One-rep max formulas compared: Epley vs Brzycki vs Lombardi

Why the formulas disagree

Epley adds 1/30 of the weight for every rep, a straight line. Brzycki puts the weight you can lift for r reps at 102.78 percent of your max less 2.78 percent for each rep, and dividing by that falling line bends his multiplier upward. Lombardi raises the reps to the power 0.10, which climbs most over the first few reps and then flattens.

From 1 to 10 reps they stay within 5.9 percent of each other and sit closest at 7 reps, 2.8 percent apart. Brzycki gives the lowest estimate from 2 to 7 reps and Lombardi from 8 reps on. Epley and Brzycki both put a 10-rep set at 75.0 percent of the max, so at 10 reps they agree to 0.03 percent. Brzycki’s printed 1.0278 and 0.0278 are 37/36 and 1/36 rounded to four places. Written with those fractions, as 36 ÷ (37 − r), his line meets Epley’s at exactly 10 reps, so the rounding alone separates Epley’s 133.3 kg from Brzycki’s 133.4 kg in the answer.

Past 10 reps Brzycki’s curve climbs away from Epley’s line and Lombardi’s flattens below both, so the spread reaches 12.4 percent at 12 reps and 24.9 percent at 15. All three assume you took the set to failure. Stop with reps in hand and you enter fewer reps than you could do, and every estimate comes out low. Natera and colleagues (2024), citing LeSuer and colleagues (1997) among others, add that the exercise and the equipment change how valid an estimate is, a back squat against a leg press or a free bar against a Smith machine, and so do the lifter’s sex, age and training history.

The formulas

Epley [1]

$$\mathrm{1RM} = w\left(1 + \frac{r}{30}\right)$$

Brzycki [2]

$$\mathrm{1RM} = \frac{w}{1.0278 - 0.0278\,r}$$

Lombardi [3]

$$\mathrm{1RM} = w\,r^{0.10}$$

Sources

1. Epley B. Poundage chart. In: Boyd Epley Workout. Lincoln, NE: Body Enterprises; 1985: 86. The book has no DOI, and no Open Library or Crossref record. Equation as printed, 1RM = load × (1 + 0.0333 × reps), in Macarilla CT, et al. Accuracy of predicting one-repetition maximum from submaximal velocity in the barbell back squat and bench press. Journal of Human Kinetics 2022;82:201-212. https://doi.org/10.2478/hukin-2022-0046
2. Brzycki M. Strength testing: predicting a one-rep max from reps-to-fatigue. Journal of Physical Education, Recreation and Dance 1993;64(1):88-90. doi:10.1080/07303084.1993.10606684
3. Lombardi VP. Beginning Weight Training: The Safe and Effective Way. Dubuque, IA: Wm. C. Brown; 1989. ISBN 0697054969. The book is not online. Equation as printed, 1RM = weight × reps^0.1, in Table 1 (from LeSuer and colleagues 1997) of Lin TY, et al. The effects of barbell resistance exercise on information processing speed and conflict-related ERP in older adults: a crossover randomized controlled trial. Scientific Reports 2021;11:9137. https://doi.org/10.1038/s41598-021-88634-5
4. Abdul-Hameed U, Rangra P, Shareef MY, Hussain ME. Reliability of 1-repetition maximum estimation for upper and lower body muscular strength measurement in untrained middle aged type 2 diabetic patients. Asian Journal of Sports Medicine 2012;3(4):267-273. Prints Brzycki’s coefficients as 102.78 and 2.78 and gives the 10-rep limit. doi:10.5812/asjsm.34549
5. Richens B, Cleather DJ. The relationship between the number of repetitions performed at given intensities is different in endurance and strength trained athletes. Biology of Sport 2014;31(2):157-161. Table 1 says what Epley’s and Brzycki’s equations rest on. doi:10.5604/20831862.1099047
6. Natera AO, Chapman DW, Chapman ND, Keogh JWL. Predicting repeat power ability through common field assessments: is repeat power ability a unique physical quality? PeerJ 2024;12:e16788. On how the exercise, the equipment and the lifter change an estimate’s validity. doi:10.7717/peerj.16788