Estimated one-rep max: the Epley and Brzycki formulas
How the Epley and Brzycki formulas estimate a one-rep max from a set of several reps, with worked examples, a percentage table and the limits of the estimate.
November 11, 2026 · 5 min read
A one-rep max (1RM) is the heaviest weight you can lift once on a given exercise. An estimated 1RM is a calculation: it takes a set you actually did, such as 100 kg for 5 reps, and projects what a single might be. Nobody has to attempt a true maximum to get the number.
The estimate is arithmetic, not a measurement. It is useful as long as you treat it that way.
The two common formulas
Both formulas take the weight lifted (w) and the number of reps completed (r).
Epley: 1RM = w × (1 + r / 30)
Brzycki: 1RM = w × 36 / (37 − r)
They were fitted to different data and make slightly different assumptions about how quickly strength falls off as reps go up. Neither is the correct one. They are two reasonable curves drawn through the same kind of observations.
Worked examples
100 kg for 5 reps.
- Epley: 100 × (1 + 5/30) = 100 × 1.1667 = 116.7 kg
- Brzycki: 100 × 36 / (37 − 5) = 100 × 36 / 32 = 112.5 kg
225 lb for 8 reps.
- Epley: 225 × (1 + 8/30) = 225 × 1.2667 = 285.0 lb
- Brzycki: 225 × 36 / (37 − 8) = 225 × 36 / 29 = 279.3 lb
The two results are a few kilograms or pounds apart. That gap is a fair picture of how precise the estimate is.
Multipliers by rep count
Each formula reduces to a multiplier applied to the weight on the bar.
| Reps | Epley | Brzycki |
|---|---|---|
| 1 | 1.033 | 1.000 |
| 2 | 1.067 | 1.029 |
| 3 | 1.100 | 1.059 |
| 4 | 1.133 | 1.091 |
| 5 | 1.167 | 1.125 |
| 6 | 1.200 | 1.161 |
| 8 | 1.267 | 1.241 |
| 10 | 1.333 | 1.333 |
| 12 | 1.400 | 1.440 |
| 15 | 1.500 | 1.636 |
| 20 | 1.667 | 2.118 |
Two things stand out. First, Epley gives a number above the weight lifted even for a single rep, which makes no sense for a true single; most calculators simply return the weight itself when r is 1. Second, the formulas agree exactly at 10 reps and drift apart on either side.
Why estimates diverge above about 10 reps
Below 10 reps, Epley is the higher of the two, and the gap stays small. Above 10, Brzycki climbs much faster. At 20 reps, Epley multiplies the weight by 1.667 and Brzycki by 2.118. For 60 kg × 20, that is 100 kg against 127 kg: too far apart to be useful.
The reason is partly mathematical. The Brzycki formula divides by (37 − r), so the result grows without limit as reps approach 37. Epley is a straight line and keeps growing at the same steady rate.
The other reason is physical. A set of 20 is limited by different things than a heavy single: endurance, breathing, tolerance for discomfort. How many reps a person can do at a given fraction of their maximum also varies between people and between exercises. The further the set is from one rep, the less it says about one rep.
A practical rule: trust estimates from sets of roughly 2 to 10 reps, and read anything from higher-rep sets as a loose indication.
What the estimate is good for
Comparing sets across rep ranges. Was 100 kg × 5 a better set than 90 kg × 8 or 80 kg × 12? With Epley:
- 100 × 5 gives 116.7 kg
- 90 × 8 gives 90 × 1.267 = 114.0 kg
- 80 × 12 gives 80 × 1.400 = 112.0 kg
Three sets that look nothing alike land on one scale.
Tracking progress. If you did 100 kg × 5 last month and 100 kg × 6 this month, the bar weight has not changed, but the Epley estimate has moved from 116.7 to 120.0 kg. Plotted over months, the estimate shows a trend even when weight and reps change from session to session.
Planning a set from a percentage. Many programs prescribe weights as a percentage of 1RM. An estimate lets you follow such a program without testing a maximum.
What it is not good for: predicting exactly what you will lift on a given day. Sleep, technique, bar path and practice with heavy singles all affect a real maximum, and no formula knows about them. Decisions about attempting maximal lifts are best made with a qualified coach.
Percentage table
Turning the formulas around gives the share of a 1RM that corresponds to a given number of reps.
| Reps | Epley | Brzycki |
|---|---|---|
| 1 | 100% | 100% |
| 2 | 93.8% | 97.2% |
| 3 | 90.9% | 94.4% |
| 4 | 88.2% | 91.7% |
| 5 | 85.7% | 88.9% |
| 6 | 83.3% | 86.1% |
| 8 | 78.9% | 80.6% |
| 10 | 75.0% | 75.0% |
| 12 | 71.4% | 69.4% |
To use it in reverse: with an estimated 1RM of 120 kg and a plan calling for sets of 5, Epley suggests 120 / (1 + 5/30) = 102.9 kg, which rounds to 102.5 kg on the bar. Brzycki suggests 120 × 0.889 = 106.7 kg. Treat the table as a starting point and let the first set tell you whether the weight is right.
Keeping the estimate honest
A few habits make the number more meaningful over time:
- Use one formula and stick with it. The trend matters more than the absolute value, and switching formulas breaks the trend.
- Only count completed reps done to the same standard each time. A half rep is not a rep.
- Estimate per exercise. A squat estimate says nothing about a front squat.
- Do not mix units. Compute in kilograms or in pounds, not both.
All of this depends on having the sets written down. If you are not sure what to record, how to keep a lifting log covers the basics. In Quintal, an iPhone lifting log, a 1RM calculator sits next to the log, and the estimated 1RM for each exercise can be charted over time.
Estimated maximums are also a common starting point for ramping up to a heavy set; how to plan warm-up sets walks through that arithmetic.
This guide is general information, not medical or personal training advice. Ask a qualified professional about your own situation.