What is the Brzycki Equation?
The Brzycki equation is a mathematical formula used to estimate the one-repetition maximum (1RM) -- the heaviest weight a person can lift for a single repetition of a given exercise. Developed by Matt Brzycki and published in 1993, the equation allows athletes and coaches to predict maximal strength from a submaximal effort, eliminating the need for a potentially risky all-out lift.
The one-rep max is the cornerstone of percentage-based strength training. Nearly every structured strength program prescribes working weights as a percentage of the 1RM. A powerlifting peaking program might call for sets at 90 to 95 percent of the 1RM, while a hypertrophy block might use 70 to 80 percent. Without knowing your 1RM, you are essentially guessing at the appropriate training load.
The Brzycki equation has become one of the most popular 1RM prediction methods because of its simplicity and reasonable accuracy for sets of up to 10 repetitions.
The Formula
The Brzycki equation is:
[\text{1RM} = \frac{W}{1.0278 - 0.0278 \times R}]
Where:
- 1RM is the estimated one-repetition maximum.
- W is the weight lifted during the set.
- R is the number of repetitions completed.
The equation is linear with respect to repetitions. As the repetition count increases, the denominator decreases, producing a higher 1RM estimate. At exactly 37 repetitions, the denominator reaches zero and the equation becomes undefined, which is why the formula is not used above 36 reps.
Calculation Example
You bench press 250 pounds for 8 repetitions before reaching failure.
Step 1: Calculate the denominator.
[\text{1.0278} - 0.0278 \times 8 = 1.0278 - 0.2224 = 0.8054]
Step 2: Divide the weight by the denominator.
[\text{1RM} = \frac{250}{0.8054} \approx 310.4 \text{ lb}]
Your estimated one-rep max for the bench press is approximately 310.4 pounds.
1RM Estimate Table (250 lb Working Weight)
| Reps | Estimated 1RM (lb) |
|---|---|
| 1 | 250.0 |
| 3 | 272.7 |
| 5 | 297.6 |
| 8 | 310.4 |
| 10 | 333.3 |
| 12 | 360.6 |
Notice how the estimate grows less reliable as repetitions increase. The jump from 10 to 12 reps adds nearly 30 pounds to the estimate, reflecting the equation's diminishing accuracy at higher rep ranges.
Using Your 1RM for Training
Once you know your estimated 1RM, you can programme training weights for any goal:
- Maximal strength (1-5 reps): Use 85 to 100 percent of your 1RM. This range builds pure strength by recruiting the largest motor units and training the nervous system to produce maximal force.
- Hypertrophy (6-12 reps): Use 67 to 85 percent of your 1RM. This range balances mechanical tension with metabolic stress to stimulate muscle growth.
- Muscular endurance (12-20+ reps): Use 50 to 67 percent of your 1RM. This range trains the muscle's ability to sustain repeated contractions over time.
For example, if your estimated bench press 1RM is 310 pounds and your programme calls for 5 sets of 5 at 80 percent, your working weight would be 310 × 0.80 = 248 pounds. You would round to the nearest available increment -- 250 pounds on a standard barbell.
Comparing 1RM Equations
Several 1RM prediction equations exist, each with different assumptions:
| Equation | Formula | Best Range |
|---|---|---|
| Brzycki | W / (1.0278 - 0.0278 × R) | 1 - 10 reps |
| Epley | W × (1 + R / 30) | 1 - 10 reps |
| Lander | 100 × W / (101.3 - 2.67 × R) | 1 - 10 reps |
| O'Conner | W × (1 + 0.025 × R) | 1 - 10 reps |
The Brzycki and Epley equations are the most widely used. They produce nearly identical results at low rep counts but diverge at higher reps, with Epley tending to produce higher estimates. For practical purposes, either equation is acceptable for sets of 10 or fewer reps.
Common Mistakes in 1RM Estimation
Several pitfalls reduce the accuracy of 1RM predictions and lead to poor training decisions:
Stopping short of failure. The Brzycki equation assumes you performed the maximum possible number of repetitions with the given weight. If you stopped two reps short of true failure because of discomfort or caution, the calculator will underestimate your 1RM. The resulting training weights will be too light to produce optimal adaptations. If you are unsure whether you reached failure, err on the side of reporting one fewer rep rather than one more.
Using high rep counts. The equation's accuracy degrades significantly above 10 repetitions. At 15 reps, individual differences in muscular endurance dominate the prediction, and two lifters with identical 1RM values may produce very different rep counts. If your test set exceeds 10 reps, increase the weight and retest with a heavier load that limits you to the 3-to-8 rep range.
Testing while fatigued. Performing the test set after a full workout produces artificially low rep counts and underestimates the 1RM. The test set should come early in the session, after a thorough warm-up but before accumulated fatigue sets in. A good protocol is: warm up with progressively heavier sets of 5, 3, and 1 rep, then perform one all-out set at the target weight.
Ignoring exercise specificity. The Brzycki equation was validated primarily on major barbell lifts. Its accuracy varies by exercise. Compound multi-joint movements like squats and bench press produce more consistent results than isolation exercises like bicep curls or leg extensions, where fatigue and form breakdown follow different patterns.
Exercise-Specific Considerations
Different exercises produce different relationships between submaximal reps and the true 1RM. The bench press and squat track the Brzycki prediction closely because they involve large muscle groups working through a consistent range of motion. The deadlift tends to produce lower rep counts at a given percentage of 1RM because grip fatigue and spinal loading limit endurance more than pure muscular strength.
For overhead pressing movements, the prediction is generally accurate but shoulder fatigue and stabiliser weakness can limit reps independently of the primary mover strength. For machine-based exercises, the prediction may be inflated because the guided movement path eliminates the stabiliser demand that limits free-weight performance.
Practical Tips for Accurate Estimates
- Use sets of 3 to 7 reps. The equation is most accurate in this range. Sets of 1 to 2 reps leave little room for prediction, and sets above 10 introduce too much endurance variability.
- Go to true failure. The equation assumes you performed as many reps as physically possible. If you stopped short of failure, the estimated 1RM will be lower than your actual capability.
- Use compound lifts. The equation works best for multi-joint exercises like the squat, bench press, deadlift, and overhead press. It is less reliable for isolation exercises where fatigue patterns differ.
- Retest regularly. Strength changes over time with training. Re-estimate your 1RM every 4 to 8 weeks to keep your training weights appropriately calibrated.
- Warm up thoroughly. A fatigued muscle produces fewer reps with a given weight, leading to an underestimate. Complete a proper warm-up before your test set to ensure the result reflects your true capability.