Brzycki Formula: 1RM Calculator and Complete Guide

History and origin

Matt Brzycki published his 1RM prediction formula in 1993 in the Journal of Physical Education, Recreation & Dance. Brzycki was Strength Coach at Princeton and worked extensively with collegiate athletes; he developed the formula by analyzing rep-to-failure performance against tested 1RMs in trained populations. The formula is essentially a hyperbolic function — 1RM = weight × 36/(37 − reps) — that accounts for the non-linear drop-off in strength as reps accumulate. Because Brzycki's equation is grounded in a larger sample of trained athletes than Epley's original work, it is the most commonly cited formula in peer-reviewed 1RM prediction research.

How to use the Brzycki 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 Brzycki equation. 1RM = weight × 36 / (37 − 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 Brzycki 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 Brzycki formula has been evaluated in multiple peer-reviewed studies of 1RM prediction accuracy. Selected findings:

Matt Brzycki: the Princeton background

Matt Brzycki served for over three decades as the Coordinator of Recreational Fitness and Wellness Programs at Princeton University, with previous roles at Rutgers and the University of Massachusetts. He is one of the most prolific writers in the strength & conditioning literature: more than 500 articles across JOPERD, Scholastic Coach, Athletic Journal, and several books on resistance training methodology.

Brzycki is associated with the High-Intensity Training (HIT) school of strength coaching — the Arthur Jones / Mike Mentzer / Ellington Darden tradition that emphasizes single-set-to-failure work. His 1RM formula was developed from observations of HIT-style athletes performing reps-to-fatigue with submaximal weights. Despite the HIT origin, the formula generalizes well to non-HIT populations and has been re-validated repeatedly in the broader literature.

The 1993 paper that introduced his equation — “Strength Testing — Predicting a One-Rep Max from Reps-to-Fatigue”, published in the Journal of Physical Education, Recreation & Dance (Vol. 64, No. 1, pp. 88-90) — is one of the most-cited references in 1RM prediction research. Researchers favor it over Epley because it appeared in a peer-reviewed publication with explicit derivation methodology, making it directly citable.

Mathematical derivation

The Brzycki equation has the form 1RM = w × 36 / (37 − r). The 36 and 37 aren't arbitrary — they fall out of fitting a hyperbolic function to rep-to-failure data with two specific anchor points:

• At r = 1: 1RM = w × 36/(37-1) = w × 36/36 = w. (A 1-rep max is the weight you lifted — the formula is self-consistent.)
• At r = 10: 1RM = w × 36/27 = 1.333w. (A 10RM is approximately 75% of 1RM — Brzycki's assumption.)
• At r = 37: The denominator becomes zero and the formula is undefined. Brzycki considered any rep count approaching this asymptote unreliable as a max predictor.

The hyperbolic structure captures the non-linear nature of strength endurance better than Epley's linear model. As reps climb from 5 to 10, the per-rep contribution to 1RM decreases — exactly what hyperbolic functions produce. The asymptotic behavior near r = 37 is a feature, not a bug: it tells you the formula has a hard validity ceiling.

Brzycki vs Epley at common rep ranges

For a 225 lb working set, here's how the two formulas diverge across rep counts:

The two formulas converge around 10 reps, with Brzycki exceeding Epley above that and Epley exceeding Brzycki below it. For most testing rep ranges (3-8), Brzycki produces the lower (more conservative) number.

Brzycki in research literature

Brzycki's formula is the default reference in 1RM prediction research. Selected papers that used it as a primary or comparator equation:

• LeSuer et al. (1997) — Foundational comparative study of seven 1RM prediction equations on bench, squat, deadlift. Brzycki produced one of the lowest standard error of estimates for bench press.
• Reynolds et al. (2006) — 1RM prediction validation across multiple rep-max protocols. Brzycki was the recommended formula for low-rep ranges.
• Mayhew et al. (1992) — Used Brzycki as a baseline for evaluating their own exponential model on bench press.
• Wood et al. (2002) — Older-adult 1RM prediction study; Brzycki produced acceptable accuracy with a slight tendency to overestimate.

When to choose Brzycki over the alternatives

• Reproducing peer-reviewed research. If a study used Brzycki, replicate with Brzycki for direct comparability.
• Trained athlete in low-rep range (1-6). Brzycki + Wathan agree closely here and are the most accurate single formulas.
• Conservative programming starting point. For a new training cycle, Brzycki's output below 10 reps tends to err on the lower side of Epley — fewer overshoot risks.
• Multi-formula averaging. Brzycki is one of the seven formulas our main calculator averages with a trimmed mean — it consistently appears in the “middle five” that contribute to the final estimate.

References

1. Original publication: Brzycki, M. (1993). Strength testing—Predicting a one-rep max from reps-to-fatigue. Journal of Physical Education, Recreation & Dance, 64(1), 88-90.
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.