The 1RM (One Rep Max) Calculator
An Introduction To The 1RM Calculator (One Rep Max)
The 1-repetition maximum (1-RM) test is the gold standard test for evaluating the maximal dynamic strength of a muscle or group of muscles. 1-RM is defined as the maximal weight that can be lifted once with correct technique. However, an actual determination of muscle strength in the laboratory situations includes the use of isometric and isokinetic dynamometers which require sophisticated equipment and trained personnel. Comparatively, a 1-RM in a gym using a barbell, free-weights, or a machine is relatively easy to learn, does not require expensive laboratory-grade equipment, and can be used by all types of athletes.
Due to the wide use of 1-RM testing, it is important for the 1-RM to be a reliable measurement. However, a 1-RM test might not always be feasible or appropriate. Therefore, an alternative method is the estimation of 1-RM (e1-RM) with a prediction equation based on performing repetitions to failure at a specific weight. In this blog we’ll cover the research and history behind e1-RM testing along with a few common questions then provide you with an evidence-based 1-RM calculator to use.
The Science Behind Estimating Your 1RM (One Rep Max)
Prediction equations are at the heart of correctly estimating a 1-RM. In fact, research on e1-RM goes back to the 1990s, but the most famous formulas from the early era are the Epley poundage chart (Epley, 1985), which wasn’t validated scientifically until much later. Another chart was developed by Lander, at a similar time, but it wasn’t as popular nor validated until later.
Jumping forward to the 1990s, one of the first studies attempting to estimate 1-RM tested several populations (i.e., college and high school students, football players, etc.,]. The authors found an exponential relationship between a repetition maximum test and 1-RM that resulted in a r2 of 0.90-0.97, which means the formula explained ~90-97% of the variance in predicted 1-RM (Figure 1). This experiment used the bench press and more than 400 people using intensities from 55-95% of their actual 1-RM. Practically, the results of this study meant there was a validated equation test that could accurately predict true 1-RM.
Figure 1. Difference between the Lander equation (linear) and Mayhew equation (exponential) for e1-RM in the bench press (Mayhew et al., 1992).
The next study used a 7-10 repetition knee extension test. The authors tested a prediction equation prior to 18 weeks of resistance training and afterward, finding that an equation used after training was better (r2 = 0.89) than before (r2 = 0.91), but not by much. This finding isn’t surprising although it did encourage further research on e1-RM testing. It also helped us start to think about who should be using 1-RM vs e1-RMs (see FAQ below).
A few years later, one of the most common formulas was developed, known as the Brzycki equation. It was published with an accompanying chart that coaches and trainers would hang up in their gym. However, this was not technically based on scientific research, rather on an article detailing strength testing. The author provided an equation for predicting a 1RM based on reps-to-fatigue, but does not say on what information the equation was created from.
Table 1. Popular estimated 1-RM prediction equations
|Name||Equation||Type of equation|
|Brzycki||1-RM = 100 * rep wt/(102.78 – 2.78*reps)||linear|
|Epley||1-RM = (1+0.033*reps) * rep weight||linear|
|Lander||1-RM = 100 * rep wt / (101.3 – 2.67*repetitions)||linear|
|Mayhew||1-RM = 100 * rep wt/(52.2+41.9e-055reps)||exponential|
It wasn’t until 1995 that all of the popular equations (Table 1) were tested against each other. The study was fairly simple, with 45 college football players doing bench press and back squats. The results of the study indicated that the Mayhew equation underestimated 1-RM (-3.1kg) while the Epley (+4.8kg), Lander (+14.1kg), and Brzycki (+14.2kg) equations significantly overestimated 1-RM. Clearly, some of those are pretty far off from a person’s actual 1-RM. Practically, we can say that for higher repetitions in an e1-RM, linear equations are not as effective in predicting actual e1-RM. Furthermore, of those listed above the most accurate is the Mayhew equation. All equations seemed to perform better with fewer repetitions (<10) with heavier loads (>80% 1-RM) for the bench press and squat.
We leap forward another 10 years where a study by Reynolds et al., (2006) tested prediction equations for 1-RM on a Cybex leg press and chest press machine. This was the first study to test e1-RM on machines. The authors found that 1-RM strength, compared to a multiple repetition maximum load, had a nonlinear relationship, in which the magnitude of the decline in load becomes smaller with increasing repetitions used in RM testing. Furthermore, of the 5, 10, and 20 repetition max (RM) they tested, the best repetition RM to use for prediction of 1-RM strength in the leg press and chest press was the 5-RM.
From 2006 onward, there were a ton of prediction equations created (see Table 2) all based on different populations, exercises, and repetition ranges. These were subsequently tested in women because up to then, only a limited number of strength prediction studies have acknowledged including women as participants. The main finding of this study was that the Tucker and Mayhew equations best predicted e1-RM for women.
Table 2. Prediction equations to estimate 1-RM from repetitions to fatigue for bench press (from Mayhew et al., 2008).
|Adams||e1RM = Rep weight / (1 – 0.02 RTF)|
|Berger||e1RM = Rep weight / (1.0264 – 0.00266 RTF)|
|Brown||e1RM = (Reps * .0338 + 0.09849) * Rep weight|
|Cummings & Finn||e1RM = 1.175*Rep weight + 0.839*Reps – 4.29787|
|Lombardi||e1RM = RTF0.1 * Rep weight|
|O’Connor||e1RM = 0.025 (Rep weight * RTF) + Rep weight|
|Reynolds||e1RM = Rep weight / (0.5551 e-0.0723*RTF + 0.487)|
|Tucker||e1RM = 1.139 * Rep Weight + 0.352 * Reps + 0.243|
|Wathen||e1RM = Rep weight / (0.488 + 0.538e-0..075*RTF|
|Welday||e1RM =(RTF * 0.0333) Rep weight + Rep weight|
|Rep Weight = repetition weight, load less than 1-RM to perform reps; RTF = repetitions to failure.|
Should YOU Use A 1RM (One Rep Max) Calculator…?
Using an e1-RM calculator is a great tool if you aren’t a powerlifter or weightlifter. That’s because the risk to reward ratio for a 1-RM is often too high or it’s too time consuming (or not worth the time you could spend training) when you can use an estimation of your 1-RM. Plus, after a warm-up only 1 set is needed to predict an estimated 1RM, compared to multiple sets and load increases with a traditional 1-RM.
In order to increase accuracy, prediction equations must be exercise specific (i.e., bench press, back squat). In addition, most of the current equations function best when using a load that will produce a range of 2 to 10 repetitions. Overall, the best equation based on science is the Mayhew equation, especially for more than 10 repetitions. Other formulas you could use are the Epley and Brzycki formula if you want to overpredict your 1-RM. The reason you may want to do this is to increase the intensity of your training if it is based on 1-RM percentage. Finally, the most important aspect is to use the same equation each time you predict your 1-RM and adjust your training load to fit your desired repetition or percentage range. YOu should use the e1-RM as either a check-on-progress or an initial tool to set your training load.
Frequently Asked Questions
Is My 1RM A Reliable Strength Assessment?
An important part to ensure reliability in 1RM testing is the use of familiarization. Some previous studies reported that multiple familiarization sessions are needed before assessing maximal strength in order to avoid an improvement in muscle strength due to improved motor coordination or other neural adaptations. Also it has been suggested that a familiarization process prior to 1RM strength test is essential for ensuring reliable test results, and minimize learning effects or systematic bias. However, a recent systematic review found that a 1-RM test has excellent test-retest reliability. This was true regardless of the previous resistance training experience, sex, and age of the participants. Furthermore, it doesn’t matter whether or not the testing procedure includes familiarization sessions or whether the exercises are classified as single- or multi-joint. However, just because something has great test-retest reliability, defined as the consistency of results across repeated measurements, doesn’t mean it’s a good idea for everyone. Using your best judgment on if it is appropriate in your program (or for your client) is just as important when considering a 1-RM test.
Should I Still Find and Use My 1RM or e1RM If I’m New To Lifting?
In the literature, being familiar with exercise is known as being “trained” while being unfamiliar is known as being “untrained.” Though actual 1-RM testing is the most reliable test for evaluating the maximal dynamic strength of a muscle or group of muscles, untrained people are not always able to reach their 1-RM due to several reasons:
- People new to lifting may be reluctant to continue adding weight to reach a true maximal effort
- Fatigue may occur and may reduce the accuracy of the 1-RM assessment.
- Performing a 1-RM is time consuming because adequate recovery is required between sets (3-5 minutes).
- Injuries may occur if a person is does the movement incorrectly
This means that using a good 1-RM calculator can be beneficial for those who are starting (or re-starting) a training program.
Are There Any Novel Approaches To Estimating Your 1RM?
The use of velocity-based training has led to several new formulas to predict 1-RM. If you’re interested in using the VBT method read this study and this one. It’s a lot more complicated than plugging in a repetition weight and number into a formula, but there is some software that can help.
Is Using The RPE or RIR Scale Better Than Using Your 1RM To Estimate?
We’ve written articles on RIR and RPE, as well as the topic of training to failure, because both have a place in training. However, we cannot say that they’re superior to using an estimated 1RM (one rep max) because they’re simply different methods. In fact, they can be used together quite well. Oftentimes as coaches we will recommend estimating your 1RM to have a good ballpark idea of where you should be aiming to finish your sets at and to utilize the RIR or RPE scale alongside that estimated 1RM as a way to ensure you’re not training to failure or walking right into injury. Put simply, our advice is to use both — use your one rep max as a north star, pointing you towards an “ideal number” to hit, while keeping a close watch on your RPE/RIR scale to stay within the correct proximity to failure.
- Berger, RA. Relationship between dynamic strength and dynamic endurance. Res Q 41:115-116, 1970.
- Braith RW, Graves JE, Leggett SH, Pollock ML. Effect of training on the relationship between maximal and submaximal strength. Medicine & Science in Sports & Exercise. 1993;25(1):132–138.
- Brzycki, M. Strength testing: predicting a one-rep max from reps-to-fatigue. JOPHERD 64:88-90. 1993.
- Brown, HL. Lifetime Fitness (3rd ed.). Scottsdale, AZ: Gorsceach Scarisbrick, 1992.
- Cummings, B and Finn, KJ. Estimation of a one repetition maximum bench press for untrained women. J Strength Cond Res 12(4):262-265, 1998.
- Landers, J. Maximum based on reps. NSCA 1984.
- Macht JW, Abel MG, Mullineaux DR, Yates JW. Development of 1rm prediction equations for bench press in moderately trained men. The Journal of Strength & Conditioning Research. 2016;30(10):2901–2906.
- Mayhew, JL, Ball, TE, Arnold, MD, and Bowen, JC. Relative muscular endurance performance as a predictor of bench press strength in college men and women. J Appl Sports Sci Res 6:200-206, 1992.
- Mayhew, JL, Ball, TE, and Bowen, JC. Prediction of bench press ability from submaximal repetitions before and after training. Sports Med Train Rehabil 3:195-201, 1992.
- Mayhew, JL, Prinster, JL, Ware, JS, Zimmer, DL, Arabas, JR, and Bemben, MG. Muscular endurance repetitions to predict bench press strength in men of different training levels. J Sports Med Phys Fitness 35:108-113, 1995.
- O’Connor, B, Simmons, J, and O’Shea, P. Weight Training Today. St. Paul, MN:West Publishing, 1989. pp. 201-204.
- Picerno P, Iannetta D, Comotto S, et al. 1RM prediction: a novel methodology based on the force-velocity and load-velocity relationships. Eur J Appl Physiol. 2016;116(10):2035-2043.
- Reynolds, JM, Gordon, TJ, and Robergs, RA. Prediction of one repetition maximum strength from multiple repetition maximum testing and anthropometry. J Strength Cond Res 18:227-235, 2004.
- Richens B, Cleather DJ. The relationship between the number of repetitions performed at given intensities is different in endurance and strength trained athletes. Biol Sport. 2014;31(2):157-161.
- Seo D il, Kim E, Fahs CA, et al. Reliability of the one-repetition maximum test based on muscle group and gender. J Sports Sci Med. 2012;11(2):221-225.
- Thompson SW, Rogerson D, Ruddock A, Greig L, Dorrell HF, Barnes A. A novel approach to 1rm prediction using the load-velocity profile: a comparison of models. Sports (Basel). 2021;9(7):88.
- Tucker, JE, Pujol, TJ, Fisher, CL, Nahikian-Nelms, ML, Barnes, JT, and Langenfeld, ME. One-repetition maximum prediction equation for traditional college-age novice females. Med Sci Sport Exerc 38:S293, 2006.
- Wathen, D. Load assignment. In: Essentials of Strength Training and Conditioning. Baechle, TR. ed. Champaign, IL:Human Kinetics, 1994. pp. 435-439.
- Welday, J. Should you check for strength with periodic max lifts? Scholastic Coach 57(9):49-68, 1988.