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 commonly used 1RM formulas, complete with examples and insights to help you pick the best one for you.

Try our specialized bench press, squat, and deadlift 1RM calculators, which use a dynamically weighted average of these formulas for enhanced accuracy.

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 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

Adams Formula

Best for: 5-15 reps, leg press

Origin: Dr. Gene M. Adams, 1998, Exercise Physiology Laboratory Manual

Equation: 1RM = weight × (1/(1 - 0.02 × reps)

Example: For 225 lbs and 5 reps, 1RM = 250 lbs

Notes: Linear model; simple; may underestimate low reps

Baechle Formula

Best for: 2-10 reps, general fitness

Origin: Thomas R. Baechle and Roger W. Earle, 2000, Essentials of Strength Training and Conditioning

Equation: 1RM = weight × (1 + 0.033 × reps)

Example: For 225 lbs and 5 reps, 1RM = 262 lbs

Notes: Linear model; aligns with coaching standards; similar to Epley

Berger Formula

Best for: 2-10 reps, general use

Origin: Richard A. Berger, 1961, Research Quarterly

Equation: 1RM = weight / (1.0261 × e^(-0.0262 × reps))

Example: For 225 lbs and 5 reps, 1RM = 26 lbs

Notes: Exponential model; accurate for moderate reps

Brown Formula

Best for: 2-10 reps, general use

Origin: H. Larry Brown, 1992, Lifetime Fitness

Equation: 1RM = (weight × reps × 0.0338) + weight

Example: For 225 lbs and 5 reps, 1RM = 259 lbs

Notes: Linear model; simple; similar to Epley

Brzycki Formula

Best for: 3-8 reps, bench press and squat

Origin: Matt Brzycki, 1993, Journal of Physical Education, Recreation & Dance

Equation: 1RM = weight × (36 / (37 - reps))

Example: For 225 lbs and 5 reps, 1RM = 253 lbs

Notes: Rational model; accurate for moderate reps; validated for compound lifts

Desgorces Formula

Best for: 10-20 reps, bench press

Origin: François Desgorces et al., 2010, Journal of Strength and Conditioning Research

Equation: 1RM = (100 × weight) / (83.7677 × e^(-0.0338 × reps) + 17.6846)

Example: For 225 lbs and 5 reps, 1RM = 254 lbs

Notes: Exponential model; optimized for high reps; validated for bench press

Epley Formula

Best for: 2-10 reps, squat and deadlift

Origin: Boyd Epley, 1985, Boyd Epley Workout

Equation: 1RM = weight × (1 + reps / 30)

Example: For 225 lbs and 5 reps, 1RM = 262 lbs

Notes: Linear model; simple and widely used; may overestimate high reps

Kemmler Formula

Best for: 3-15 reps, older adults

Origin: Wolfgang Kemmler et al., 2006, Journal of Strength and Conditioning Research

Equation: 1RM = weight × (1 + 0.025 × reps)

Example: For 225 lbs and 5 reps, 1RM = 243 lbs

Notes: Linear model; designed for elderly; considers age-related factors

Landers Formula

Best for: 2-10 reps, all major lifts

Origin: Jeff Landers, 1985, National Strength and Conditioning Association Journal

Equation: 1RM = (100 × weight) / (101.3 - 2.67123 × reps)

Example: For 225 lbs and 5 reps, 1RM = 256 lbs

Notes: Rational model; balanced accuracy; good for general use

Lombardi Formula

Best for: 10-20 reps, endurance-based lifts

Origin: Pat Lombardi, 1989, Beginning Weight Training

Equation: 1RM = weight × reps0.1

Example: For 225 lbs and 5 reps, 1RM = 264 lbs

Notes: Power model; handles high reps well; underestimates low reps

Mayhew Formula

Best for: 3-10 reps, bench press, squat, deadlift

Origin: Jerry L. Mayhew et al., 1992, Journal of Applied Sport Science Research

Equation: 1RM = (100 × weight) / (52.2 + 41.9 × e^(-0.055 × reps))

Example: For 225 lbs and 5 reps, 1RM = 268 lbs

Notes: Exponential model; high accuracy for moderate reps; research-backed

Naclerio Formula

Best for: 2-10 reps, free weight exercises

Origin: Fernando Naclerio et al., 2009, Journal of Human Sport and Exercise

Equation: 1RM = weight × (1 + 0.03 × reps)

Example: For 225 lbs and 5 reps, 1RM = 263 lbs

Notes: Linear model; validated for free weights

O’Connor Formula

Best for: 2-10 reps, general strength training

Origin: Bob O’Connor, Jerry Simmons, Pat O’Shea, 1989, Weight Training Today

Equation: 1RM = weight × (1 + reps / 40)

Example: For 225 lbs and 5 reps, 1RM = 253 lbs

Notes: Linear model; conservative estimates; less common

Wathen Formula

Best for: 2-10 reps, powerlifting and athletic training

Origin: Dan Wathen, 1994, in Essentials of Strength Training and Conditioning

Equation: 1RM = (100 × weight) / (48.8 + 53.8 × e^(-0.075 × reps))

Example: For 225 lbs and 5 reps, 1RM = 262 lbs

Notes: Exponential model; accurate for low reps; used in sports settings

Comparing the Formulas

Each formula gives a different 1RM estimate, especially as reps increase. For example, for 5 reps of 225 lbs, predictions range from 243 lbs (Kemmler) to 268 lbs (Mayhew). The graph below shows the estimated percentage of 1RM for 1-20 reps, with the formulas diverging greatly after 10 reps.

Graph comparing 1RM formulas for 1-20 reps
One-rep max (1RM) formula comparison for 1-20 reps

Observations:

  • Low Reps (2-5): Epley 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): Desgorces and Mayhew perform better, though accuracy drops above 15 reps.
  • Consistency: Landers, Baechle, and Brown offer balanced predictions but aren’t specialized.

Accuracy and Limitations

Research suggests formulas are most accurate for 2-10 reps, with errors of 2-10% compared to tested 1RMs. Accuracy decreases for:

  • High Reps (>15): 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

The best formula depends on your 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 Landers
    • Advanced (1-5 reps): Wathen or Mayhew
  • High Reps (10-20): Desgorces or Mayhew for hypertrophy
  • General Use: Landers, Baechle, or Brown for balanced predictions
  • Special Populations: Kemmler for older adults

Want to crunch the numbers? Use our 1RM Calculator and select a formula of your choice, or try our specialized bench press, squat, and deadlift calculators for improved accuracy. For more on one-rep max, check out our 1RM Overview or explore all of our Fitness Guides.