Three formulas dominate one-rep-max estimation: Epley, Brzycki, and Lombardi. They take the same two inputs — the weight you lifted and the reps you got — and each returns a slightly different estimated max. This article puts them head-to-head: how each is built, how they behave across rep ranges, and which one deserves to be your default anchor.
Before diving into the equations, it helps to know why anyone bothered inventing three of them. Each was published by a different researcher working with a different pool of lifters, and each was trying to solve the same practical problem: how do you estimate a maximum you'd rather not test directly? They arrived at different curves because they started from different data, and each has quietly persisted in strength culture ever since — baked into apps, spreadsheets, and coaching lore, usually without anyone noticing which one they're using.
The three formulas
Each formula is a compact equation relating load and reps to an estimated max. Here they are, with w = weight lifted and r = reps completed:
| Formula | Equation | Character |
|---|---|---|
| Epley | w × (1 + r ÷ 30) | Linear, middle-of-the-road |
| Brzycki | w × 36 ÷ (37 − r) | Slightly conservative at higher reps |
| Lombardi | w × r^0.10 | Curved, reads higher at high reps |
At a single rep, all three correctly return the weight itself. The interesting behavior — and the disagreement — emerges as reps increase.
How they behave across rep ranges
The formulas track each other closely at low reps and fan out as reps climb. A worked example makes it concrete. Suppose you lift 100 kg and want the estimated max:
| Reps | Epley | Brzycki | Lombardi |
|---|---|---|---|
| 3 | 110 | 106 | 112 |
| 5 | 117 | 113 | 122 |
| 8 | 127 | 124 | 138 |
| 10 | 133 | 133 | 148 |
Two lessons jump out. First, at 3–5 reps the three agree within a handful of kilograms — the safe zone for estimating. Second, by 8–10 reps they diverge sharply, with Lombardi reading aggressively high because its power curve keeps climbing. That spread is the visual proof that high-rep sets make poor estimation inputs.
Epley: the balanced default
Epley's linear form sits between the other two across most of the useful range. It doesn't get wild at higher reps the way Lombardi can, and it isn't as conservative as Brzycki at the top end. For a general trainee who wants one dependable anchor, Epley is the sensible default — predictable, moderate, and easy to reason about.
Brzycki: the low-rep specialist
Brzycki's denominator (37 − r) means it behaves beautifully at low reps and gets unstable as r approaches the mid-thirties — a set of 30+ reps would send it toward nonsense, which is really just the formula warning you that you're far outside its valid range. In the 1–6 rep window where serious strength work lives, many powerlifters prefer it because it tends to read slightly conservative, and a conservative anchor keeps prescribed percentages honest.
Lombardi: use with caution
Lombardi's power function reads reasonably at low reps but inflates quickly as reps rise. If you feed it a high-rep set, it will hand you an optimistic max that your body may not honor under a real bar. It's not wrong so much as sensitive — it demands low-rep inputs to stay believable. Treat any Lombardi estimate from an 8+ rep set with suspicion.
Which should you standardize on?
The comparison leads to a clear, practical policy:
- Default to Epley for its balance, unless you have a reason not to.
- Prefer Brzycki if you train and test at low reps and want a conservative anchor.
- Only trust Lombardi from 1–5 rep sets, where its optimism is contained.
- Always feed 3–5 rep sets. In that range the choice barely matters — the formulas converge — which is the strongest argument of all: standardize your inputs and the formula debate mostly disappears.
Consistency beats correctness here. Pick one, use it forever, and your training percentages stay internally coherent regardless of the small absolute bias.
Don't forget the cost of the session
Heavy strength work isn't free metabolically — big compound sets, short rest, and the recovery afterward all burn energy, even if lifting isn't "cardio." If you're managing bodyweight alongside a strength phase, it helps to know roughly what a training session costs.
Use a calorie-burn estimate to sanity-check how much your lifting adds to daily expenditure — usually less than people assume, which is why nutrition, not "burning it off," drives composition during a strength block.
Beyond the big three: RPE and velocity
The three classic formulas share a blind spot — they assume everyone hits the same number of reps at a given percentage. Two newer approaches sidestep that assumption by measuring you on the day, and they're worth understanding even if you never leave the formulas behind.
RPE and reps-in-reserve. Rating of Perceived Exertion asks how hard a set felt on a 1–10 scale, usually framed as reps in reserve (RIR) — how many more reps you could have done. A set taken to "RPE 8" means roughly two reps left in the tank. Modern programs prescribe loads by RPE precisely because it autoregulates for daily readiness: on a strong day you'll put more weight on the bar to reach RPE 8, on a weak day less. It turns the fixed percentage table into a living one. You can even blend the two — use a formula to set a starting weight, then adjust by feel to hit the target RPE.
Velocity-based training. Bar speed drops predictably as load approaches your max: light weights move fast, near-maximal weights crawl. A velocity tracker measures how fast the bar moves and infers, in real time, how close you are to your limit that day. Because your true max fluctuates, velocity gives a daily readout that no static formula can — some lifters set a target bar speed and simply load the bar until they hit it.
Neither approach makes the classic formulas obsolete. RPE requires experience to rate honestly, and velocity tools cost money and need calibration. But both reinforce the central lesson of comparing Epley, Brzycki, and Lombardi in the first place: your one-rep max is not a fixed number etched in stone. It's a moving target that shifts with sleep, stress, and fatigue. The smartest system, whichever tools you use, is one that estimates a starting load, then lets today's performance fine-tune it — rather than forcing a percentage a formula computed weeks ago.
The bottom line
Epley, Brzycki, and Lombardi disagree mainly at high reps, where no estimate should be trusted anyway. Epley is the balanced default, Brzycki the conservative low-rep pick, and Lombardi the optimist to keep on a short leash. But the real fix isn't choosing the perfect formula — it's feeding all of them the clean 3–5 rep sets where they agree, then standardizing on one so your programming stays consistent from block to block.