The four formulas, side by side
Each formula is an algebraic curve fit to historical submax-rep data. They're mathematical, not empirical, and they all return slightly different numbers from the same input. The differences matter most at high reps, where prediction error grows for everyone.
- Epley:
weight × (1 + reps / 30). The workhorse. Tends to overshoot at high reps. - Brzycki:
weight × 36 / (37 − reps). Sharp at low reps; undefined at 37 reps (asymptote). Calculator caps at 20 to stay clear. - Lombardi:
weight × reps^0.1. Flattest curve of the four. Conservative at high reps. - O'Conner:
weight × (1 + reps × 0.025). The most conservative overall.
Reliability bands — why the confidence widens
LeSuer 1997 validated multiple 1RM prediction equations against true 1RM testing across bench, squat, and deadlift. The headline directional finding: prediction error stays low at ≤5 reps and grows sharply past 10 — the specific ±2/±5/±10% bucket values here are StrengthMath methodology synthesizing that direction, not exact bounds LeSuer published. The reliability bands surfaced above are StrengthMath methodology informed by LeSuer's directional findings — the specific ± bounds are a defensible synthesis, not a verbatim LeSuer table. The engine labels them as such in its output.
- HIGH (≤5 reps): ±2% StrengthMath band. Use for programming and for estimating peak attempts.
- MEDIUM (6–10 reps):±5% StrengthMath band. Programming reference; don't use for one-off comparisons.
- NOISY (11–15 reps): ±10% StrengthMath band. Treat as a programming hint, not a real 1RM estimate.
- VERY NOISY (16+ reps): ±15% StrengthMath band. The four formulas diverge sharply; the headline is directional only.
A worked example — 100 kg × 5 bench
Run 100 kg × 5 reps in the calculator above with the lift set to bench. The math:
- Epley: 100 × (1 + 5/30) = 116.7 kg
- Brzycki: 100 × 36 / (37 − 5) = 112.5 kg
- Lombardi: 100 × 5^0.1 = 117.5 kg
- O'Conner: 100 × (1 + 5 × 0.025) = 112.5 kg
Cross-formula average ≈ 114.8 kg. Confidence band at HIGH reliability (±2% StrengthMath band) ≈ 112.5–117.1 kg. That's a tight 5 kg window, which is what you want a 1RM estimate to look like.
Now bump reps to 12 with the same 100 kg. The four formulas spread from ~125 to ~135 kg — a 10 kg disagreement that the ±10% NOISY band honestly admits. Higher rep input, wider error bar.
Frequently asked
Which 1RM formula is most accurate?
It depends on the rep range — no single formula wins across all reps and all athletes. At ≤5 reps the four agree closely; past 10 they fan out. Epley overshoots at high reps; Brzycki holds up at low reps but has an asymptote at 37 reps that breaks the math; Lombardi runs flatter; O'Conner is the most conservative. The cross-formula average is the most defensible single number when you don't have a strong reason to prefer one. The per-formula breakdown above shows the spread so you can see how much agreement you're getting; the ±2/5/10% reliability bands are informed by LeSuer 1997.
How many reps should I use?
≤5 if you want a tight estimate. The StrengthMath reliability bands on this calculator are HIGH at ≤5 reps (~±2%), MEDIUM at 6–10 (~±5%), NOISY at 11–15 (~±10%), and VERY NOISY past 15 — informed by LeSuer 1997's directional findings on rep-count vs prediction error, with the specific ± bounds being a defensible synthesis. A 5-rep set with a real working weight is the most informative single set you can run for 1RM estimation. A 12+ rep set is a programming hint, not a 1RM prediction.
Is the cross-formula average better than picking one?
For most people, yes. Each formula was fit to a different historical dataset and tends to over- or under-shoot in different rep ranges. Averaging across all four cancels some of that systematic bias. The four-way spread itself is also a signal — if all four formulas agree closely, your input is in a range where the math is well-behaved; if they disagree by 5–10%, you're in a noisier rep range and the headline number deserves wider error bars.
Should I actually max out to verify?
Only with a coach, a spotter, and a structured warm-up. A real 1RM test is high-CNS, high-injury-risk, and ruins the rest of your session. The calculator above is for programming purposes — knowing roughly where 80% sits so you can prescribe a working weight. For an actual one-rep-max attempt (powerlifting meet, programmed peak), follow a tested warm-up protocol and have someone watching the bar.
Why does the calculator cap reps at 20?
Because past ~15 reps the four formulas diverge sharply and the underlying validation literature thins out. Brzycki specifically has an asymptote at 37 reps where the math becomes undefined; staying well clear of that boundary keeps the estimate sane. If you're hitting 20+ reps with a given weight, that weight is closer to 50% 1RM than to anything you can productively extrapolate from. Re-test with a heavier weight in the 3–8 rep range.
Does the lift type change the math?
No. The 1RM formulas are weight × f(reps) — the lift label is descriptive only. A 5-rep estimate from a bench press uses the same Epley/Brzycki/Lombardi/O'Conner math as a 5-rep estimate from a squat. The reason for separate landing pages (incline-bench, dumbbell-bench, etc.) is that the surrounding context differs: incline bench has its own strength relationship to flat bench, dumbbell pressing needs different math because of stability and ROM differentials, and so on. The calculator engine is shared.
What I'd do next
- Convert 1RM into working weights
Strength / hypertrophy / peaking percentages — the most common next step after a 1RM update.
- Why ≤5 reps gives the tightest estimate
The HIGH / MEDIUM / NOISY band logic, what each one means for programming use.
- Why most coaches program off training max
TM (~90% of 1RM) absorbs the daily-readiness variance. Worth knowing before you write percentages off the headline.
Also in this cluster
- Incline bench 1RM →
- Dumbbell bench 1RM →
- Plate calculator →
- Best 1RM formula per lift →
- Is an 80 kg squat good? →
- Is an 80 kg bench good? →
- Is a 100 kg deadlift good? →
- Is a 60 kg overhead press good? →
- Is 70 kg bench press good? →
- Good bench press for a 70 kg man →
- Is 60 kg bench good for a woman? →
- Is 60 kg bench good for beginners? →
By Jimmy L Wu. The four 1RM prediction formulas (Epley, Brzycki, Lombardi, O'Conner) are reproduced from their original publications. Reliability bands are StrengthMath methodology grounded in LeSuer 1997 (“Accuracy of prediction equations for strength performance”) — directional findings across the validation literature, labeled as such. Engine logic in lib/strength/oneRepMax.ts. Not medical advice — for max attempts, work with a qualified strength coach. Methodology covers the full sourcing posture.