One-rep max formulas compared: Epley vs. Brzycki vs. Lombardi, and where they break down

Why estimate a one-rep max instead of testing it

A true one-rep max — the heaviest weight you can lift once with good form — is fatiguing and carries real injury risk to test directly, especially for lifters without a spotter or safety pins. Instead, most programs estimate it from a lighter set taken to or near failure at a known rep count. All three formulas below solve the same underlying problem: given a weight and a rep count, predict what one all-out rep would have looked like.

The three formulas

Epley (1985): 1RM = weight × (1 + reps/30). Originally published not as a peer-reviewed study but as a chart in Boyd Epley's Poundage Chart training manual — it's the most widely used estimator today despite that informal origin, largely because of how closely it tracks other formulas at low rep counts.

Brzycki (1993): 1RM = weight × 36/(37 − reps). Published in the Journal of Physical Education, Recreation & Dance, this one is algebraically very close to Epley under about 6 reps and diverges more as reps climb, because its denominator approaches zero as reps approach 37 — an extreme case the formula was never meant to be pushed toward.

Lombardi (1989): 1RM = weight × reps^0.10. From V.P. Lombardi's Beginning Weight Training textbook, this is the odd one out: a pure exponential curve rather than a linear adjustment, so it behaves differently — usually predicting a higher max — at higher rep counts than the other two.

Worked example: 100 kg for 5 reps

• Epley: 100 × (1 + 5/30) = 100 × 1.167 = 116.7 kg
• Brzycki: 100 × 36/(37 − 5) = 100 × 1.125 = 112.5 kg
• Lombardi: 100 × 5^0.10 = 100 × 1.175 = 117.5 kg

At 5 reps the three formulas land within about 5 kg of each other — a gap you'd expect from three different regression fits on three different lifter samples, not a sign that any one of them is "wrong."

Where the gap widens: higher reps

Push the same idea to 60 kg for 10 reps and the formulas separate more:

• Epley: 60 × (1 + 10/30) = 80 kg
• Brzycki: 60 × 36/27 = 80 kg
• Lombardi: 60 × 10^0.10 = 60 × 1.259 = 75.5 kg

Here Lombardi's exponential curve actually predicts a lower max than the linear formulas — the relationship flips depending on rep range, which is exactly why no single formula is "most accurate" across the board. Push toward 12 reps or beyond and Brzycki's denominator (37 − reps) gets uncomfortably small, amplifying any error in the rep count or the weight used.

Why the formulas disagree at all

Each formula was fit to a different sample of lifters tested to failure at different rep ranges, so each one encodes slightly different assumptions about how fast strength drops off as reps climb. Epley's chart came from training-gym observation rather than a controlled study; Brzycki's came from a published fatigue-curve analysis; Lombardi's came from a strength-training textbook aimed at a general fitness audience rather than competitive lifters. None of the three claims to be exercise-specific — they treat a bench press rep and a leg-press rep as interchangeable, even though real fatigue curves differ by movement pattern, joint involvement and how much stabilizer muscle is required. That's a structural limitation no amount of formula-picking fixes.

What the validation research actually found

LeSuer and colleagues directly tested seven prediction equations, including Epley and Brzycki, against measured one-rep maxes in the bench press, squat and deadlift, published in the Journal of Strength and Conditioning Research (1997). All the equations correlated strongly with actual 1RM performance (r > 0.95), but the average predicted-versus-actual difference was statistically significant for most equations on the bench press and squat, and every equation in the study significantly underestimated the deadlift (journal abstract). In plain terms: these formulas are good enough to plan training, but which one runs high or low depends on the specific lift, not just the rep count.

Using the estimate to program actual work sets

The output that matters for programming isn't the estimated max itself — it's the percentage table built from it. Most strength programs are written as a percentage of 1RM (e.g., "3 sets of 5 at 80%"), so once you have an estimate, use the percentage chart in the one-rep max calculator to translate that into an actual loadable weight, then check it against the plate loading calculator to work out which plates go on the bar. Because the underlying number is an estimate, not a measurement, treat the chart as a planning tool: recalculate every few weeks as your strength changes, rather than programming off one number from months ago.

The practical rule

Keep your test sets at 1–5 reps if you want the tightest agreement between formulas, use whichever formula the rest of your program already references so your percentages stay internally consistent, and don't trust any estimate from a set taken much past 10 reps — that's where fatigue and technique breakdown start to matter more than the arithmetic.

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This article explains published training formulas and is general information, not medical or coaching advice for your specific situation. Always warm up properly and use a spotter or safety pins when working near a true maximum.