What a one rep max is and why you estimate it
Your one rep max is the heaviest load you can move once through a full range of motion with acceptable technique. It is the reference point almost all strength programming is expressed against: 5 × 5 at 80%, a top single at 90%, a back-off set at 65%. Without a number to take percentages of, none of that is actionable.
Testing a true maximum has real costs. It is fatiguing enough to disrupt a training week, technique degrades at the limit, and the risk of injury is higher than at any other load. It also requires a genuine attempt at failure, which needs competent spotting and a willingness to miss a lift. Most lifters, and almost all coaches working with beginners, therefore estimate instead.
The estimate works because the relationship between load and repetitions is remarkably consistent within an individual. If you can do five reps with a weight, that weight sits at a fairly stable fraction of your maximum, and every formula on this page is an attempt to describe that fraction as a function of reps.
What varies is the individual. Two lifters with identical maxima can differ substantially in how many reps they get at 80%, because fibre type composition, training history and the exercise itself all affect endurance at a given percentage. That variation is the fundamental limit on all of these formulas, and no refinement of the arithmetic gets round it.
The five formulas and how they differ
Epley is linear: it adds 1/30 of the load for each rep, so five reps is 116.7% of the weight lifted. It is the simplest to do in your head and the most widely used.
Brzycki is a hyperbola, 36/(37 − r), which behaves differently at the ends. Below ten reps it returns a lower estimate than Epley; above ten it returns a higher one. The two cross at exactly ten reps, where both put the load at 75% of maximum — a coincidence worth remembering, because it means the choice of formula does not matter at all for a ten-rep set.
Lombardi is a power law, w × r^0.10, and it produces the highest estimates at low reps and the lowest at high reps. Because the exponent is small, its curve is much flatter than the others.
Lander is another hyperbolic form with a steeper slope, and it tends to sit near the top of the range at high rep counts.
O'Conner is linear like Epley but shallower, adding 2.5% per rep against Epley's 3.33%. At five reps it gives 112.5%, matching Brzycki exactly.
The practical consequence is that agreement is tight at low reps and poor at high ones. At five reps with 100 kg the five span 112.5 to 117.5 kg, under 5%. At twelve reps with 80 kg they span 102.6 to 115.5 kg, which is nearly 13% — larger than most people's honest uncertainty about their own max.
Worked example: 100 kg for 5 reps
- Epley. 100 × (1 + 5/30) = 100 × 1.16667 = 116.7 kg.
- Brzycki. 100 × 36 ÷ (37 − 5) = 3,600 ÷ 32 = 112.5 kg.
- Lombardi. 100 × 5^0.10 = 100 × 1.17462 = 117.5 kg.
- Lander. 100 × 100 ÷ (101.3 − 2.67123 × 5) = 10,000 ÷ 87.944 = 113.7 kg.
- O'Conner. 100 × (1 + 0.025 × 5) = 100 × 1.125 = 112.5 kg.
The spread is 117.5 − 112.5 = 5.0 kg, or 4.3% of the Epley figure. That is the honest precision of the method: your max is somewhere around 115 kg, plus or minus a couple of kilos, and no formula on this page can do better than that.
Now turn the estimate into training loads. Taking Epley's 116.7 kg, a 5 × 5 at 80% is 93.3 kg — 92.5 kg once rounded to the nearest 2.5 kg plate increment. A top single at 90% is 105 kg. And the same formula run backwards says an eight-rep set should be 116.7 ÷ (1 + 8/30) = 92.1 kg, which is essentially the same load as the 80% five-rep work. That equivalence is why percentage charts and rep-max charts describe the same thing.
How to use the estimate without fooling yourself
Three conditions have to hold before the number means anything.
The set must be close to failure. All five equations were fitted on maximal repetition sets. A set of five with three reps left in reserve is really an eight-rep set performed for five, and feeding it in produces an estimate roughly 10% below your true maximum. If you habitually stop short, your estimated max will drift down even as you get stronger.
The rep count should be low. Five or fewer gives the tightest agreement between formulas and the smallest individual variation. Above ten, you are measuring muscular endurance as much as maximal strength, and the two are only loosely related.
The exercise matters. These equations were largely validated on the bench press, and they transfer reasonably to other multi-joint barbell lifts. They transfer poorly to exercises where technique or stability fails before the muscle does, and to single-joint isolation work where high-rep endurance is disproportionately good.
Read the result as a band, not a point. Use it to set training percentages, to compare month to month, and to decide opening attempts. Do not use it to claim a number you have never lifted, and do not chase a rising estimate by picking the most generous of the five formulas — pick one and stay with it, so that the comparison over time is honest.
Percentage of 1RM by repetitions
| Reps | Epley % | Brzycki % |
|---|---|---|
| 1 | 100.0% | 100.0% |
| 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% |
| 7 | 81.1% | 83.3% |
| 8 | 78.9% | 80.6% |
| 9 | 76.9% | 77.8% |
| 10 | 75.0% | 75.0% |
| 11 | 73.2% | 72.2% |
| 12 | 71.4% | 69.4% |
Below ten reps Brzycki sits above Epley; above ten it sits below. Multiply your estimated max by the percentage to get a working load — 85.7% of 116.7 kg is 100 kg, which is the set you started from.
What can make the estimate wrong
- Reps in reserve. The formulas assume the set ended at or very near failure. Leaving three reps in the tank understates your maximum by roughly the difference between a five-rep and an eight-rep prediction.
- Too many reps. Beyond ten the formulas disagree with each other by more than 10%, and endurance rather than strength starts to dominate the result.
- Individual fibre-type differences. Some lifters get twelve reps at 80% and others get six. No formula can see that, and it is the largest single source of error.
- Exercise selection. The equations were validated mainly on the bench press. Deadlifts tend to allow fewer reps at a given percentage, and isolation exercises far more.
- Technique breakdown. A set where form degrades on the last reps produces a rep count your muscles earned and your joints did not. Count only reps you would repeat.
- Comparing different formulas over time. Switching from Brzycki to Epley after a five-rep set adds 4 kg to your "max" with no change in strength. Pick one and keep it.
If you do test a true max
Warm up thoroughly with progressively heavier singles, leave several minutes between attempts, use competent spotters or safety pins, and stop when technique changes rather than when the bar stops moving. A missed attempt under a loaded bar without safeties is the single most avoidable injury in the gym. For most lifters an estimate from a heavy triple gives everything a true test would, at a fraction of the cost.
Where 1RM estimates fit in programming
Percentage-based programming assumes a fixed maximum for the length of a block, which is why most templates re-test or re-estimate every four to twelve weeks. A common compromise is to program from a training max set at 90% of the estimate, which absorbs day-to-day variation and keeps the prescribed loads achievable on a bad day.
The main alternative is autoregulation by rating of perceived exertion. Instead of prescribing 80%, you prescribe a set of five at RPE 8 — meaning two reps left in reserve — and the load floats with how you feel that day. The two approaches are compatible: RPE-to-percentage charts are built from exactly the same load-repetition relationship as the formulas here, and you can convert between them.
For comparing lifters of different body weights, the raw maximum is not enough, since larger athletes lift more in absolute terms and less relative to their size. Powerlifting uses allometric scoring for this, and a total of 500 kg means something different at 66 kg body weight than at 120 kg.
Finally, remember that strength gains need enough energy and protein to support them. If your estimated max is stalling on a diet, the constraint may not be the programme — set intake with the TDEE calculator and check the protein figure against the protein intake calculator before rewriting the block. Body composition matters here too: the Navy body fat calculator will tell you whether a rising body weight is bringing lean mass with it, and the macro split calculator turns the calorie figure into daily grams.