Mayhew Formula: 1RM Calculator and Complete Guide

History and origin

Jerry L. Mayhew and colleagues published their bench press 1RM prediction equation in 1992 in the Journal of Applied Sport Science Research. The study examined 251 college men and women performing reps-to-fatigue tests with 70-100% of estimated 1RM. Mayhew's formula uses an exponential decay model — 100 × weight / (52.2 + 41.9 × e^(−0.055 × reps)) — that captures the non-linear drop-off in reps-per-percentage at higher loads. The formula was originally developed for bench press but generalizes well to other compound lifts. It is one of the most accurate single-formula predictors across the full 1-15 rep range.

How to use the Mayhew formula (step by step)

1. Perform a heavy submaximal set. Perform a clean set of 2-10 reps to near-failure (RPE 8-9) on the lift you want to test. Record the weight and the rep count.
2. Apply the Mayhew equation. 1RM = 100 × weight / (52.2 + 41.9 × e^(−0.055 × reps))
3. Read the estimated 1RM. The output is your estimated 1RM. For programming, multiply by 0.9 to derive your Training Max — this absorbs daily strength variability and reduces overshoot risk.
4. Cross-check against other formulas. Run the same numbers through every other formula and compare. The main calculator does this automatically using a trimmed mean.

How Mayhew compares to the other six formulas

The same submaximal set — 225 lb × 5 reps — produces different 1RM estimates depending on which formula you use. Here are all seven, side by side:

See the full formula comparison page for accuracy data and decision-making guidance.

Validation research

The Mayhew formula has been evaluated in multiple peer-reviewed studies of 1RM prediction accuracy. Selected findings:

Jerry Mayhew: 30+ years of 1RM prediction research

Dr. Jerry L. Mayhew is Professor Emeritus of Exercise Science at Truman State University and one of the most prolific researchers in 1RM prediction and athletic performance assessment. He's a Fellow of the American College of Sports Medicine and the National Strength and Conditioning Association — the two most authoritative bodies in the field — and has published more than 200 peer-reviewed papers across exercise physiology, motor performance, and load assignment.

Mayhew's 1RM work didn't stop with the 1992 paper. He has subsequently published validation studies extending his original formula to women (Mayhew et al., 2002), high school athletes, and older adults — adapting the exponential model coefficients for each population. In the strength & conditioning literature, “Mayhew” is shorthand for an entire research lineage of rigorous 1RM prediction methodology rather than a single formula.

The 1992 study: methodology and findings

The Mayhew formula came from a study published in the Journal of Applied Sport Science Research (Vol. 6, No. 4, 1992) titled “Relative Muscular Endurance Performance as a Predictor of Bench Press Strength in College Men and Women.” Methodological details that matter for understanding why the formula works:

• Sample: 251 college students (mostly bench-press-only training) — large enough that subgroup analyses by training experience were statistically meaningful.
• Test protocol: Each subject performed reps-to-fatigue at multiple percentages of their tested 1RM (typically 70%, 80%, 90%). The team then fit different mathematical models to the resulting rep × percentage data.
• Model selection: Linear, hyperbolic, and exponential functions were all evaluated. The exponential decay model — a variant of the form f(r) = A + B × e^(−k·r) — produced the lowest standard error of estimate across the full rep range tested.
• Coefficient fit: The 52.2, 41.9, and −0.055 coefficients in 1RM = 100w / (52.2 + 41.9 × e^(−0.055 × r)) come directly from the regression fit on this 251-subject dataset.

Why exponential beats linear at high reps

The fundamental insight Mayhew captured: the rate at which strength endurance falls off with repetitions is itself non-linear. Linear formulas (Epley, O'Conner) assume each additional rep removes a fixed percentage of 1RM — but real-world rep capacity drops fastest in the first few reps and flattens as you approach maximum reps to failure.

At 5 reps, the difference between linear and exponential models is small (1-3%). At 12-15 reps, it becomes substantial: a linear formula will overshoot 1RM by 5-10% because it doesn't account for the rep-capacity curve flattening. Mayhew's exponential model captures this flattening, which is why it remains accurate where Epley starts to fail.

Mayhew variants and population-specific calibrations

When Mayhew is the right formula

• Hypertrophy programming. If your working sets cluster in the 8-12 rep range, Mayhew is more accurate than Epley or Brzycki for converting those sets to a usable 1RM estimate.
• High-rep test sets (10-15 reps). Linear formulas (Epley, O'Conner) overestimate dramatically here. Mayhew stays accurate.
• Mixed-rep training data. If you have test sets at multiple rep ranges and want a single coherent estimate, Mayhew and Wathan handle the full range better than fixed-shape linear formulas.
• Reproducing peer-reviewed research. Mayhew is one of the most-cited 1RM prediction equations in the literature; if you're replicating a study that used it, use the same.
• Combined with Wathan for triangulation. The two exponential models often agree within 1-2% in the 5-10 rep range — a useful sanity check.

References

1. Original publication: Mayhew, J.L., Ball, T.E., Arnold, M.D., & Bowen, J.C. (1992). Relative muscular endurance performance as a predictor of bench press strength in college men and women. Journal of Applied Sport Science Research, 6(4), 200-206.
2. LeSuer et al. (1997): 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.
3. Reynolds et al. (2006): 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.
4. Wood et al. (2002): 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.
5. Wikipedia: One-repetition maximum — general reference for 1RM prediction equations.
6. Essentials of Strength Training and Conditioning (NSCA, Human Kinetics) — NSCA CSCS textbook chapter on load assignment.