1RM Formulas Explained
Your one-rep max (1RM) is the heaviest weight you can lift for a single repetition with proper form. It’s a key metric in strength training, whether you’re programming workouts or tracking progress. Direct 1RM testing can be intense, so formulas estimate it using the weight you lift and the number of reps. We’ve compiled the most accurate 1RM formulas, complete with examples and insights to help you pick the best one for you.
What Are 1RM Formulas?
1RM formulas predict your maximum lift based on a submaximal effort—like lifting 225 pounds for 5 reps. Developed by coaches and researchers, these equations model the relationship between reps and intensity for the most accurate 1RM estimates. Each formula has its strengths, depending on the lift, rep range, and your experience level. Let’s break them down.
The Formulas
Epley Formula
Best for: 2–10 reps, especially squat and deadlift.
Origin: Developed by Boyd Epley in 1985 for powerlifting programs.
Equation: 1RM = weight × (1 + reps / 30)
Example: 225 lbs for 5 reps: 1RM = 225 × (1 + 5/30) = 225 × 1.1667 = 262.5 lbs
Pros: Simple, widely used, reliable for low to moderate reps.
Cons: Overestimates for high reps (>10) due to linear scaling.
Brzycki Formula
Best for: 3–8 reps, ideal for bench press and squat.
Origin: Introduced by Matt Brzycki in 1993, based on strength research.
Equation: 1RM = weight / (1.0278 - 0.0278 × reps)
Example: 225 lbs for 5 reps: 1RM = 225 / (1.0278 - 0.0278 × 5) = 225 / 0.8888 = 269.8 lbs
Pros: Accurate for moderate reps, validated for compound lifts.
Cons: Less reliable for very low (10) reps.
Lander Formula
Best for: 2–10 reps, versatile for all major lifts.
Origin: Created by John Lander in the 1980s, based on lifting data.
Equation: 1RM = (100 × weight) / (101.3 - 2.67123 × reps)
Example: 225 lbs for 5 reps: 1RM = (100 × 225) / (101.3 - 2.67123 × 5) = 22500 / 87.94385 = 248.3 lbs
Pros: Balanced accuracy across rep ranges, good for general use.
Cons: Complex equation, less popular than Epley or Brzycki.
Lombardi Formula
Best for: 10–20 reps, suited for endurance-based lifts.
Origin: Developed by Dr. Daniel Lombardi in the 1990s for high-rep training.
Equation: 1RM = weight × reps^0.1
Example: 225 lbs for 5 reps: 1RM = 225 × 5^0.1 ≈ 225 × 1.2589 = 283.3 lbs
Pros: Handles high reps well, simple to calculate.
Cons: Underestimates for low reps (<5), less accurate for powerlifting.
Mayhew Formula
Best for: 3–10 reps, validated for bench press, squat, deadlift.
Origin: Developed by Jerry Mayhew in 1992, based on college athletes.
Equation: 1RM = (100 × weight) / (52.2 + 41.9 × e^(-0.055 × reps))
Example: 225 lbs for 5 reps: 1RM = (100 × 225) / (52.2 + 41.9 × e^(-0.055 × 5)) ≈ 22500 / 82.716 = 267.3 lbs
Pros: High accuracy for moderate reps, research-backed.
Cons: Complex, requires a calculator.
O’Conner Formula
Best for: 2–10 reps, general strength training.
Origin: Proposed by Brian O’Conner in 1988, based on lifting studies.
Equation: 1RM = weight × (1 + reps / 40)
Example: 225 lbs for 5 reps: 1RM = 225 × (1 + 5/40) = 225 × 1.125 = 253.1 lbs
Pros: Simple, slightly conservative compared to Epley.
Cons: Less accurate for high reps, less widely used.
Wathen Formula
Best for: 2–10 reps, powerlifting and athletic training.
Origin: Developed by Dan Wathen in 1994 for sports performance.
Equation: 1RM = (100 × weight) / (48.8 + 53.8 × e^(-0.075 × reps))
Example: 225 lbs for 5 reps: 1RM = (100 × 225) / (48.8 + 53.8 × e^(-0.075 × 5)) ≈ 22500 / 81.548 = 263.7 lbs
Pros: Accurate for low reps, used in athletic settings.
Cons: Complex, less common than Mayhew or Brzycki.
Baechle Formula
Best for: 2–10 reps, general fitness and coaching.
Origin: Published by Baechle and Earle in 2000, in “Essentials of Strength Training”.
Equation: 1RM = weight × (1 + 0.033 × reps)
Example: 225 lbs for 5 reps: 1RM = 225 × (1 + 0.033 × 5) = 225 × 1.165 = 262.1 lbs
Pros: Simple, aligns with coaching standards.
Cons: Similar to Epley, less accurate for high reps.
Comparing the Formulas
Each formula gives a different 1RM estimate, especially as reps increase. For 225 lbs at 5 reps, predictions range from 248.3 lbs (Lander) to 283.3 lbs (Lombardi). The graph below shows how they diverge across 1–20 reps, with Lombardi spiking at higher reps and Brzycki staying conservative.
Graph: One-rep max (1RM) formula comparison for 225 lbs, 1–20 reps.
Key Observations:
- Low Reps (2–5): Epley, Mayhew, and Wathen are closest to actual 1RM, based on powerlifting studies.
- Moderate Reps (6–10): Brzycki and Mayhew excel, with errors under 5% in research.
- High Reps (10–20): Lombardi is best, but accuracy drops above 15 reps due to fatigue.
- Consistency: Lander and Baechle offer balanced predictions but aren’t specialized.
Accuracy and Limitations
Research (e.g., Mayhew et al., 1992) shows formulas are most accurate for 2–10 reps, with errors of 2–5% compared to tested 1RMs. Accuracy decreases for:
- High Reps (>10): Fatigue and endurance skew results.
- Beginners: Inconsistent form affects submaximal lifts.
- Isolation Exercises: Formulas work best for compound lifts like squats, not bicep curls.
Limitations:
- Formulas assume linear or exponential strength curves, which vary by individual.
- They don’t account for technique, fatigue, or equipment (e.g., lifting belts).
- Inaccurate predictions can mislead training plans if taken as exact.
Choosing the Right Formula
Your choice depends on the lift, rep range, and training level. Here’s a guide:
- Bench Press:
- Beginner (3–8 reps): Brzycki or Mayhew
- Advanced (2–5 reps): Mayhew or Wathen
- Squat:
- Beginner (5–10 reps): Epley or Baechle
- Advanced (2–6 reps): Mayhew or Brzycki
- Deadlift:
- Beginner (3–8 reps): Epley or Lander
- Advanced (1–5 reps): Wathen or Mayhew
- High Reps (10–20): Lombardi for hypertrophy and endurance-focused lifts
- General Use: Lander or Baechle for balanced predictions across lifts
Want to crunch the numbers? Use our 1RM Calculator to test these formulas with your lifts. For more on one-rep max, check out our 1RM Overview or explore all Fitness Guides.