Multiple formulas exist for estimating your one-rep max (E1RM) from a multi-rep set. The most common are Epley, Brzycki, Lombardi, McGlothin, Mayhew, Wathen, and O'Conner. Each produces different results at different rep ranges, and no single formula is universally most accurate. This page compares all major formulas, shows how they differ, and lets you calculate your E1RM with all of them simultaneously.
Epley Formula
Strengths
- Most widely cited formula in strength research
- Simple linear structure - easy to calculate by hand
- Reasonable accuracy across most practical rep ranges
- Default formula in many strength tracking apps
- Works equally well for upper and lower body lifts
Limitations
- Overestimates at very high rep ranges (15+)
- Does not account for RPE (actual proximity to failure)
- Same formula for all lifts regardless of exercise specificity
Best When
Use Epley as your primary formula for day-to-day E1RM tracking, as it is the most commonly cited and widely understood. When comparing E1RM across different apps and calculators, Epley is usually the default, making comparisons easier.
Brzycki Formula
Strengths
- Very similar accuracy to Epley for most lifters
- Well-researched in US academic settings
- Slightly more conservative at 8-10 reps
- Built into many NSCA-certified trainer tools
Limitations
- Becomes mathematically undefined above 36 reps
- Small accuracy gap vs Epley typically within measurement error
- Like all formulas, does not account for RPE or effort level
Best When
Use Brzycki if you are following an NSCA-certified program that specifies the Brzycki formula, or if you prefer a slightly more conservative estimate at the 8-10 rep range. At most rep ranges the difference from Epley is negligible.
Side-by-Side Comparison
| Attribute | Epley Formula | Brzycki Formula |
|---|---|---|
| Formula | Epley (1985) | Brzycki (1993) |
| Equation | 1RM = w * (1 + r/30) | 1RM = w * (36 / (37 - r)) |
| Best for | Rep ranges 1-10 | Rep ranges 1-10 |
| At 10 reps | Slightly higher estimate | Slightly lower estimate |
| At 1 rep | Exact (returns input weight) | Exact (returns input weight) |
| Popularity | Most widely cited | Common in US strength research |
All E1RM Formulas
| Formula | Equation | Notes |
|---|---|---|
| Epley (1985) | w × (1 + r/30) | Most cited; works well for 1-10 reps |
| Brzycki (1993) | w × (36 / (37 - r)) | Common in US strength research; similar to Epley |
| Lombardi (1989) | w × r^0.10 | Tends to overestimate at higher reps |
| Mayhew (1992) | 100w / (52.2 + 41.9 × e^(-0.055 × r)) | Based on large sample research; good for 6-20 reps |
| O'Conner (1989) | w × (1 + 0.025 × r) | Conservative estimate; useful for beginners |
| Wathen (1994) | 100w / (48.8 + 53.8 × e^(-0.075 × r)) | Used in NSCA recommendations |
| McGlothin (1989) | 100w / (101.3 - 2.67123 × r) | Linear approximation; simple but less accurate at extremes |
Compare All E1RM Formulas
Enter your weight and reps to see every formula's estimate side by side.
| Formula | E1RM () | vs Average |
|---|---|---|
| Average | - | |
| RPE-Adjusted | Most accurate |
Verdict
For practical training use, the differences between all major E1RM formulas are small enough that they rarely change programming decisions. The RPE-adjusted approach (entering your RPE along with weight and reps) is more accurate than any fixed formula because it accounts for how close you actually were to failure. Use the calculator below to see all formulas at once - the average of multiple formulas typically outperforms any single formula.
Why E1RM Formulas Give Different Results
Every E1RM formula is derived from statistical regression on a sample of lifters. The formula that best fits the data depends on who was in the sample (powerlifters, recreational lifters, athletes), what exercises were tested, and the rep ranges studied. This is why formulas diverge more at high rep ranges - the data gets sparse and noisy above 10 reps.
The fundamental limitation of all rep-based E1RM formulas is that they assume you performed a set to failure, or very close to it. If you did 5 reps with 100kg but had 5 more reps in reserve, the formula will dramatically underestimate your 1RM. This is precisely why RPE-adjusted E1RM calculations are more accurate - they account for the actual proximity to failure.
In practice, the difference between formulas at common training rep ranges (3-8 reps) is typically 2-5% - small enough that it rarely changes which weights you load on the bar. The more important variable is accurate RPE rating.
RPE-Adjusted E1RM: The More Accurate Approach
Standard E1RM formulas assume you trained to failure or near-failure. RPE-adjusted E1RM combines the formula output with the Tuchscherer RPE chart to account for how many reps you had left. The process: calculate a raw E1RM from weight and reps, then adjust upward based on RPE (since RPE 8 means you had 2 reps left, your actual 1RM is higher than the formula suggests from a 2-rep-easy set).
For example: if you do 5 reps with 100kg at RPE 8, a simple formula gives an E1RM of roughly 116kg. But the RPE chart tells us that 5 reps at RPE 8 corresponds to 86% of 1RM, giving an E1RM of 100/0.86 = 116kg - which happens to align well. At RPE 6, however, the formulas diverge significantly from RPE-adjusted estimates because the set was far from failure.
The E1RM calculator on this site always applies RPE adjustment when an RPE value is entered, giving you a more accurate estimate than any formula alone.
Accuracy Comparison: Which Formula Wins?
Multiple studies have compared E1RM formula accuracy, and the results consistently show no single formula wins across all scenarios. Epley and Brzycki tend to perform best for 1-10 reps and are most commonly used in research. Mayhew and Wathen are designed for higher rep ranges (6-20). Lombardi tends to overestimate, particularly at higher reps.
A practical recommendation from the research: when precision matters, use the average of multiple formulas rather than any single one. Averaging Epley, Brzycki, and one exponential model (Mayhew or Wathen) typically reduces error compared to any individual formula.
The E1RM calculator on this site shows all formulas simultaneously so you can see the full range and use the average for the most robust estimate. When RPE is entered, the RPE-adjusted estimate is shown prominently as the most accurate option.
Frequently Asked Questions
Calculations are for educational purposes. Individual results vary. Always consult your federation rulebook for official scoring and equipment rules.