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Formula comparison

1RM Formula Comparison

Same submaximal set, seven different formulas, side by side. Use this page to see which formulas converge, which formulas diverge, and which result is safest for programming.

Seven formulas
Five worked examples
Dataset schema

What this comparison answers

Most 1RM calculators ask for weight and reps, then return one precise-looking number. That hides the uncertainty. The same 100 kg x 5 set can mean different things depending on whether the calculator uses Epley, Brzycki, Lombardi, O'Conner, Mayhew, Wathan, or Lander.

This page keeps the input fixed and shows every formula. If all seven estimates land close together, the input set is probably useful. If the range is wide, the set may be too high-rep, too far from failure, or too technique-dependent to produce a confident training max.

Formula reference

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Formula Equation Model Best range
Epley 1RM = w x (1 + r / 30) linear rep multiplier 2-8 reps
Brzycki 1RM = w x 36 / (37 - r) linear denominator model 1-6 reps
Lombardi 1RM = w x r^0.10 power curve 2-10 reps
O'Conner 1RM = w x (1 + 0.025r) linear rep multiplier 2-8 reps
Mayhew 1RM = 100w / (52.2 + 41.9 x e^(-0.055r)) exponential decay model 2-10 reps
Wathan 1RM = 100w / (48.8 + 53.8 x e^(-0.075r)) exponential decay model 2-10 reps
Lander 1RM = 100w / (101.3 - 2.67123r) linear denominator model 2-10 reps

Example 1: 100 kg x 5 reps

A typical moderate-rep strength set where most formulas should converge.

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Formula Calculation 1RM estimate Note
Epley 100 x (1 + 5 / 30) 116.7 kg practical default; often higher than Brzycki as reps rise
Brzycki 100 x 36 / (37 - 5) 112.5 kg conservative; often lower than Epley and Wathan
Lombardi 100 x 5^0.10 117.5 kg non-linear; often near the middle for common rep ranges
O'Conner 100 x (1 + 0.025 x 5) 112.5 kg conservative linear estimate; often close to Brzycki
Mayhew 100 x 100 / (52.2 + 41.9 x e^(-0.055 x 5)) 119 kg research-derived curved model; often useful as an upper-body cross-check
Wathan 100 x 100 / (48.8 + 53.8 x e^(-0.075 x 5)) 116.6 kg curved model; often near Epley for moderate reps
Lander 100 x 100 / (101.3 - 2.67123 x 5) 113.7 kg middle estimate; often between Brzycki and Epley

Range: 112.5 kg - 119 kg. Mean: 115.5 kg. Recommendation: use the middle of the range when the set was clean, and use the lower third when the set was high-rep, grindy, or technically inconsistent.

Example 2: 225 lb x 8 reps

A higher-rep bench-style example where aggressive formulas begin to separate.

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Formula Calculation 1RM estimate Note
Epley 225 x (1 + 8 / 30) 285 lb practical default; often higher than Brzycki as reps rise
Brzycki 225 x 36 / (37 - 8) 279.4 lb conservative; often lower than Epley and Wathan
Lombardi 225 x 8^0.10 277 lb non-linear; often near the middle for common rep ranges
O'Conner 225 x (1 + 0.025 x 8) 270 lb conservative linear estimate; often close to Brzycki
Mayhew 100 x 225 / (52.2 + 41.9 x e^(-0.055 x 8)) 284.1 lb research-derived curved model; often useful as an upper-body cross-check
Wathan 100 x 225 / (48.8 + 53.8 x e^(-0.075 x 8)) 287.3 lb curved model; often near Epley for moderate reps
Lander 100 x 225 / (101.3 - 2.67123 x 8) 281.5 lb middle estimate; often between Brzycki and Epley

Range: 270 lb - 287.3 lb. Mean: 280.6 lb. Recommendation: use the middle of the range when the set was clean, and use the lower third when the set was high-rep, grindy, or technically inconsistent.

Example 3: 60 kg x 3 reps

A low-rep example where almost every formula lands close together.

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Formula Calculation 1RM estimate Note
Epley 60 x (1 + 3 / 30) 66 kg practical default; often higher than Brzycki as reps rise
Brzycki 60 x 36 / (37 - 3) 63.5 kg conservative; often lower than Epley and Wathan
Lombardi 60 x 3^0.10 67 kg non-linear; often near the middle for common rep ranges
O'Conner 60 x (1 + 0.025 x 3) 64.5 kg conservative linear estimate; often close to Brzycki
Mayhew 100 x 60 / (52.2 + 41.9 x e^(-0.055 x 3)) 68.4 kg research-derived curved model; often useful as an upper-body cross-check
Wathan 100 x 60 / (48.8 + 53.8 x e^(-0.075 x 3)) 65.4 kg curved model; often near Epley for moderate reps
Lander 100 x 60 / (101.3 - 2.67123 x 3) 64.3 kg middle estimate; often between Brzycki and Epley

Range: 63.5 kg - 68.4 kg. Mean: 65.6 kg. Recommendation: use the middle of the range when the set was clean, and use the lower third when the set was high-rep, grindy, or technically inconsistent.

Example 4: 315 lb x 3 reps

A heavier strength example suitable for powerlifting percentage planning.

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Formula Calculation 1RM estimate Note
Epley 315 x (1 + 3 / 30) 346.5 lb practical default; often higher than Brzycki as reps rise
Brzycki 315 x 36 / (37 - 3) 333.5 lb conservative; often lower than Epley and Wathan
Lombardi 315 x 3^0.10 351.6 lb non-linear; often near the middle for common rep ranges
O'Conner 315 x (1 + 0.025 x 3) 338.6 lb conservative linear estimate; often close to Brzycki
Mayhew 100 x 315 / (52.2 + 41.9 x e^(-0.055 x 3)) 359.1 lb research-derived curved model; often useful as an upper-body cross-check
Wathan 100 x 315 / (48.8 + 53.8 x e^(-0.075 x 3)) 343.3 lb curved model; often near Epley for moderate reps
Lander 100 x 315 / (101.3 - 2.67123 x 3) 337.7 lb middle estimate; often between Brzycki and Epley

Range: 333.5 lb - 359.1 lb. Mean: 344.3 lb. Recommendation: use the middle of the range when the set was clean, and use the lower third when the set was high-rep, grindy, or technically inconsistent.

Example 5: 140 kg x 10 reps

A high-rep example that shows why estimates become less reliable near the upper limit.

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Formula Calculation 1RM estimate Note
Epley 140 x (1 + 10 / 30) 186.7 kg practical default; often higher than Brzycki as reps rise
Brzycki 140 x 36 / (37 - 10) 186.7 kg conservative; often lower than Epley and Wathan
Lombardi 140 x 10^0.10 176.2 kg non-linear; often near the middle for common rep ranges
O'Conner 140 x (1 + 0.025 x 10) 175 kg conservative linear estimate; often close to Brzycki
Mayhew 100 x 140 / (52.2 + 41.9 x e^(-0.055 x 10)) 183.3 kg research-derived curved model; often useful as an upper-body cross-check
Wathan 100 x 140 / (48.8 + 53.8 x e^(-0.075 x 10)) 188.6 kg curved model; often near Epley for moderate reps
Lander 100 x 140 / (101.3 - 2.67123 x 10) 187.7 kg middle estimate; often between Brzycki and Epley

Range: 175 kg - 188.6 kg. Mean: 183.5 kg. Recommendation: use the middle of the range when the set was clean, and use the lower third when the set was high-rep, grindy, or technically inconsistent.

When formulas diverge

  • Higher reps above eight: Epley, Mayhew, and Wathan may produce larger estimates, while Brzycki and O'Conner usually stay more conservative.
  • Low reps from one to three: all formulas converge because the input set is already close to a maximal lift.
  • Beginner lifters: conservative formulas are usually safer because technique and proximity to failure are less consistent.
  • Experienced lifters: Epley, Lombardi, Wathan, or the formula cluster mean may match real maxes better when the lifter knows how to grind safely.
  • Technical lifts: formulas can estimate load, but they cannot judge bar path, rack position, lockout quality, or movement standard.

Which 1RM formula should you use?

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Rep range Recommended formula Why
1-3Any formula or formula meanThe estimates are usually close because the set is already near max strength.
4-6Brzycki or EpleyMost useful range for common strength training estimates.
7-10Brzycki, O'Conner, or lower clusterRep endurance adds noise, so conservative estimates are safer.
10+Retest with heavier loadToo much individual variation in muscular endurance.

Practical rule

If the seven formulas agree within about 3-5%, the input set is useful for programming. If they differ by more than that, do not pick the highest number. Use the lower estimate for your training max, or repeat the test with a heavier set of three to five reps.

Sources

  • Brzycki 1993 - Strength testing: predicting a one-rep max from reps-to-fatigue.
  • Mayhew et al. 1992 - Relative muscular endurance performance as a predictor of bench press strength.
  • LeSuer et al. 1997 - The accuracy of prediction equations for estimating 1-RM performance.