1RM Formulas Compared: Epley, Brzycki and 4 More
Which 1RM formula is most accurate? None is best for everyone. The six common formulas were built from different lifters and different maths, and studies have found their accuracy changes with the exercise and the number of reps. For a set of 3–6 hard reps they all land within about 6–8% of each other; above 10 reps they drift much further apart.
What a 1RM formula does
A one rep max (1RM) formula predicts the heaviest single you could lift from a set you did for several reps. Every formula takes the weight lifted (w) and the reps completed (r) and returns an estimated 1RM. The difference between them is the shape of the relationship they assume:
- Linear formulas (Epley, O’Conner) add a fixed percentage per rep.
- Brzycki rises slowly at first and then steeply as reps climb.
- Lombardi is a power curve that flattens out at higher reps.
- Mayhew and Wathan are exponential curves fitted to measured data.
| Formula | Equation | Origin | How it behaves |
|---|---|---|---|
| Epley | 1RM = w × (1 + r ÷ 30) | Boyd Epley’s 1985 poundage chart — a coaching tool rather than a peer-reviewed study. | Linear: adds 3.33% per rep. Sits in the middle of the six from 2 to 10 reps. |
| Brzycki | 1RM = w × 36 ÷ (37 − r) | Matt Brzycki, Journal of Physical Education, Recreation & Dance (1993). | Lowest of the six at 2–5 reps (tied with O’Conner at 5), identical to Epley at 10 reps, and highest at 11–12 reps as its curve steepens. Undefined at 37 reps. |
| Lombardi | 1RM = w × r^0.10 | V. P. Lombardi’s textbook Beginning Weight Training (1989). | Power curve that flattens as reps rise: mid-pack at low reps, lowest of the six at 11–12 reps. |
| Mayhew | 1RM = 100w ÷ (52.2 + 41.9e^(−0.055r)) | Mayhew and colleagues (1992), fitted to bench-press data from college men and women. | Exponential. Highest of the six at 1–6 reps: it is not anchored to a single (it gives about 109% of the weight for 1 rep), so it reads high on very heavy sets. |
| O'Conner | 1RM = w × (1 + 0.025 × r) | O’Conner, Simmons and O’Shea’s textbook Weight Training Today (1989). | Linear: adds 2.5% per rep. Lowest of the six at 6–10 reps. |
| Wathan | 1RM = 100w ÷ (48.8 + 53.8e^(−0.075r)) | Dan Wathen’s chapter in the NSCA textbook Essentials of Strength Training and Conditioning (1994); often spelled “Wathan”. | Exponential. Within about 1% of Epley at 3–8 reps and highest of the six at 7–10 reps. |
w = weight lifted, r = reps completed, e ≈ 2.718.
The formulas compared, rep by rep
The table below shows each formula’s estimate as a percentage of the weight you lifted. It is generated from the same code the calculator runs, so the two always match.
| Reps | Epley | Brzycki | Lombardi | Mayhew | O'Conner | Wathan | Average | Spread |
|---|---|---|---|---|---|---|---|---|
| 2 | 106.7% | 102.9% | 107.2% | 111.4% | 105.0% | 105.1% | 106.4% | 8.3% |
| 3 | 110.0% | 105.9% | 111.6% | 114.0% | 107.5% | 109.0% | 109.7% | 7.7% |
| 4 | 113.3% | 109.1% | 114.9% | 116.5% | 110.0% | 112.8% | 112.8% | 6.8% |
| 5 | 116.7% | 112.5% | 117.5% | 119.0% | 112.5% | 116.6% | 115.8% | 5.8% |
| 6 | 120.0% | 116.1% | 119.6% | 121.5% | 115.0% | 120.3% | 118.8% | 5.6% |
| 7 | 123.3% | 120.0% | 121.5% | 123.9% | 117.5% | 124.0% | 121.7% | 5.6% |
| 8 | 126.7% | 124.1% | 123.1% | 126.3% | 120.0% | 127.7% | 124.6% | 6.4% |
| 9 | 130.0% | 128.6% | 124.6% | 128.6% | 122.5% | 131.2% | 127.6% | 7.1% |
| 10 | 133.3% | 133.3% | 125.9% | 130.9% | 125.0% | 134.7% | 130.5% | 7.8% |
| 11 | 136.7% | 138.5% | 127.1% | 133.2% | 127.5% | 138.2% | 133.5% | 8.9% |
| 12 | 140.0% | 144.0% | 128.2% | 135.4% | 130.0% | 141.5% | 136.5% | 12.3% |
Read across a row: for a set of 100 lb (or kg) × 5 reps, Epley estimates 116.7, Mayhew 119.0. “Spread” is the gap between the highest and lowest formula, relative to the lowest.
What the comparison shows
- The formulas agree most closely at 5–7 reps, where the spread is under 6%.
- They disagree more at 1–3 reps, mostly because Mayhew is not anchored to a single: for one rep it returns about 109% of the weight, so it reads high on very heavy sets. (StrengthCalc never estimates from a single — 1 rep returns the weight you lifted.)
- They diverge most above 10 reps. At 12 reps the spread is over 12%: Brzycki has become the highest estimate and Lombardi the lowest.
- O’Conner is the most conservative formula from 6 to 10 reps; Wathan is the most generous from 7 to 10.
Why the formulas disagree
Each equation was developed from a different group of people, a different lift or a different method. Epley’s formula comes from a coaching chart; Mayhew’s was fitted to bench-press data from college men and women; Wathen’s appeared in an NSCA textbook. None was designed to be universal, so none should be expected to fit every lifter on every lift.
Your own muscular endurance matters too. Two lifters with the same 1RM can do very different numbers of reps at 80% of it — and a formula can only assume an average.
What research says about accuracy
- In a comparison of seven equations against tested maxes in college students, predictions were strongly correlated with real 1RMs, but every equation significantly underestimated the deadlift (LeSuer et al., 1997). Accuracy, in other words, depends on the lift.
- In a study of 70 adults, predictions from a 5-rep maximum were more accurate than from 10- or 20-rep maximums (Reynolds et al., 2006).
Both findings point the same way: estimate from a heavy set of roughly 3–6 reps, and expect lift-to-lift differences.
When estimates become less reliable
- More than about 10 reps. The formulas diverge and fatigue, not strength, ends the set. StrengthCalc warns above 10 reps and shows no number above 12.
- Reps that were not to (or near) failure. If you could have done two more, the estimate reads low.
- Inconsistent technique — bounced, half-range or loosened reps make the set easier than a strict single and inflate the estimate.
- Lifts the formulas were not studied on, such as rows or isolation exercises.
Why StrengthCalc shows all six, plus an average
Showing one formula hides how uncertain an estimate is. StrengthCalc shows all six and the Average Estimate — the plain arithmetic mean of the six. The average is a convenient summary of where the formulas cluster; it is not a scientifically validated consensus, and we do not claim it beats any individual formula. The spread between the lowest and highest result is just as important: a wide spread is a sign to treat the number cautiously.
Lander’s formula, which appears on some calculators, is not included until its equation can be verified against its original published source. See the methodology for every other rule the calculator follows.