1RM Formulas Compared

What is each formula?

Epley (1985 chart): w × (1 + r / 30). Brzycki (1993): w × 36 / (37 − r). Lombardi (1989 book): w × r^0.10. Lander (1985): 100w / (101.3 − 2.67123r). Mayhew et al. (1992): 100w / (52.2 + 41.9e^(−0.055r)). O'Conner, Simmons, and O'Shea (1989): w × (1 + 0.025r). Wathen (1994, in Baechle): 100w / (48.8 + 53.8e^(−0.075r)).

Spellings vary. O'Conner is often written O'Connor. Wathen is sometimes misspelled Wathan. The equations above are the ones this site runs.

Which formula should you use?

Average, if you want a single number that admits the disagreement. Mayhew if the lift is a bench variation and you want the curve that was built there. Brzycki on conventional or sumo deadlifts, and keep the reps down. Epley everywhere else is a reasonable simple default.

Do not switch formulas to chase a bigger max. You will 'gain' strength in the spreadsheet.

Why do they disagree at high reps?

They were fit on different people and different lifts. Straight-line formulas and exponential curves cannot stay together as reps climb. Brzycki's denominator shrinks and the estimate runs away. The calculator drops it if the math breaks.

LeSuer and colleagues tested seven equations on bench, squat, and deadlift in untrained students. Correlations were high, and the equations still missed, including a systematic underestimation of the deadlift.

Worked example: 100 kg for 5

Example only. Take 100 kilograms for 5 reps. Epley is 100 × (1 + 5 / 30) = 116.7. Brzycki is 100 × 36 / 32 = 112.5. O'Conner is 100 × (1 + 0.025 × 5) = 112.5. Lombardi is 100 × 5^0.10, about 117.5. Lander is 100 × 100 / (101.3 − 2.67123 × 5), about 113.7. Mayhew is 100 × 100 / (52.2 + 41.9 × e^(−0.055 × 5)), about 119.0. Wathen is 100 × 100 / (48.8 + 53.8 × e^(−0.075 × 5)), about 116.6.

The mean of those seven is about 115.5 kilograms. The spread from lowest to highest is about 6.5 kilograms, on a set that was not even that hard to count. At 10 reps the spread is wider, and Brzycki's denominator is shrinking. The calculator warns above 10 reps and refuses inputs above 20.

Display rounding on this site is the nearest 0.5 kilogram or the nearest pound, after the math. Do not round each formula to a mood. How to calculate your 1RM is the same example as a procedure. The accuracy page is what happened when someone checked equations against real singles.

Which number should a program use?

If the program wants one number, use the average and then take a training percent under it. If you switch to Mayhew because it printed 119 instead of 115, you did not get stronger. You edited the spreadsheet. Next month, use the same choice or the log is a different sport.

Bench variations default to Mayhew on this site because that curve was fit on the bench press. Conventional and sumo default to Brzycki, and the page asks you to keep the reps down. Everything else defaults to Epley, which is the simple line. You can still override them. Write the override down.

A percent chart built on the average will not match a chart built on Mayhew. The chart page shows one worked max so you can see the multiplication. Build yours once, from one rule.

What did the 1997 comparison actually say?

LeSuer, McCormick, Mayhew, Wasserstein, and Arnold tested seven prediction equations on the bench press, squat, and deadlift in untrained college students. The correlations with tested maxes were high, above 0.95 in their report, and the equations still missed. They also found a systematic underestimation of the deadlift. High correlation means the estimates rise when the true max rises. It does not mean each estimate landed on the single.

That sample was untrained students, not a meet platform. Do not export their error onto a equipped powerlifter and call it a law. Do not ignore it either. A calculator that pretends to be exact is lying about a literature that already showed the miss.

Use a heavier, lower-rep set if you need a tighter estimate. Use the range, not only the average, when a program would break if the truth were 5 kilograms lower. And do not test a single just to scold the formula. Testing has a cost the equation does not.

How do you keep the formulas from lying to the log?

Pick the rule once. Average, Mayhew on the bench, Brzycki on the deadlift, or Epley because you want the simple line. Write it at the top of the page. If a later month uses a different formula, mark the change so you do not call the jump a gain. The 100-by-5 example above moves from 112.5 to 119 depending on the equation. That is not a training effect.

Feed the formula a set you could show someone. A spotter who pulled the last rep, a bounce, a hitch, a squat that was two inches high: those are different exercises, and the equation cannot see them. Reps above ten are where the lines peel apart. The warning on the calculator is there because the math gets confident while the evidence gets thin.

Use the estimate to choose a percent, then judge the percent by the set. If the set was supposed to be easy and was not, believe the set. Update the max from a cleaner effort next time, not from the formula that flatters you. The table is an example so you can see the spread with one round number. Your log should show the same spread the first time you compare two formulas, and then you should stop comparing them every week.

Example: 100 kg for 5 reps

Example only. Unrounded math is in the middle column, then nearest 0.5 kg. This is not your set.

Key takeaways

• At one rep, every formula returns the weight you lifted.
• By ten reps the equations have already split.
• The average admits the disagreement instead of hiding it.
• Do not change formulas to print a bigger max.

FAQ

Sources

1. Brzycki (1993). Predicting a one-rep max from reps-to-fatigue. JOPERD, 64(1), 88–90.
2. Mayhew et al. (1992). Bench press endurance and strength. JSCR, 6(4), 200–206.
3. LeSuer et al. (1997). Accuracy of 1-RM prediction equations. JSCR, 11(4), 211–213.

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