Estimating 1-Repetition Maximum

Effective rehabilitation requires appropriate dosing of therapeutic exercise. Dosing is traditionally based on 1-repetition maximum (1-RM) lifting. Achieving therapeutic goals are related to using the appropriate percentage of a given 1-RM. A Soviet sports scientist named A.S. Prilepin developed the Prilepin’s Chart to facilitate the optimal relationship between percentage of 1-RM and the number of repetitions and sets one should perform. Column 1 has the percentage of the 1-RM weight to be lifted. Column 2 is the number of repetitions performed in each set at the given percentage of 1-RM. Column 3 represents the optimal total repetitions recommended at the given 1-RM. Finally, column 4 is the range of total repetitions that may be performed for a given percentage of 1-RM.

Percentages	Reps per Set	Optimal Total Reps	Total Range
55-65	3-6	24	18-30
70-80	3-6	18	12-24
80-90	2-4	15	10-20
90+	1-2	4	2-10

Let’s demonstrate a dosage for a squat. The individual can perform a 1-RM with 200 pounds. If the elected exercise percentage is 70%, 3-6 repetitions should be performed. If 4 repetitions can be achieved before “form-fatigue” occurs, then 4-5 sets should be completed to achieve 16-20 total repetitions. This is within the recommended total range (12-24) and close to the optimal total repetitions (18). The same calculations can be performed for 60% 1-RM or 80% 1-RM.

As simple as this calculation can be, there is an inherent problem. We need to know the 1-RM to perform these calculations. If an individual’s condition does not permit them to safely perform a 1-RM, what can you do? Fortunately there are 7 prediction equations to extrapolate a 1-RM: Brzycki (1993), Epley (1985), Lander (1985), Lombardi (1989), Mayhew, Ball, Arnold, & Bowen (1992), O’Connor, Simmons, & O´Shea (1989), and Wathen (1994). These equations use the weight lifted and the number of repetitions to determine what the 1-RM would be. Below are the 7 equations:

Researcher	Formula
Brzycki (1993)	Weight ÷ [1.0278 – ( 0.0278 × Number of repetitions)]
Epley (1985)	Weight ÷ [1 + (0.0333 x reps)]
Lander (1985)	(100 × Weight) ÷ [101.3 – (2.67123 × Number of repetitions )]
Lombardi (1989)	(Weight x Number of repetitions)^0.1
Mayhew, Ball, Arnold, & Bowen (1992)	100 x weight ÷ 52.2 + 41.9e^{-0.055 repetitions}
O’Connor, Simmons, & O´Shea (1989)	Weight x [1 +(repetitions/40)]
Wathen (1994)	100 x weight ÷ 48.80 + 53.8e^{-0.075 repetitions}

LeSuer et al (1997) performed a study to determine the accuracy of the 7 equations in the predicting of a 1-RM. The study included 67 participants who performed a bench test, squat, and deadlift. All correlation coefficients were high (r > 0.95) but the accuracy of prediction equations varied over different resistance exercises. The Mayhew, Ball, Arnold et al. (1992), Epley (1985), and Wathen (1994) formulas evidenced the lowest average error and highest relative accuracy over the resistance exercises examined. However, average error was high for all formulas over all exercises. The graph below displays the relationship.

There have several issues identified that could account for the variability in 1-RM testing. Different exercises, trained vs untrained, and endurance vs strength trained to name a few. However, given a lack of options when a 1-RM cannot be tested directly, Richen and Cleather (2014) suggested that traditional guidelines may underestimate the potential number of repetitions that can be completed at a given percentage of 1-RM.

In summary, the formulas provided simply offer you options to extrapolate 1-RM when the actual measurement is not possible or perceived to be potentially unsafe. More cutting-edge orthopedic information can be found in iOrtho+ Premium Mobile App.

Subscribe for the low annual rate of only $9.99. If you prefer to just try iOrtho+ Premium for 1 month, you can do so for only $1.99 Please visit https://iortho.xyz/ Prior blog posts are also available at https://iortho.xyz/

For more information about evidence-based orthopedic clinical tests in iOrtho+ PREMIUM Mobile App, please visit: https://iortho.xyz/

If you would like to learn more about the Mobil-Aider orthopedic measurement device to quantify joint mobility, please visit: https://mobil-aider.com/

LeSuer, Dale A.; McCormick, James H.; Mayhew, Jerry L.; Wasserstein, Ronald L.; Arnold, Michael D. “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.
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;31:157-161
Wood TM, Maddalozzo GF, Harter RA. Accuracy of seven equations for predicting 1-RM performance of apparently healthy, sedentary older adults. Measure of Physical Education and Exercise Science. 2009; 67-94