1RM Formula Comparison
All seven major 1RM prediction formulas — equations, accuracy data, study citations, and head-to-head comparisons. The page that answers “which 1RM formula is the most accurate” with research-grounded specifics.
All 7 formulas at a glance
| Formula | Year | Equation | Best for | Accuracy | Bias |
|---|---|---|---|---|---|
| Epley | 1985 | 1RM = weight × (1 + reps / 30) | 2-10 reps | ±5% | balanced |
| Brzycki | 1993 | 1RM = weight × 36 / (37 − reps) | 1-10 reps | ±3% for reps under 10 | balanced |
| Lombardi | 1989 | 1RM = weight × reps^0.10 | 3-12 reps | ±4% for trained individuals | underestimates |
| O'Conner | 1989 | 1RM = weight × (1 + reps × 0.025) | 1-12 reps | ±6% across all rep ranges | underestimates |
| Mayhew | 1992 | 1RM = 100 × weight / (52.2 + 41.9 × e^(−0.055 × reps)) | 1-15 reps | ±4% consistently | balanced |
| Wathan | 1994 | 1RM = 100 × weight / (48.8 + 53.8 × e^(−0.075 × reps)) | 1-12 reps | ±3% for heavy loads | balanced |
| Lander | 1985 | 1RM = 100 × weight / (101.3 − 2.67123 × reps) | 1-10 reps | ±5% with built-in safety margin | underestimates |
Click any formula name to see its history, calculator, validation data, and FAQ.
Side-by-side: same set, all 7 formulas
How much do the formulas actually disagree? Here are four sample sets run through every formula. Notice the spread tightens at low reps and widens at higher reps.
| Set | Epley | Brzycki | Lombardi | O'Conner | Mayhew | Wathan | Lander |
|---|---|---|---|---|---|---|---|
| 135 lb × 10 spread: 13 lb | 180 | 180 | 170 | 169 | 177 | 182 | 181 |
| 225 lb × 5 spread: 15 lb | 263 | 253 | 264 | 253 | 268 | 262 | 256 |
| 315 lb × 3 spread: 25 lb | 347 | 334 | 352 | 339 | 359 | 343 | 338 |
| 405 lb × 1 spread: 36 lb | 419 | 405 | 405 | 415 | 441 | 410 | 411 |
Amber = highest estimate · Blue = lowest estimate. The trimmed-mean average (used by our main calculator) drops the highest and lowest, then averages the middle five for stability.
Pick the right formula for your situation
Testing 1-3 reps (heavy singles/doubles)
Use Wathan or Brzycki. Both are calibrated on heavy training data and produce the most accurate predictions when reps are limited.
Testing 4-8 reps (most common)
Almost any formula works — they converge in this range. Use Epley for fast back-of-envelope math or the trimmed-mean average from our main calculator.
Testing 10+ reps (high-rep sets)
Use Mayhew — its exponential structure stays accurate at high rep counts where linear formulas (Epley, O'Conner) start to overestimate significantly.
Validation research
Mayhew, Wathan, and Brzycki produced the smallest error across bench, squat, and deadlift. Most formulas underestimated 1RM as reps increased.
LeSuer, D.A., McCormick, J.H., Mayhew, J.L., Wasserstein, R.L., & Arnold, M.D. (1997). The accuracy of prediction equations for estimating 1-RM performance in the bench press, squat, and deadlift. Journal of Strength and Conditioning Research, 11(4), 211-213.
Standard error of estimate ranged from 5.6 to 7.9 kg across formulas; high reps (>10) reduced accuracy meaningfully.
Reynolds, J.M., Gordon, T.J., & Robergs, R.A. (2006). Prediction of one repetition maximum strength from multiple repetition maximum testing and anthropometry. Journal of Strength and Conditioning Research, 20(3), 584-592.
In older adults, most formulas overestimated 1RM by 5-15%; conservative choices (Lander, O'Conner) outperformed.
Wood, T.M., Maddalozzo, G.F., & Harter, R.A. (2002). Accuracy of seven equations for predicting 1-RM performance of apparently healthy, sedentary older adults. Measurement in Physical Education and Exercise Science, 6(2), 67-94.