The Naclerio 1RM Formula
The Naclerio 1RM formula, attributed to Dr. Fernando Naclerio and colleagues, is an exponential model developed from empirical submaximal lifting data. While not originally published as a standalone formula, it emerged from a best-fit analysis of repetitions-to-failure data collected during strength testing protocols. It provides a scientifically grounded and safe alternative for estimating one-repetition maximum (1RM), particularly within the 3-10 rep range.
About Dr. Fernando Naclerio
Dr. Fernando J. Naclerio is a professor of sport and exercise science at the University of Greenwich (UK), formerly affiliated with the European University of Madrid. His research specializes in resistance training, strength and conditioning, and sports performance optimization. With dozens of peer-reviewed publications, Dr. Naclerio is recognized for developing practical assessment protocols that emphasize both safety and scientific validity—particularly for populations where maximal effort testing poses unnecessary risk.
Origin and Development
The Naclerio formula was first presented in a 2009 review article in the Journal of Human Sport and Exercise, titled “Assessing Strength and Power in Resistance Training.” In this study, Naclerio and colleagues gathered submaximal lift data from 11 physically active university students, tracking repetitions to failure across a range of intensities (30-95% 1RM) on the bench press.
Using regression analysis, the authors observed that the relationship between the number of reps completed and the percentage of 1RM was exponential, especially at lighter and heavier ends of the load spectrum. The formula that best fit the data was:
%1RM = 0.951 × e-0.021 × r
This expression was then inverted and algebraically rearranged to estimate 1RM directly from submaximal lifts, leading to what is now known as the Naclerio 1RM Formula.
The Naclerio Formula
The Naclerio 1RM formula estimates 1RM with the equation:
1RM = w × (1 / (0.951 × e-0.021 × r))
Where:
- w = submaximal weight lifted
- r = number of repetitions performed to failure
Example:
If you lift 100 kg for 5 reps:
1RM = 100 × (1 / (0.951 × e-0.021 × 5)) = 100 × (1 / (0.951 × e-0.105)) ≈ 100 × (1 / (0.951 × 0.9003)) ≈ 100 × (1 / 0.8562) ≈ 116.82 kg
The estimated one-rep max in this case would be approximately 117 kg.
Structure and Characteristics
The formula’s exponential design reflects the real-world curvilinear decay in force output as reps increase. Compared to linear models like Epley or Brzycki, this model better accounts for how fatigue accelerates rep-to-rep as volume climbs, especially outside the ideal 3-10 rep range.
Unlike other exponential models such as Mayhew or Wathen, Naclerio’s formula is derived directly from new data and does not rely on extrapolated competition or training data from athletes.
Validation and Accuracy
While the formula has not been independently validated in follow-up trials, its reported correlation with actual 1RM values was strong in the original study:
- Correlation coefficient (R²) ≈ 0.95
- Standard error of estimate (SEE) ≈ ±4.2%
The authors explicitly note that the formula performs best in the 3-10 rep range, where the relationship is approximately linear. It becomes less reliable for sets of fewer than 3 or more than 10 reps, where fatigue and energy system limitations make predictions more erratic.
Naclerio’s Contribution to Strength Science
The Naclerio formula is one of the few 1RM estimation tools derived from recent empirical testing protocols with modern submaximal loads. While not originally presented as a standalone calculator, its elegant curve-fitting solution makes it valuable for researchers and coaches alike.
Dr. Naclerio’s broader body of work emphasizes the relationship between strength, velocity, and power, and the importance of individualized neuromuscular profiling. His formula complements this philosophy by offering a middle-ground between simplicity and scientific sophistication.
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