seven, so all three are 81.1 per cent and all three estimate 123.3 kg from 100 kg. The table below holds the weight at 100 kg and moves only the effort, every row computed with the app's model.

Each RPE point on a set of five is worth about 4 kg of estimate. A triple at RPE 8 and a five with no RPE land on the same cell, which is the plainest way to see what a missing rating costs. The chart runs from RPE 6 to RPE 10, so a rating below 6 is treated as a max rather than extrapolated, and any rating is snapped to the nearest half point before the lookup.

One cell deserves a caveat. The chart defines one rep at RPE 10 as 100 per cent, but when Helms and colleagues had fifteen powerlifters work up to a true max on squat, bench and deadlift, the RPE they reported at that max averaged 9.6 to 9.7, not 10 [2]. Lifters rarely feel a real limit as a clean 10. The model follows the chart anyway, which means a heavy single rated 9.5 is credited a little above the bar weight, and that is the right reading of a single that moved.

Epley and Brzycki on the same set

The two formulas most calculators still use predate RPE and have no place for it. Epley multiplies the weight by one plus the reps over 30. Brzycki multiplies the weight by 36 and divides by 37 minus the reps, a formula proposed for predicting a one-rep max from a set taken to fatigue [3]. Both assume the set was taken to failure, because that is the only kind of set they were built on.

On 100 kg for five at RPE 8, Epley gives 116.7 kg, Brzycki gives 112.5 kg and the app's model gives 123.3 kg, all computed with the app's model. The gap is the two reps in reserve, which the classic formulas cannot see and the chart can. Remove the reserve by rating every set RPE 10 and the three methods agree closely up to ten reps, then part ways.

Brzycki's denominator shrinks toward zero as the reps approach 37, which is why a set of 30 comes out at 514.3 kg. Epley stays sane but still assumes failure. The published chart stops at 12 reps, and past that the app's curve continues with the same shape as Epley, flagged as rough, so a set of 20 still gets a number without being allowed to run away. Estimates stop at 30 reps because nothing beyond that is worth printing.

How far can you trust it?

The app labels every estimate with a confidence. With an RPE logged, a set of five reps or fewer is high confidence, six to twelve is medium, and anything above twelve is low. Without an RPE the ceiling drops: medium up to ten reps and low beyond. Those bands are not arbitrary.

Reynolds and colleagues had 70 people aged 18 to 69 perform 1, 5, 10 and 20 rep maxes on the bench press and leg press [4]. The five-rep set predicted the true max best, explaining 99.3 per cent of the variance on the bench press, and the authors concluded that no more than ten reps should be used in a linear equation to estimate a 1RM [4]. Lifters differ most in how many reps they can grind out at a light percentage, so the further a set sits from a single, the more of the estimate is the chart's average rather than the lifter.

The RPE also costs more the higher the reps go. On 100 kg for five, one RPE point moves the estimate by about 4 kg, as the first table shows. On 100 kg for ten, RPE 8 estimates 147.1 kg and RPE 10 estimates 135.3 kg, a swing of 11.8 kg for the same two points, all computed with the app's model. A half-point of optimism on a set of twelve is a bigger lie than the same half-point on a triple.

Experience matters for the rating itself. In the Zourdos study, experienced squatters reported a higher RPE at their true max than novices did [1]. A lifter in their first months may call a set RPE 8 with four reps in reserve, and the chart will take them at their word. Early estimates are for watching the trend, and loading from them comes later.

Fatigue counts too. A fourth working set estimates lower than the first, so the estimates worth comparing come from the same position in the session, at the same rep count and RPE. And the model is one strictly decreasing curve, so a 15RM can never come out above a 12RM. If the app shows that, one of the two sets is logged with the wrong reps or RPE, and the set with the higher estimate is the one to check first.

Reading the ladder

Once a set has become a max, the same curve runs backwards into a rep-max ladder: the weight that max predicts for any rep count at RPE 10. From the 123.3 kg estimate, the ladder below is what the app would print, computed with the app's model.

The ladder is how a max becomes a prescription. A lifter planning eight reps at RPE 8 wants eight reps with two in reserve, which is the ten-rep cell, so the weight is 91.1 kg; the model's inverse function gives the same 91.1 kg when asked directly for eight at RPE 8 from 123.3 kg. The round trip is exact in the other direction as well. An estimate of 98.1 kg prescribes 72.5 kg for eight at RPE 8, and 72.5 kg for eight at RPE 8 estimates 98.1 kg. What to do with that next weight once it is on the bar is the subject of progressive overload for hypertrophy.

What the number is for

An estimated 1RM is a trend line, not a test result. One set gives one point on it, and one point can be moved by a bad night's sleep, a long first set, or a generous RPE. Four weeks of sets from the same position in the session give a line, and the line is the thing worth reading. It should drift upward on a lift that is progressing and sit flat on one that has stalled, and it will do both without anyone attempting a single.

Two habits make the line trustworthy. Rate every working set, because a set without RPE is scored as a max and will read low on every day the lifter had reps in hand. And resist picking a max attempt from the estimate alone. The chart is an average across lifters, and the lifter standing under the bar is not an average.

The next step is a small one. Take the last top set you logged, with its weight, reps and RPE, and run it through the one-rep max calculator. If the number surprises you, the surprise is usually the RPE.