1RM Formulas Explained: Epley, Brzycki and Lombardi

A 1RM formula estimates the most you could lift for one rep from a heavier set you did for several reps. The three most common, Epley, Brzycki and Lombardi, give nearly the same answer for sets of 1 to 5 reps and drift apart as reps climb, so they are most useful with sets of roughly 3 to 6 reps taken close to failure. Pick one, use it consistently, and treat the result as a trend line rather than a promise.

The three formulas

With w as the weight lifted and r as the reps completed:

Formula	Equation	Shape
Epley	1RM = w x (1 + r/30)	Straight line: each rep adds about 3.3%
Brzycki	1RM = w x 36 / (37 - r)	Curve that bends upward as reps rise
Lombardi	1RM = w x r^0.10	Curve that flattens as reps rise

Where they came from

Epley is attributed to Boyd Epley, longtime strength coach at the University of Nebraska, and comes from a 1985 poundage chart used to assign training loads. It is simple enough to do in your head: divide reps by 30, add 1, multiply by the weight.

Brzycki was published by Matt Brzycki in a short 1993 article on predicting a one-rep max from reps to fatigue (Brzycki, 1993). It was intended for sets of up to about 10 reps, and it is often written in the equivalent form w / (1.0278 - 0.0278 x r).

Lombardi comes from V. Patteson Lombardi’s 1989 weight-training textbook. Raising reps to the power 0.10 means each extra rep adds less to the estimate than the one before.

LeSuer et al. (1997) tested seven prediction equations, including these three, against real 1RM tests in the bench press, squat and deadlift. All correlated strongly with tested maxes (r above 0.95), but most showed significant average errors for at least one lift, and every equation underestimated the deadlift.

Worked example: 100 kg x 5

Say you squat 100 kg (220 lb) for 5 reps.

Epley: 100 x (1 + 5/30) = 100 x 1.1667 = 116.7 kg
Brzycki: 100 x 36 / (37 - 5) = 3,600 / 32 = 112.5 kg
Lombardi: 100 x 5^0.10 = 100 x 1.1746 = 117.5 kg

A 5 kg spread on a 5-rep set. That is the size of uncertainty to keep in mind whenever you read an e1RM. The 1RM calculator shows all three side by side so you can see the range for your own numbers.

How they differ across rep counts

Here is the same 100 kg plugged in at different rep counts:

Reps at 100 kg	Epley	Brzycki	Lombardi
1	100*	100.0	100.0
3	110.0	105.9	111.6
5	116.7	112.5	117.5
8	126.7	124.1	123.1
10	133.3	133.3	125.9
12	140.0	144.0	128.2
15	150.0	163.6	131.1

*Taken literally, Epley returns 103.3 for a single rep, so most calculators simply return the weight lifted when r = 1.

A few patterns stand out:

At 1 to 5 reps, Brzycki gives the lowest estimate, and Epley and Lombardi sit close together slightly above it.
At 10 reps, Epley and Brzycki give exactly the same answer (133.3 kg). This is the crossover point.
Above 10 reps, Brzycki overtakes Epley and climbs faster and faster. Because it divides by (37 - r), it breaks down completely as reps approach the high 30s.
Lombardi is the most conservative from about 8 reps up, because its curve flattens. By 15 reps it is almost 20 kg below Epley and over 30 kg below Brzycki.

So “which one is conservative” depends on the rep count. For a heavy triple, Brzycki is the cautious choice. For a set of 12 or more, Lombardi is.

Why estimates get worse above about 10 reps

High-rep sets measure more than maximal strength. Muscular endurance, breathing, pacing and how willing you are to grind all affect how many reps you get, and none of that shows up in a true single.

Reynolds et al. (2006) tested 1RM, 5RM, 10RM and 20RM in the bench press and leg press. The drop in load as reps increased was clearly nonlinear, and the 5RM gave the best prediction of the 1RM. Their recommendation was not to use more than 10 reps in linear equations like Epley.

There is also a measurement problem. A 5-rep set at RPE 8 means you had about 2 reps left, so you should plug in 7, not 5. The repetitions-in-reserve scale gives you a way to make that adjustment (Zourdos et al., 2016), but small errors in judging reps left matter more as the set gets longer. Our RPE chart shows how RPE maps to reps in reserve.

Individual differences

The formulas describe an average lifter on an average exercise. You are neither.

Hoeger et al. (1990) had trained and untrained men and women perform as many reps as possible at 40%, 60% and 80% of 1RM across several exercises. The number of reps at the same percentage varied widely between exercises, with the leg press allowing far more reps than movements like the leg curl or arm curl. Training status and sex made a difference too.

In practice, that means:

Some lifts allow many more reps at a given percentage, like the leg press in Hoeger’s data, so a high-rep set on those lifts can overestimate your 1RM.
Other lifts go the opposite way. In LeSuer et al. (1997), every equation underestimated the tested deadlift.
Your own history matters. Trained and untrained lifters did not get the same reps at the same percentage, so a formula that fits one lifter well can miss for another.

Use e1RM to track progress, not to replace testing

The most useful thing an e1RM does is let you compare sets with different rep counts on the same scale. If your log shows 100 kg x 5 in March and 95 kg x 8 in May, the e1RM tells you whether you got stronger (Epley says 116.7 vs 120.3, so yes).

For that job, consistency matters more than accuracy. Use the same formula, the same lift and a similar rep range every time, and the trend will be meaningful even if the absolute number is off by a few kilograms. Our guide on tracking progressive overload shows how to put e1RM into a weekly log.

If you need an actual 1RM, for a competition or to set percentages at the start of a 12-week strength block, test it with a structured warm-up, a spotter or safety arms, and solid technique. Stop if anything hurts and get it checked by a qualified professional.

Reading a %1RM table

A %1RM table runs the formula in reverse: given a rep target, what percentage of your 1RM should you load? Here are Epley and Brzycki side by side:

Reps	Epley %1RM	Brzycki %1RM
1	100%	100%
3	91%	94%
5	86%	89%
8	79%	81%
10	75%	75%
12	71%	69%

Read it as “if your 1RM is 140 kg (309 lb), a 5-rep max is around 120 to 125 kg”. Those percentages assume each set is taken to failure. If you want to stop with reps in reserve, move down the table: a set of 5 at RPE 8 is roughly a 7-rep max, so the load drops accordingly. The 1RM calculator builds this table from your own number.

Questions lifters ask

Which 1RM formula is the most accurate?

No single formula wins for everyone or every lift. Studies comparing equations find strong correlations with tested maxes but systematic errors that differ by exercise, so the practical choice is to pick one formula and use it consistently.

How many reps should I use to estimate my 1RM?

Sets of roughly 3 to 6 reps taken close to failure give the most reliable estimates. Accuracy falls off as reps increase, and above about 10 reps the formulas disagree enough that the estimate is a loose guide at best.

Why does my calculated 1RM not match what I can actually lift?

The formulas assume an average relationship between reps and load. Your own relationship depends on the exercise, your training history and how close to failure the set really was, so an estimate can be several kilograms off in either direction.

Sources

Brzycki M. Strength Testing - Predicting a One-Rep Max from Reps-to-Fatigue . Journal of Physical Education, Recreation & Dance, 1993;64(1):88-90
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 . Journal of Strength and Conditioning Research, 1997;11(4):211-213
Reynolds JM, Gordon TJ, Robergs RA. Prediction of one repetition maximum strength from multiple repetition maximum testing and anthropometry . Journal of Strength and Conditioning Research, 2006;20(3):584-592
Hoeger WWK, Hopkins DR, Barette SL, Hale DF. Relationship between Repetitions and Selected Percentages of One Repetition Maximum: A Comparison between Untrained and Trained Males and Females . Journal of Applied Sport Science Research (now Journal of Strength and Conditioning Research), 1990;4(2):47-54
Zourdos MC, Klemp A, Dolan C, Quiles JM, Schau KA, Jo E, Helms E, Esgro B, Duncan S, Garcia Merino S, Blanco R. Novel Resistance Training-Specific Rating of Perceived Exertion Scale Measuring Repetitions in Reserve . Journal of Strength and Conditioning Research, 2016;30(1):267-275

This guide is general education about training, not medical advice. If something hurts, stop and get it checked by a qualified professional.