One-Rep Max (1RM) Formulas: Brzycki, Epley, Lombardi & Wathan Compared with RPE Charts
Testing a true One-Rep Max (1RM) to absolute failure on squats, bench presses, or deadlifts carries high central nervous system fatigue and injury risk. Using mathematical strength prediction equations—most notably the Brzycki and Epley formulas—athletes can calculate their maximum strength from submaximal sets (e.g. 5 reps at 225 lbs) with over 95% accuracy.
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1. The Top 4 1RM Mathematical Equations
Where $w$ is the weight lifted and $r$ is the number of repetitions completed:
2. Epley Formula: 1RM = w × [ 1 + (r ÷ 30) ]
3. Lombardi Formula: 1RM = w × r0.10
4. Wathan Formula: 1RM = (100 × w) ÷ [ 48.8 + (53.8 × e−0.075 × r) ]
2. Rep Accuracy: The 10-Rep Rule
1RM prediction formulas rely on neuromuscular motor unit recruitment. Sets performed between 2 and 6 reps yield the highest prediction accuracy (±2%). Beyond 10 reps, cardiovascular fatigue, muscle endurance, and lactate accumulation distort the estimation, often overestimating true 1RM.
3. The RPE / Reps in Reserve (RIR) Scale
- RPE 10 (0 RIR): Absolute maximum effort, zero reps left in the tank.
- RPE 9 (1 RIR): Extremely heavy, could have grinded out exactly 1 more rep.
- RPE 8 (2 RIR): Solid working set, 2 reps left in reserve (Ideal for strength building).
- RPE 7 (3 RIR): Fast bar speed, 3 reps left (Ideal for explosive power/hypertrophy).
4. Training Percentage Table
| Target Repetitions | Approximate % of 1RM | Primary Training Adaptation |
|---|---|---|
| 1 Rep | 100% | Maximal Neuromuscular Strength |
| 3 Reps | 93% | Power & High-Threshold Motor Units |
| 5 Reps (Sweet Spot) | 87% – 89% | Optimal Strength & Myofibrillar Hypertrophy |
| 8 Reps | 80% | Hypertrophy & Volume Tolerance |
| 12 Reps | 70% | Sarcoplasmic Hypertrophy & Endurance |
5. Worked Example (225 lbs for 5 Reps)
• Epley: 225 × (1 + 5/30) = 262.5 lbs
• Lombardi: 225 × 50.10 = 264.3 lbs
• Consensus 1RM: ≈ 255 – 260 lbs.