Key Takeaways
- Your 3RM is the heaviest weight you can lift for 3 reps. This calculator estimates it from a hard set of 2 to 10 reps, or from a 1RM you already know, using seven published equations[2].
- The 3RM is not a fixed share of the 1RM. The seven equations put a triple at 87.7% to 94.4% of the 1RM, and a published RPE chart gives 91%[2][6]. Any single "90%" rule is a rough guide.
- The equations were built to predict a 1RM from reps to fatigue, using sets of about 10 reps or fewer[1][2]. I found no study that tests them for predicting a 3RM, so the result is an estimate to confirm with a real set.
- Accuracy depends on the lift. In one study of untrained college students, all seven equations underestimated the deadlift 1RM by 9 to 14%, and most underestimated the squat and bench press by smaller amounts[2].
- I left out strength standards, periodization tables and test protocols because I could not source them. The last section lists what is missing.
What a 3RM Is, and What It Is Not
A 3 rep max (3RM) is the heaviest weight you can lift for exactly 3 reps with the form you would accept in a working set. If you can do a fourth rep, the weight was below your 3RM.
The number you get here is a prediction, not a test. It is roughly what a hard triple should be, based on a set you already did or a 1RM you already know.
Is a 3RM test safer than a 1RM test?
Some pages say it is. I did not find evidence that settles it. One small conference abstract (20 healthy adults) reported a higher heart rate in a 3RM test than in a 1RM test, with no difference in blood pressure or rating of effort[9].
Its authors concluded the 1RM test may strain the heart less, but the rate-pressure numbers in the abstract do not match its own text, so I would not lean on it. A study of 52 people on a unilateral squat called both tests safe, but it did not compare injury risk[10].
That leaves me with no safety claim either way.
How the Estimate Works
Every equation here was written to turn a set taken to fatigue into a 1RM. The calculator runs each one forward to get a 1RM, then runs the same equation backwards to get the load for 3 reps.
What happens when you press Calculate
- Each equation turns your weight and reps into a 1RM estimate.
- The same equation then divides that 1RM by its own 3-rep factor to get a 3RM.
- The page shows the lowest, highest and average of the seven answers.
- For comparison, it also applies the Helms chart, which puts 3 reps at RPE 10 at 91% of 1RM[6].
The seven equations are printed in LeSuer and colleagues' Table 1[2]. Here they are with the share of 1RM each one gives for a triple:
| Equation | Form | 3 reps as % of 1RM | Original publication |
|---|---|---|---|
| Epley | 1RM = w × (1 + 0.0333 × r) | 90.9% | Epley, Poundage Chart, 1985 (not opened) |
| Brzycki | 1RM = 100 × w ÷ (102.78 − 2.78 × r) | 94.4% | Brzycki, 1993 (opened and checked) |
| Lander | 1RM = 100 × w ÷ (101.3 − 2.67123 × r) | 93.3% | Lander, NSCA Journal, 1985 (not opened) |
| Lombardi | 1RM = w × r^0.1 | 89.6% | Lombardi, Beginning Weight Training, 1989 (not opened) |
| Mayhew | 1RM = 100 × w ÷ (52.2 + 41.9 × e^(−0.055 × r)) | 87.7% | Mayhew et al., J Appl Sport Sci Res, 1992 (not opened) |
| O'Conner | 1RM = w × (1 + 0.025 × r) | 93% | O'Conner et al., Weight Training Today, 1989 (not opened) |
| Wathan | 1RM = 100 × w ÷ (48.8 + 53.8 × e^(−0.075 × r)) | 91.8% | Wathan, in Baechle (ed.), 1994 (not opened) |
w is the weight lifted and r is the reps to fatigue. The last column is arithmetic on each equation at 3 reps.
Brzycki's own paper has a table of results for this equation. For example, 200 lb for 3 reps predicts a 1RM of 212 lb, and 225 lb for 10 reps predicts about 300 lb[1]. The calculator reproduces those values in its tests.
I opened only Brzycki's paper. The other six come from LeSuer's printed table, and I did not open their original publications, so treat those coefficients as second-hand.
Worked example: 100 kg for 5 reps to failure
Brzycki 1RM = 100 × 100 ÷ (102.78 − 2.78 × 5) = 112.5 kg
Brzycki 3RM = 112.5 ÷ (100 ÷ (102.78 − 2.78 × 3)) = 106.3 kg
Epley 1RM = 100 × (1 + 0.0333 × 5) = 116.7 kg
Epley 3RM = 116.7 ÷ (1 + 0.0333 × 3) = 106.1 kg
The average is there because most people want one number. The studies I read do not name a best equation, and I found no test of the average itself, so lean on the range.
How Accurate Is It?
Here is what each study looked at, so you can judge how far to trust a number:
| Source | What it found | Limit |
|---|---|---|
| LeSuer et al., 1997[2] | 67 untrained college students (some skipped the squat and deadlift). All seven equations correlated highly with the measured 1RM (r above 0.95). Bench press: only Mayhew and Wathan did not differ significantly from the measured 1RM, and the rest underestimated it by 0.8 to 6% on average. Squat: only Wathan did not differ, and the rest underestimated by 2 to 8%. Deadlift: all seven underestimated, by 9 to 14%. | Untrained students. Predicted a 1RM, not a 3RM. |
| Reynolds et al., 2006[3] | 70 people aged 18 to 69 did 1, 5, 10 and 20RM tests on the barbell bench press and a plate-loaded leg press. The 5RM gave the best 1RM prediction, and the authors advise using no more than 10 reps in linear equations. | Bench press and leg press only. No 3RM test. |
| Mayhew et al., 2008[4] | 103 young women did bench press tests before and after 12 weeks of training. Prediction equations were more accurate when fewer than 10 reps to fatigue were used. | Young women, bench press only. |
| Kemmler et al., 2006[5] | 70 trained women around age 57 did sets from 3RM to 20RM on four machines (leg press, bench press, rowing, leg adduction). A cubic polynomial predicted the 1RM with a mean absolute difference of 1.5 to 3.1%. | Machines only, and a different equation from the seven used here. |
- Use a heavy set with few reps. Brzycki says his equation is only valid below 10 reps to fatigue (his own table still runs to 10)[1]. LeSuer describes the equations as built on 10 or fewer[2], Reynolds advises no more than 10[3], and Mayhew found better accuracy below 10[4]. That is why the calculator accepts 2 to 10 reps and warns at 8 or more.
- The set must go to failure. These equations were built from reps to fatigue. A pooled analysis of 12 studies found lifters tend to under-predict how many reps they have left, by about 1 rep on average, with large differences between studies[8]. That study was about predicted reps, not stopped sets, but the same bias would mean a set you call "failure" may have had a rep or so left, which makes the equations read low.
- The 3RM is a stretch of the method. The studies test the 1RM that comes out. I found none that checks a 3RM from the same equation, so a 3RM from this page can be off by an amount I cannot quote.
- Who and what was studied. Mostly students and adults aged 18 to 69, plus one group of trained postmenopausal women[2][3][5]. Accuracy data cover the bench press, squat and deadlift, plus a few machine lifts. I did not find data for teenagers, people over 70 or other lifts, so the calculator warns outside 18 to 69.
3RM as a Percentage of 1RM
You will often see a 3RM given as about 90% of the 1RM. The seven equations give 87.7% to 94.4% at 3 reps, so the rule of thumb sits inside that spread but does not match any one of them closely[2].
The Helms chart gives another view. For 3 reps it lists a share of 1RM at each RPE, from RPE 10 (no reps left) down to RPE 7 (about 3 reps left)[6][7]:
| RPE | 10 | 9.5 | 9 | 8.5 | 8 | 7.5 | 7 |
|---|---|---|---|---|---|---|---|
| 3 reps, % of 1RM | 91% | 89% | 87% | 86% | 85% | 84% | 83% |
Estimated % of 1RM for 3 reps by RPE (Helms et al., 2016, Table 2). Almost all of the chart is estimated, not measured.
That is why the calculator offers an RPE choice. If your set stopped short of failure, the seven equations would read low, so the page uses this chart instead and says so. To work out your RPE from reps in reserve, use the RIR to RPE Calculator.
Using the Result
- Start from a set of 3 to 5 hard reps if you can. Fewer reps keep you well inside the range the equations were built for[1][3].
- Read the range, not just the average. If the range is wide, you have less reason to trust any single number.
- Treat the result as a starting load for a real set. A rested, warmed-up set with a spotter or safety bars tells you more than an equation.
- If you need a 1RM for planning, the 1RM card shows the same seven equations run forward. For a program built on a 1RM, see the Smolov Jr Calculator.
What This Page Leaves Out, and Why
Where I could not trace a table, claim or constant to a primary source, I left it out. Here is what is missing:
- A fixed 0.90 factor. The equations disagree on the share of 1RM at 3 reps, and no single factor fits all seven.
- Strength levels and standards for a 3RM. I did not find a primary source for 3RM standards, so I do not show a level, a rank or a benchmark.
- Periodization, cluster, wave and pause plans, and rep targets by percentage. I did not find a primary source that ties these to a 3RM.
- A 3RM testing protocol and recovery rules. I could not source a protocol written for a 3RM, so I do not give one.
- Conversions to a 5RM, 8RM or 10RM by a flat percentage. The calculator's rep table runs each equation in reverse for 1 to 10 reps and labels the result an estimate.
Frequently Asked Questions
Sources & References
- Strength testing: predicting a one-rep max from reps-to-fatigue. Brzycki M. Journal of Physical Education, Recreation & Dance 64(1):88-90 (1993)
- The accuracy of prediction equations for estimating 1-RM performance in the bench press, squat, and deadlift. LeSuer DA, McCormick JH, Mayhew JL, Wasserstein RL, Arnold MD. Journal of Strength and Conditioning Research 11(4):211-213 (1997)
- Prediction of one repetition maximum strength from multiple repetition maximum testing and anthropometry. Reynolds JM, Gordon TJ, Robergs RA. Journal of Strength and Conditioning Research 20(3):584-592 (2006)
- Accuracy of prediction equations for determining one repetition maximum bench press in women before and after resistance training. Mayhew JL, Johnson BD, LaMonte MJ, Lauber D, Kemmler W. Journal of Strength and Conditioning Research 22(5):1570-1577 (2008)
- Predicting maximal strength in trained postmenopausal woman. Kemmler WK, Lauber D, Wassermann A, Mayhew JL. Journal of Strength and Conditioning Research 20(4):838-842 (2006)
- Application of the repetitions in reserve-based rating of perceived exertion scale for resistance training. Helms ER, Cronin J, Storey A, Zourdos MC. Strength and Conditioning Journal 38(4):42-49 (2016)
- Novel resistance training-specific rating of perceived exertion scale measuring repetitions in reserve. Zourdos MC, Klemp A, Dolan C, Quiles JM, Schau KA, Jo E, Helms E, Esgro B, Duncan S, Garcia Merino S, Blanco R. Journal of Strength and Conditioning Research 30(1):267-275 (2016)
- Accuracy in predicting repetitions to task failure in resistance exercise: a scoping review and exploratory meta-analysis. Halperin I, Malleron T, Har-Nir I, Androulakis-Korakakis P, Wolf M, Fisher J, Steele J. Sports Medicine 52(2):377-390 (2022)
- Cardiovascular and subjective responses to one repetition (1RM) and three repetition maximum (3RM) testing (conference abstract; only the abstract was available to me). Pinkham, Soldner, Swank, Adams, Durham, Kipp. Medicine & Science in Sports & Exercise 33(5, Suppl):S300 (2001)
- The reliability of 1- and 3RM tests of unilateral strength in trained and untrained men and women. McCurdy K, Langford GA, Cline AL, Doscher M, Hoff R. Journal of Sports Science and Medicine 3(3):190-196 (2004)
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Disclaimer: This tool is for informational and personal journaling purposes only. Results are estimates based on published formulas and may vary based on individual factors such as genetics, training history, and measurement technique.