Kellner 1RM Formula Misattribution
The so-called Kellner formula is listed in several places online as a method to estimate one-repetition maximum (1RM), but no published source attributes it to an author named Kellner, and it lacks validation.
The Listed Kellner Formula
The formula often cited is:
1RM = w × (102 × e-0.0338 × r)
Where:
- w is the submaximal weight lifted (in kg)
- r is the number of repetitions to failure
- e is the base of the natural logarithm (~2.71828)
This suggests an exponential decay of strength with more reps, which is not realistic.
Example:
For 100 kg lifted for 5 reps:
1RM = 100 × (102 × e-0.0338 × 5) ≈ 8608 kg
This unrealistic result indicates the formula is flawed.
Origin and Mistake
No published study or author named Kellner is associated with this formula, and searches of strength-training literature yield no evidence of its existence. However, the formula resembles the Desgorces formula from a 2010 bench press study by Degorces et al., which reported:
%1RM = 83.7677 × e-0.0338 × r + 17.6846
This model, with a high fit (R² ≈ 0.99), included an offset not present in the Kellner version. The listed Kellner formula appears to be a misinterpretation or possibly an incorrect simplification of the Desgorces equation which added the offset and the coefficient and rounded up to 102. The name “Kellner” may stem from a confusion with an unrelated researcher or an erroneous attribution, with no known publication supporting it.
Due to its lack of a verified source and validation, the Kellner formula should not be used for 1RM estimation. Coaches and athletes should rely on established formulas like Epley, Brzycki, or others for 1RM estimation.
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