Picture two lifters arguing in a group chat. One did 275 for 6 and a calculator told him his max is 330. The other ran the identical numbers through a different site and got 319. Eleven pounds apart, same weight, same reps. Somebody's tool must be broken.
Neither is. They ran different equations, and the equations were never built to agree. There is no single one-rep-max formula. There are at least a dozen published ones, and the three you meet most often, Epley and Brzycki and Lombardi, each model the relationship between reps and max with a different kind of curve. Once you can see the shape underneath each one, the disagreement stops looking like a bug and starts looking like exactly what it is: three educated guesses built on different assumptions.
Three shapes of one guess
Every rep-max formula answers the same question. If you can lift a weight for r reps, what could you lift for one? The differences come down to how each one bends as the reps climb.
Epley's is a straight line. Written out, it reads 1RM = w × (1 + r/30). Every extra rep adds a fixed slice, one thirtieth of the working weight, to the estimate. Do a weight for 6 reps and Epley adds 20 percent (6/30). For 12 reps it adds 40 percent. The climb never accelerates or eases. It stays linear all the way up.
Brzycki bends the other way. Its form is 1RM = w × 36 / (37 − r). The reps sit in the denominator, so as they rise the divisor shrinks and the estimate accelerates. Down low the two formulas track each other closely. Up high, Brzycki starts pulling ahead, then pulling away hard, because dividing by a shrinking number is a fast way to grow.
Lombardi takes a third route: 1RM = w × r^0.10. That's a power curve, and a gentle one. Raising reps to the tenth power means the estimate rises quickly over the first few reps and then flattens, adding less and less with each additional rep. It stays the most conservative of the three once you get past mid-range reps.
Same inputs, three curves, three answers. Nothing is malfunctioning.
Where the equations actually came from
None of this is anonymous internet math. Each formula has an author and a date.
Boyd Epley was a strength coach at the University of Nebraska, and the formula that carries his name traces to a 1985 poundage chart he built for the Cornhuskers' weight room. It was a coaching shortcut long before it was a web widget, a way to fill in a percentage table without testing a true single on every athlete every week.
Matt Brzycki published his version in 1993, in an article for the Journal of Physical Education, Recreation and Dance with the plainspoken title "Strength Testing: Predicting a One-Rep Max from Reps-to-Fatigue." His table topped out around 10 reps for a reason he stated openly. Past that, the prediction gets soft.
Lombardi's comes from a 1989 textbook, "Beginning Weight Training," by V. Patteson Lombardi. The power-curve form was aimed at teaching, and it behaves itself across a wide rep range without ever producing wild numbers.
Those three are only the popular ones. Lander (1985), Mayhew (1992), Wathan (1994), and O'Conner (1989) all published their own, several using an exponential-decay term instead of a line or a simple power. A calculator that offers you a formula picker is really offering you a choice among decades of competing academic guesses, most of them fit to small groups of college athletes decades ago.
The same three, side by side
Here's what the popular three look like next to each other, using 185 lb as the working weight:
| Formula | Equation | Published | Estimate at 1 rep | Behavior at high reps |
|---|---|---|---|---|
| Epley | w × (1 + r/30) | 1985 | 191 lb (overshoots) | Climbs at a steady, linear rate |
| Brzycki | w × 36 / (37 − r) | 1993 | 185 lb (exact) | Accelerates, then blows up near 37 reps |
| Lombardi | w × r^0.10 | 1989 | 185 lb (exact) | Rises fast early, then flattens out |
The "at 1 rep" column hides a small embarrassment for Epley. Plug in r = 1 and it returns w × (1 + 1/30), or 1.033w, about 191 lb when you fed it 185. A formula predicting your one-rep max from a one-rep set should hand back the weight you just lifted. Epley overshoots by roughly 3 percent. Brzycki and Lombardi both return the input exactly at one rep, which is the more honest behavior, though the gap is small enough that nobody programming off these numbers ever notices.
The rep count where Epley and Brzycki agree exactly
Here's the fact that surprises people who assume these formulas are always at odds. Epley and Brzycki cross at exactly 10 reps and produce the identical number there.
Set the two equal, (30 + r)/30 = 36/(37 − r), and the algebra collapses to r² − 7r − 30 = 0, which factors to (r − 10)(r + 3) = 0. The only sensible root is r = 10. Run 225 lb for 10 reps through both and each returns 300 lb on the nose. Below 10 reps Epley reads a touch higher. Above 10, Brzycki takes the lead and never gives it back. The single point they meet sits right at the edge of the range Brzycki said he trusted.
That crossover is why comparing formulas at 5 reps tells you something different than comparing them at 15. At low reps they bunch within a few pounds of each other. The famous disagreements all live out past the range every one of these authors actually validated their work in.
Where a reciprocal curve breaks
Brzycki's denominator is the cautionary tale. As reps approach 37, that 37 − r term slides toward zero, and dividing by almost-zero sends the estimate racing toward infinity. At 36 reps Brzycki predicts a one-rep max of 36 times the working weight, which is nonsense. At 37 it's a divide-by-zero. Nobody benches 315 for 36, so in practice this rarely bites, but any calculator running Brzycki has to guard that denominator or it will eventually spit out an impossible number or an outright error.
Epley never blows up. A straight line just keeps rising. But at very high reps it drifts high in its own way, overstating a max off a set of 20 by a wide margin. Lombardi's flattening curve stays the most plausible up there, and yet "most plausible" among high-rep estimates is still a guess nobody should load a bar with.
Why low reps were the whole point
Read the original sources and a pattern emerges. Every one of these authors built and checked their formula against sets in roughly the 1-to-10 range, because that's where lifters actually test. The equations are interpolations across data that lived at low reps. Push a formula to 15 or 20 reps and you're asking it to extrapolate into territory its author never sampled. That's not a flaw in any single equation. It's the reason they fan apart exactly where the data runs out.
So the practical read is simpler than the math suggests. Inside about 5 reps, pick whichever formula you like, since they land within a few pounds of each other. Between 6 and 10, expect a spread of 10 to 20 pounds and treat the number as a range rather than a verdict. Past 10, the formula you choose starts mattering more than your actual strength does, which is a strange thing to be true of a strength estimate, and a good sign to stop trusting the decimal places.
If you want to watch the three curves diverge on your own numbers, switching between Epley, Brzycki, and Lombardi on the same set and seeing the estimate move, Onemax puts all three on one screen and recomputes live as you change the rep count. It's a quick way to feel where they agree and where they start telling stories.