Why Different Formulas Give Different Results
Ever wonder why Epley says your max is 315 but Brzycki says 308? Let's explore the mathematical and physiological reasons behind formula variations and which one you should trust.
If you've used multiple 1RM calculators, you've probably noticed they rarely give the same answer. The difference can be as much as 20-30 pounds on a 300-pound lift. This isn't a bug—it's a feature that reflects the complex reality of human strength.
Each formula was developed using different populations, methodologies, and assumptions about how strength drops off with increasing repetitions. Understanding these differences helps you choose the right formula for your situation.
The Core Problem: Strength Isn't Linear
The fundamental challenge all formulas face is that the relationship between weight and repetitions isn't perfectly predictable. Here's why:
Individual Variation Factors
Physiological Differences:
- • Muscle fiber type distribution
- • Nervous system efficiency
- • Lactate threshold
- • ATP-PC system capacity
- • Muscle architecture
Training Factors:
- • Training history and style
- • Recent training emphasis
- • Technical proficiency
- • Mental approach to max efforts
- • Competition experience
The Result: Someone who trains primarily with singles and doubles will have a different strength curve than someone who does sets of 8-12. This is why no single formula can be perfectly accurate for everyone.
Head-to-Head Formula Comparison
Let's see how different formulas estimate 1RM from the same input (225 lbs × 8 reps):
| Formula | Calculation | Result | Variance |
|---|---|---|---|
| Epley | 225 × (1 + 8/30) | 284 lbs | +4 lbs |
| Brzycki | 225 × (36/(37-8)) | 279 lbs | -1 lb |
| Lombardi | 225 × 8^0.10 | 282 lbs | +2 lbs |
| O'Conner | 225 × (1 + 8/40) | 270 lbs | -10 lbs |
| Lander | 100 × 225/(101.3-2.67×8) | 281 lbs | +1 lb |
| Average | - | 280 lbs | ±5 lbs |
Range: 270-284 lbs (14 lb spread or 5% variation)
Variance Increases with Rep Count
The disagreement between formulas grows as reps increase:
Why Each Formula Behaves Differently
Linear vs. Exponential Models
Linear Models (Epley, O'Conner):
Assume each rep adds/subtracts a fixed percentage of your max.
- • Simple calculation
- • Works well for 1-10 reps
- • Overestimates at high reps
- • Underestimates endurance athletes
Exponential Models (Mayhew, Wathan):
Account for non-linear strength decay with fatigue.
- • Complex calculation
- • Better at all rep ranges
- • More accurate for 10+ reps
- • Accounts for fatigue better
Population-Specific Biases
Epley - General Population
Developed using recreational lifters. Tends to be optimistic for average trainers. Most widely used due to simplicity and reasonable accuracy for most people.
Brzycki - College Athletes
Based on NCAA football players. Very accurate for explosive athletes with good technique. May underestimate for endurance-trained individuals.
Lombardi - Powerlifters
Developed using competitive powerlifters. Accounts for superior neural efficiency in experienced lifters. Often underestimates beginners.
Mayhew - Large Dataset
Based on hundreds of subjects across different training backgrounds. Most balanced but may not be optimal for specific populations.
Real-World Examples
Let's see how different athlete types might see formula variance:
Example 1: Powerlifter Profile
Athlete: 5 years training, primarily singles and doubles
Test: 405 lbs × 3 reps on squat
True 1RM: 450 lbs
| Formula | Estimate | Error | Accuracy |
|---|---|---|---|
| Brzycki | 441 lbs | -9 lbs | 98% |
| Lombardi | 448 lbs | -2 lbs | 99.5% |
| Epley | 446 lbs | -4 lbs | 99% |
Best fit: Lombardi (designed for powerlifters)
Example 2: CrossFit Athlete
Athlete: 3 years training, lots of metabolic conditioning
Test: 185 lbs × 12 reps on bench press
True 1RM: 245 lbs
| Formula | Estimate | Error | Accuracy |
|---|---|---|---|
| Epley | 259 lbs | +14 lbs | 94% |
| Mayhew | 248 lbs | +3 lbs | 99% |
| O'Conner | 241 lbs | -4 lbs | 98% |
Best fit: O'Conner (conservative for endurance athletes)
Which Formula Should You Trust?
Decision Framework
If you're testing with 1-3 reps:
Use Brzycki - most accurate at low reps
If you're testing with 4-6 reps:
Use Epley or average multiple formulas
If you're testing with 8-12 reps:
Use Mayhew or Wathan - exponential models handle fatigue better
If you're a beginner:
Use O'Conner or Lander - more conservative estimates
If you're experienced (3+ years):
Use Lombardi for low reps, Brzycki for general use
When in doubt:
Average all formulas - reduces individual formula bias
Important Considerations
- • Track your own data: Over time, you'll learn which formula matches your strength curve best
- • Exercise matters: Deadlifts often underperform predictions, bench press usually matches closely
- • Use the same formula consistently: This allows accurate progress tracking even if the absolute number is off
- • Consider fatigue state: All formulas assume you're relatively fresh
Practical Application Tips
Creating Your Personal Correction Factor
Here's how to calibrate formulas to your individual strength curve:
- 1. Test your actual 1RM (or very heavy single)
- 2. Within a week, test 3RM, 5RM, and 8RM on separate days
- 3. Calculate estimated 1RM from each test using different formulas
- 4. Find your correction factor:
Correction = Actual 1RM ÷ Formula Estimate - 5. Apply this factor to future calculations with that formula
Example: If Epley estimates 300 but your actual max is 285, your correction factor is 0.95. Multiply all future Epley estimates by 0.95.
The Bottom Line
Formula differences aren't errors—they're features that reflect the complexity of human strength. No formula will be perfect for everyone because we all have different:
- • Muscle fiber compositions
- • Training histories
- • Neural efficiencies
- • Fatigue resistance
- • Technical proficiency
The best approach? Use multiple formulas, understand their biases, and track which one best predicts your actual performance. Over time, you'll develop an intuitive sense of how to interpret the numbers for your body.
Remember: These are tools for training, not definitive measurements. Use them to guide programming, but always listen to your body and adjust based on actual performance.
Compare all 7 formulas with our calculator:
See Your Formula Comparison