1RM Formulas Explained: Epley vs. Brzycki vs. Lombardi (Which Is Most Accurate)
Compare the Epley, Brzycki, Lombardi, and other 1RM formulas used to estimate one-rep max from submaximal sets, including which is most accurate by rep range and lift.
1RM Formulas Explained: Epley vs. Brzycki vs. Lombardi (Which Is Most Accurate)
No single 1RM formula is most accurate across every rep range — the Epley formula performs best above 6 reps, the Brzycki formula performs best at 1-5 reps, and both lose accuracy past 10-12 reps. A 1RM formula estimates a one-rep max (1RM) from a submaximal set’s weight and rep count, without requiring a lifter to attempt an actual single-rep maximum. Every formula relies on the same underlying assumption: that strength declines in a predictable, measurable pattern as reps increase, which holds reasonably well within a moderate rep range and breaks down at the extremes.
These formulas serve 3 main purposes. They estimate 1RM without the injury risk of a maximal attempt. They give lifters and coaches a way to set training percentages between max tests. They provide a comparison point for tracking strength changes over time, since a formula applied consistently to similar rep ranges reveals a trend even when the absolute number carries some error.
The main formulas in use today are the Epley formula, the Brzycki formula, and the Lombardi formula, with the O’Conner, Wathan, and Mayhew formulas appearing in some calculators as well. All 6 take the same 2 inputs — weight lifted and reps performed — and apply different mathematical relationships to estimate 1RM.
What Is a 1RM Formula?
A 1RM formula is an equation that converts a submaximal set’s weight and rep count into an estimated one-rep max. Every formula assumes a fixed relationship between reps performed and percentage of 1RM, then works backward from a lifter’s actual set to estimate the maximum weight they could lift for a single rep.
The formulas differ in the mathematical curve they use to describe that relationship. Some, like Epley, use a simple linear adjustment. Others, like Wathan and Mayhew, use an exponential curve intended to better match how strength actually declines as reps increase.
The Epley Formula
The Epley formula estimates 1RM as: 1RM = weight × (1 + reps ÷ 30). Developed by Boyd Epley, a strength coach who helped establish sports performance training programs in American college athletics, the formula uses a simple linear relationship between reps and estimated max.
A lifter squatting 275 lb (125 kg) for 8 reps gets an Epley estimate of 275 × (1 + 8/30) = 348 lb (158 kg). The Epley formula tends to overestimate 1RM as rep count rises past 10, since its linear structure doesn’t account for the accelerating strength decline that happens at higher rep counts.
The Brzycki Formula
The Brzycki formula estimates 1RM as: 1RM = weight × 36 ÷ (37 − reps). Developed by Matt Brzycki, an exercise science researcher and strength coach, the formula assumes a slightly different curve than Epley, built around the idea that roughly 37 reps represents a practical upper limit before the formula’s structure breaks down entirely.
The same 275 lb (125 kg) for 8 reps produces a Brzycki estimate of 275 × 36 ÷ 29 = 341 lb (155 kg), close to the Epley figure at this rep range but diverging more as reps increase further. The Brzycki formula tends to be more accurate at low rep counts (1-5 reps) and tends to underestimate 1RM at higher rep counts, since the formula becomes mathematically unstable as reps approach 37.
The Lombardi Formula
The Lombardi formula estimates 1RM as: 1RM = weight × reps^0.10. This formula uses an exponential relationship rather than the linear or near-linear structures Epley and Brzycki rely on. The same 275 lb (125 kg) for 8 reps produces a Lombardi estimate of 275 × 8^0.10 ≈ 275 × 1.233 = 339 lb (154 kg).
The Lombardi formula tends to produce more conservative estimates than Epley at higher rep counts, though it’s used less frequently in modern calculators than Epley or Brzycki.
Other 1RM Formulas: O’Conner, Wathan, and Mayhew
The O’Conner formula estimates 1RM as weight × (1 + 0.025 × reps), a linear formula similar in structure to Epley but with a slightly more conservative multiplier.
The Wathan formula estimates 1RM as (100 × weight) ÷ (48.8 + 53.8 × e^(−0.075 × reps)), an exponential formula designed to model strength decline more precisely across a wider rep range than the simpler linear formulas.
The Mayhew formula estimates 1RM as (100 × weight) ÷ (52.2 + 41.9 × e^(−0.055 × reps)), developed from research specifically on bench press performance, which makes it more commonly referenced for upper-body pressing estimates than for squat or deadlift.
Accuracy Comparison by Rep Range
The table below shows how each formula’s estimate compares at different rep counts, using a lifter capable of a true 315 lb (143 kg) 1RM performing progressively lighter sets at higher reps.
| Reps | True % of 1RM (research-based) | Epley Estimate | Brzycki Estimate |
|---|---|---|---|
| 2 | 95-97% | Close match | Close match |
| 5 | 85-87% | Slight overestimate | Close match |
| 8 | 75-78% | Close match | Slight underestimate |
| 12 | 65-68% | Overestimate | Underestimate |
| 15+ | 60% or below | Significant overestimate | Significant underestimate |
Both formulas stay reasonably close to a true 1RM within the 2-8 rep range, which is why most programs base 1RM formula estimates on sets in that window rather than higher-rep sets.
Which Formula Is Most Accurate for Squat, Bench, and Deadlift
Bench press formula estimates tend to be the most accurate of the 3 competition lifts across all formulas, since bench press strength decline across a rep range follows a more consistent pattern than squat or deadlift, which are affected more by systemic fatigue. Squat and deadlift formula estimates run less reliable above 8 reps for the same reason RPE ratings run less reliable at high squat and deadlift rep counts: cardiovascular and central nervous system fatigue start to influence rep count independent of true muscular strength.
The Mayhew formula, developed specifically from bench press research, sometimes produces a closer estimate for bench press than Epley or Brzycki, though the difference is typically small within the 2-8 rep range.
Limitations of Formula-Based 1RM Estimates
Every 1RM formula assumes a fixed, universal relationship between reps and percentage of 1RM, but this relationship actually varies by individual, by lift, and by training background. A lifter with strong muscular endurance can complete more reps at a given percentage than a lifter with less endurance but equal maximal strength, which produces a formula estimate that overstates the endurance-focused lifter’s true 1RM.
Technique breakdown at higher reps introduces further error, since a set of 10 performed with degrading form doesn’t represent the same relative intensity as a set of 10 performed with consistent technique throughout. Formulas also can’t account for a lifter’s daily readiness — 2 identical sets performed on different days, one after good sleep and one after poor sleep, produce the same formula estimate despite representing different actual proximity to a true maximum that day.
How 1RM Formulas Relate to an RPE Calculator
A 1RM formula estimates max using only weight and reps, with no adjustment for how the set actually felt. An RPE calculator adds a third input — rate of perceived exertion (RPE) — which accounts for daily readiness in a way pure formulas can’t. A set of 5 reps at a genuinely hard RPE 9 and a set of 5 reps at an easier RPE 7 produce different e1RM estimates from an RPE calculator, while a formula-based calculator would treat both sets identically since it only sees the rep count.
This is why intermediate and advanced lifters commonly move from formula-based 1RM calculators toward RPE-based calculators once their RIR judgment develops: the formula gives a reasonable starting estimate, but the RPE-based approach captures day-to-day variation the formula structurally cannot. For a full comparison of the two approaches, see RPE Calculator vs. 1RM Percentage Calculator: Which Should You Use?
Tools for Calculating 1RM
Working through any of these formulas by hand means picking 1 equation and trusting it evenly across every rep range, which is where the accuracy gaps described above start to matter. The RPE calculator on this site incorporates RPE alongside weight and reps, giving a more complete estimate than a formula relying on rep count alone, particularly for lifters with developed RIR judgment. For a straightforward formula-based estimate without RPE, the 1RM calculator applies all 6 formulas and returns the results side by side.
FAQ
Which 1RM formula is most accurate? No single formula is most accurate across all rep ranges. The Brzycki formula tends to be more accurate at 1-5 reps, while the Epley formula tends to be more accurate at 6-10 reps. Accuracy drops for every formula above 10-12 reps.
What is the Epley formula for 1RM? The Epley formula is 1RM = weight × (1 + reps ÷ 30). It uses a linear relationship between reps performed and estimated maximum, developed by strength coach Boyd Epley.
What is the Brzycki formula for 1RM? The Brzycki formula is 1RM = weight × 36 ÷ (37 − reps), developed by researcher and strength coach Matt Brzycki. It’s generally considered more accurate than Epley at lower rep counts.
Is the Lombardi formula reliable? The Lombardi formula (weight × reps^0.10) produces reasonable estimates within a moderate rep range, though it’s used less often in modern calculators than the Epley or Brzycki formulas.
Why do different 1RM formulas give different results for the same set? Each formula uses a different mathematical curve to model the relationship between reps and percentage of 1RM. The formulas agree closely within a 2-8 rep range and diverge more as rep count increases past that range.
Can 1RM formulas be used for any exercise? Yes, though they’re most accurate for barbell compound lifts like squat, bench press, and deadlift, where a large research base exists. Formula estimates for isolation exercises and machines carry more uncertainty, since less research has validated the same rep-to-percentage relationship for those movements.
How many reps should I use to estimate my 1RM with a formula? Use sets of 2-8 reps for the most reliable formula-based estimate. Estimates from sets above 10-12 reps carry significantly more error for every common formula.
Do 1RM formulas account for how hard a set felt? No, standard 1RM formulas use only weight and reps as inputs, with no adjustment for perceived effort. An RPE calculator adds this missing input by incorporating a rated effort level alongside weight and reps.
Is the Mayhew formula better than Epley for bench press? The Mayhew formula was developed specifically from bench press research and can produce a closer estimate for that lift in some cases, though the practical difference from Epley or Brzycki is typically small within a 2-8 rep range.
Why does my formula-estimated 1RM not match my actual tested max? Formula estimates assume a fixed rep-to-percentage relationship that doesn’t perfectly apply to every individual. Differences in muscular endurance, technique consistency, and daily readiness all cause a formula estimate to diverge from an actual tested 1RM.
Should I trust a 1RM formula over an actual max test? An actual tested 1RM is more accurate than any formula estimate, when performed safely with proper warm-up. Formula estimates are most useful when a maximal attempt isn’t practical or safe, such as during a high-fatigue training phase.
Do these formulas work the same way for men and women? The underlying formulas apply the same equation regardless of sex, since they’re based on the mathematical relationship between reps and percentage of 1RM rather than absolute strength levels, which do differ by population.
How accurate are 1RM formulas for deadlift specifically? Deadlift formula estimates run less accurate above 8 reps compared to bench press, since systemic fatigue affects deadlift rep count more than upper-body pressing movements, introducing error into the assumed rep-to-percentage relationship.
Can I use a 1RM formula to set my training percentages for an entire program? Yes, many programs use a formula-estimated 1RM as a starting reference point, then adjust percentages over time based on actual training performance rather than relying on a single static formula estimate indefinitely.
What’s the difference between the Epley and O’Conner formulas? Both use a similar linear structure, but the O’Conner formula (weight × (1 + 0.025 × reps)) uses a slightly more conservative multiplier than the Epley formula (weight × (1 + reps ÷ 30)), producing marginally lower estimates at the same rep count.
Why do some calculators average multiple formulas together? Averaging multiple formulas can smooth out the specific overestimation or underestimation pattern of any single formula, though this approach still can’t account for individual variation in muscular endurance or daily readiness the way an RPE-based estimate can.
Is a 1-rep set the most accurate way to know my 1RM? Yes, a properly performed 1-rep maximal attempt is definitionally the most accurate measure of 1RM, since it removes the estimation step entirely. Formula estimates exist as an alternative when a maximal attempt isn’t the safest or most practical option that day.
Do 1RM formulas work for advanced lifters the same way as beginners? Formula accuracy doesn’t depend heavily on training age directly, though advanced lifters with well-developed muscular endurance can sometimes see formulas overestimate their 1RM more than a beginner would, since higher-rep sets stay closer to true failure for endurance-trained lifters.
How often should I recalculate my 1RM using a formula? Recalculate whenever a new relevant working set is logged, particularly after a noticeable change in training performance, rather than relying on a single formula estimate for many weeks or months.
Can I combine a 1RM formula with RPE for a more accurate estimate? Yes, this is exactly what an RPE-based calculator does: it uses the same underlying percentage relationship a formula relies on, while adding perceived effort as a third input to account for daily variation a formula-only estimate misses.
Get a more complete estimate than a formula alone — open the RPE calculator and factor in how your last set actually felt, or try the 1RM calculator for a quick formula-based estimate.