What is a one-rep max and why estimate it
A one-repetition maximum (1RM) is the heaviest weight a person can lift once with correct technique in a given exercise. Strength and conditioning programs typically prescribe training intensity as a percentage of 1RM, a convention documented in the NSCA's Essentials of Strength Training and Conditioning, which makes an accurate 1RM figure a useful reference point even for lifters who never attempt a true maximal single.
Testing a true 1RM requires lifting maximal loads, which demands experienced technique, an adequate warm-up and appropriate supervision such as a spotter. Prediction equations offer an alternative: they estimate 1RM from a set taken to, or near, repetition failure at a submaximal weight. Research comparing prediction equations against measured maxes, such as LeSuer and colleagues (1997) in the bench press, squat and deadlift, found the common equations estimate 1RM reasonably well when the test set is 10 repetitions or fewer.
The four formulas
The Epley formula (1985) adds one thirtieth of the load for every repetition performed beyond the first. The Brzycki formula (1993) uses a linear relationship between repetitions and percentage of maximum. Lombardi applies a power function of the repetition count, and Mayhew and colleagues (1992) fitted an exponential curve to bench-press data. All four formulas return the entered weight itself when 1 repetition is entered, since a single rep at that weight is by definition a demonstrated maximum.
- Epley (1985): 1RM = w x (1 + r / 30)
- Brzycki (1993): 1RM = w / (1.0278 - 0.0278 x r)
- Lombardi: 1RM = w x r^0.10
- Mayhew: 1RM = 100 x w / (52.2 + 41.9 x e^(-0.055 x r))
Worked comparison at low and high reps
The table below applies all four formulas to the same lift -- 80 kg -- at 5 repetitions and at 15 repetitions, the top of the typical input range on most 1RM calculators. At 5 reps the four estimates span roughly 5 kg, from 90.0 kg (Brzycki) to 95.2 kg (Mayhew). At 15 reps the spread widens to roughly 26 kg, from 104.9 kg (Lombardi) to 131.0 kg (Brzycki) -- proportionally more than four times the relative spread at 5 reps.
| Reps | Epley | Brzycki | Lombardi | Mayhew |
|---|---|---|---|---|
| 5 | 93.3 kg | 90.0 kg | 94.0 kg | 95.2 kg |
| 15 | 120.0 kg | 131.0 kg | 104.9 kg | 113.4 kg |
Why the formulas diverge more at higher rep counts
Each formula is a different mathematical curve fitted to observed reps-to-load data: Epley is linear in repetitions, Brzycki is linear in percentage terms, Lombardi is a power function, and Mayhew is exponential. These curve shapes are close to each other over the low-repetition range where most of the underlying validation data was collected, which is why the formulas agree closely at 5 reps or fewer. As repetition count rises, the curves extrapolate further from that well-validated range and increasingly diverge from one another, and from the true underlying relationship for any individual lifter.
LeSuer and colleagues (1997) found that the common equations estimate 1RM reasonably well from sets of 10 repetitions or fewer, but accuracy decreases as repetitions increase beyond that point. This is consistent with the widening spread shown above, and it is why coaches following the NSCA's published guidance generally cap estimation sets at 10 repetitions and treat 2-5 repetition sets as the most reliable input.
The %1RM training-zone table
Once a 1RM estimate is available, training loads are commonly prescribed as a percentage of it. The table below shows the widely published relationship between percentage of 1RM and the approximate number of repetitions most lifters can perform at that load, as documented in the NSCA's Essentials of Strength Training and Conditioning. It represents a population average -- individual repetition ability at a given percentage varies.
| % of 1RM | Approximate repetitions possible |
|---|---|
| 100% | 1 |
| 95% | 2 |
| 90% | 4 |
| 85% | 6 |
| 80% | 8 |
| 75% | 10 |
| 70% | 12 |
| 65% | 15 |
Safety note on testing a true 1RM
An estimated 1RM is not a demonstrated 1RM. Maximal testing places substantial demands on technique and tissue tolerance, and sports-medicine and strength-training organizations advise that true 1RM attempts be performed only after adequate technical practice, with a thorough progressive warm-up, appropriate equipment and supervision such as a spotter. Estimating 1RM from a submaximal set, using the formulas above, avoids those demands entirely and is the more practical approach for most lifters tracking training progress.
अक्सर पूछे जाने वाले सवाल
Which 1RM formula is most accurate?
No single formula is best in every situation. Epley (1985) and Brzycki (1993) are the most widely used and are mathematically identical at 10 repetitions, agreeing closely below that point. Lombardi and Mayhew provide alternative curve fits that can diverge more noticeably at higher repetitions. Comparing several formulas at once, as this article does, shows the realistic range of an estimate rather than relying on a single number.
Why do 1RM formulas give different answers at high rep counts?
Each formula fits a different mathematical curve -- linear, power or exponential -- to reps-to-load data collected mostly at low repetitions. The curves stay close together within that well-validated range but extrapolate differently as repetitions rise, so a 15-rep set can produce estimates that differ by 20 kg or more between formulas, while a 5-rep set typically differs by only a few kilograms.
How many reps should I use for the most reliable 1RM estimate?
Sets of 2 to 5 repetitions taken close to repetition failure give the most reliable estimates, because the prediction curves are steepest and best validated in that range. LeSuer and colleagues (1997) found estimates from sets of 10 repetitions or fewer to be reasonably accurate, while estimates from sets above 10 repetitions are considerably less reliable.
What is 80% of 1RM used for?
In the repetition-maximum table published by the NSCA, 80% of 1RM corresponds to a load most lifters can move for about 8 repetitions before reaching failure. Percentages in the published training literature are used as a shorthand for programming relative intensity, though individual repetition ability at a given percentage varies and program design is best guided by a qualified coach.
Is it safe to test a true one-rep max?
Maximal testing places high demands on technique and tissue tolerance. Sports-medicine and strength organizations advise that true 1RM tests be performed only with adequate technical practice, a thorough warm-up, appropriate equipment and supervision such as a spotter. Estimating 1RM from a submaximal set avoids those demands and is the more common approach outside of competitive testing settings.
संदर्भ
- Epley B. Poundage chart. Boyd Epley Workout. Lincoln, NE: Body Enterprises, 1985.
- Brzycki M. Strength testing -- predicting a one-rep max from reps-to-fatigue. Journal of Physical Education, Recreation & Dance 1993; 64(1): 88-90.
- Mayhew JL, Ball TE, Arnold MD, Bowen JC. Relative muscular endurance performance as a predictor of bench press strength in college men and women. Journal of Applied Sport Science Research 1992; 6(4): 200-206.
- LeSuer DA, McCormick JH, Mayhew JL, Wasserstein RL, Arnold MD. The accuracy of prediction equations for estimating 1-RM performance in the bench press, squat, and deadlift. Journal of Strength and Conditioning Research 1997; 11(4): 211-213.
- Haff GG, Triplett NT (eds). Essentials of Strength Training and Conditioning, 4th edition. NSCA / Human Kinetics, 2016.
- American College of Sports Medicine. ACSM's Guidelines for Exercise Testing and Prescription, 11th edition. Wolters Kluwer, 2021.