Comparing 1RM Formulas: Which One Should You Use?
Epley, Brzycki, Lombardi, Wathan and O'Conner give different answers for the same set. The difference isn't an error – it follows from how each formula models the relationship between reps and load, and it grows quickly past five reps.
Feed the same set into a 1RM calculator – say 100 kg for five reps – and the five formulas return estimates between 112.5 and 117.5 kg. Five kilos doesn't sound like much, but at twelve reps the spread is 16 kg, and at fifteen reps it passes 30. It's worth understanding where the difference comes from and when it matters.
The formulas in brief
All five formulas answer the same question: if you lifted weight w for r reps, how much could you have lifted once? They differ in the shape of the curve they assume between reps and load.
Epley (1985): 1RM = w × (1 + r/30). A straight line: every extra rep adds the same amount to the estimate, about 3.3% of the weight used. Simple, and therefore the most common.
Brzycki (1993): 1RM = w × 36 / (37 − r). A curve that steepens as reps increase and runs off to infinity at 37 reps. At low rep counts it is the most cautious of the five; at high rep counts, the most generous.
Lombardi (1989): 1RM = w × r^0.10. A power function that flattens as reps increase. It behaves as Brzycki's mirror image: at 1–5 reps it gives the highest estimate of the five, and from eight reps upward the lowest.
Wathan (1994): 1RM = 100 × w / (48.8 + 53.8 × e^(−0.075r)). An exponential model fitted to measured data. Tracks close to Epley across most rep counts.
O'Conner (1989): 1RM = w × (1 + 0.025r). A straight line like Epley, but shallower: each extra rep adds 2.5%. That keeps it consistently among the lowest estimates.
Same set, five answers
Below is each formula's estimate for a 100 kg set taken to failure. The numbers come from the same formulas the calculators on this site use.
| Reps | Epley | Brzycki | Lombardi | Wathan | O'Conner | Spread |
|---|---|---|---|---|---|---|
| 3 | 110.0 | 105.9 | 111.6 | 109.0 | 107.5 | 5.7 |
| 5 | 116.7 | 112.5 | 117.5 | 116.6 | 112.5 | 5.0 |
| 8 | 126.7 | 124.1 | 123.1 | 127.7 | 120.0 | 7.7 |
| 10 | 133.3 | 133.3 | 125.9 | 134.7 | 125.0 | 9.7 |
| 12 | 140.0 | 144.0 | 128.2 | 141.5 | 130.0 | 15.8 |
| 15 | 150.0 | 163.6 | 131.1 | 150.9 | 137.5 | 32.5 |
Two things stand out. First, the spread stays under six percent up to five reps and grows quickly after that. Second, the ranking flips: Lombardi is highest at three reps and lowest at twelve, and Brzycki does the opposite. Which formula counts as "conservative" depends on the rep count.
So which one is right?
None of them on its own. The formulas were fitted to different subjects and different lifts, and in comparison studies their ranking shifts with the exercise, the sex of the lifters and their training background. No consistent winner has emerged, and for an individual lifter the gap between formulas is often smaller than the gap between any formula and their actual max.
There are two practical answers: use the average of the formulas, or pick one and stick with it. The second matters more than the first. If you compare this month's estimate with last month's, what counts is that both were calculated the same way – otherwise switching formulas looks like progress or regression.
LiftNumbers uses the average of all five by default. The average smooths out each formula's extremes, and the same average drives the RPE chart, the percentage chart and the AMRAP estimate in the 5/3/1 calculator. The same set therefore gives the same estimated max in every calculator.
When estimates go wrong
The set wasn't taken to failure. Every formula assumes the last rep was the last one possible. If you left two reps in the tank, a five-rep set is really a seven-rep max, and the estimate comes out too low. The RPE chart corrects for this by accounting for reps in reserve.
Too many reps. The longer the set, the more the result reflects muscular endurance rather than maximal strength. An estimate from a twelve-rep set says more about endurance than about your max – and as the table shows, the formulas no longer agree with each other there either.
Not a compound lift. The formulas were developed for compound barbell lifts. Single-joint movements and machines usually allow more reps at the same relative load, so the formula overestimates the max.
You're not an average lifter. Some lifters can do unusually many reps at a given percentage of their max, others unusually few. If you have tested your max, compare it with the calculator's estimate: the difference tells you which way the formulas miss for you.
Summary
Use sets of 2–6 reps, take them close to failure or record your reps in reserve with RPE, and stay with the same formula or the average. The estimate will then be accurate enough for programming, and you won't need to test a true max separately. For when testing is still worth it, read how often to test your max.