1RM Calculation Methods Compared: From Prediction Equations to Velocity-Based Estimation

Your one-repetition maximum (1RM) is the cornerstone of percentage-based strength training programming. It determines your working loads, tracks your progress, and defines your training zones. Yet directly testing your 1RM carries inherent risks: it requires maximal effort that can cause injury, generates significant fatigue that disrupts training schedules, and may not reflect your true daily capacity due to day-to-day variability.

As a result, predicting 1RM from submaximal data has been a focus of exercise science for decades. Over a dozen prediction equations exist, ranging from the classic Epley and Brzycki formulas to modern velocity-based estimation methods. This guide systematically compares the major approaches, examines their accuracy across different exercises and populations, and helps you choose the best method for your training context.

Before diving into the methods, it is worth understanding why 1RM estimation matters and when direct testing may or may not be appropriate.

Benefits of 1RM Estimation Over Direct Testing

• Reduced injury risk: Submaximal testing eliminates the need for true maximal efforts that place peak stress on muscles, tendons, and joints
• Lower fatigue cost: A true 1RM test can require 7–10 progressively heavier singles with 3–5 minute rests, consuming an entire training session. Estimation can be derived from regular training sets.
• Frequency: You can estimate 1RM every session rather than testing every 4–8 weeks, providing a much more responsive picture of your strength trajectory
• Daily applicability: Estimation accounts for daily fluctuations in capacity, while a tested 1RM is a snapshot from one specific day

When Direct Testing Still Makes Sense

Direct 1RM testing remains valuable in specific contexts:

• Competition preparation: Powerlifters and weightlifters need to practice maximal singles as a sport-specific skill
• Validation: Periodically confirming that your estimated 1RM aligns with actual capacity
• Research protocols: Studies requiring standardized maximal strength assessment
• Psychological benchmarking: The confidence and satisfaction of achieving a new personal record under controlled conditions

Traditional 1RM prediction equations use the load lifted and the number of repetitions completed to estimate maximal strength. The most widely used formulas include:

Epley Formula (1985)

1RM = Load x (1 + 0.0333 x Reps)

The Epley equation assumes a linear relationship between load and reps, with each additional rep representing approximately 3.33% of 1RM. It is the most commonly used formula in practical settings.

Example: If you squat 100 kg for 8 reps, Epley predicts 1RM = 100 x (1 + 0.0333 x 8) = 100 x 1.267 = 126.7 kg.

Brzycki Formula (1993)

1RM = Load x (36 / (37 - Reps))

Brzycki's equation uses a slightly different mathematical model that tends to produce lower estimates at higher rep ranges (above 10) and nearly identical estimates at lower rep ranges (3–7).

Example: 100 kg for 8 reps: 1RM = 100 x (36 / (37 - 8)) = 100 x 1.241 = 124.1 kg.

Lander Formula (1985)

1RM = (100 x Load) / (101.3 - 2.67123 x Reps)

Lander's equation uses a percentage-based approach and tends to produce estimates between Epley and Brzycki for most rep ranges.

Lombardi Formula (1989)

1RM = Load x Reps^0.10

Lombardi uses an exponential model rather than linear, which can produce different estimates at very high or very low rep ranges.

Mayhew Formula (1992)

1RM = (100 x Load) / (52.2 + 41.9 x e^(-0.055 x Reps))

Mayhew's exponential model was developed specifically for bench press performance and may be less accurate for lower body exercises.

Limitations of Rep-Based Equations

All traditional prediction equations share fundamental limitations:

• Rep range sensitivity: Most equations are most accurate at 3–7 reps and increasingly inaccurate above 10 reps, where metabolic fatigue, pain tolerance, and motivation become confounding factors
• Exercise specificity: Equations developed for one exercise may not transfer accurately to others due to different muscle group involvement, stabilization demands, and fatigue patterns
• Individual variation: Muscle fiber type distribution affects the reps-to-failure relationship. An athlete with predominantly fast-twitch fibers might only get 3 reps at 85%, while a more endurance-oriented athlete might get 6 reps at the same relative intensity
• Effort requirement: All rep-based formulas require sets taken to or near failure, which carries its own fatigue and injury risks
• No daily sensitivity: The formulas assume a stable 1RM — they cannot account for the 10–18% daily variation in maximal capacity caused by sleep, stress, and recovery status

Velocity-based 1RM prediction represents a fundamentally different approach. Instead of using reps to failure, it exploits the load-velocity relationship: the consistent, predictable decrease in barbell velocity as load increases.

How It Works

The method uses two or more submaximal sets at different loads, measures the mean concentric velocity for each, and extrapolates the load at which velocity would reach the minimum velocity threshold (MVT) — the slowest velocity at which a maximal repetition can be completed.

1. Perform warm-up sets at 2–3 progressively heavier loads (e.g., 60%, 70%, 80% of estimated 1RM)
2. Record mean concentric velocity at each load (using only the best rep)
3. Plot load vs. velocity and fit a linear regression
4. Extrapolate to MVT: The load at which the regression line intersects the MVT is the predicted 1RM

Minimum Velocity Thresholds by Exercise

The MVT varies by exercise and represents the slowest possible successful repetition:

• Back squat: 0.30 m/s (range: 0.25–0.35 m/s)
• Bench press: 0.17 m/s (range: 0.13–0.22 m/s)
• Deadlift: 0.15 m/s (range: 0.10–0.20 m/s)
• Overhead press: 0.20 m/s (range: 0.15–0.25 m/s)
• Power clean: 0.65 m/s (range: 0.55–0.75 m/s)

Note the wide individual ranges. Using a population-average MVT introduces error; using your own individually determined MVT significantly improves accuracy.

Multi-Point vs. Two-Point Methods

Research by Jovanovic and Flanagan (2014) and Garcia-Ramos et al. (2018) compared different velocity-based prediction approaches:

• Multi-point method: Uses 4–6 loads to build the load-velocity profile. Most accurate but requires more warm-up sets.
• Two-point method: Uses only two loads (typically a light and a moderate load). Nearly as accurate as the multi-point method when loads are well separated (e.g., 50% and 80%).
• Single-point method: Uses one load and a generalized load-velocity equation. Least accurate but most practical.

Advantages Over Rep-Based Methods

• No failure required: All sets are submaximal with 2–3 reps, eliminating fatigue and injury risk
• Daily sensitivity: Because you measure velocity at actual loads on the actual day, the prediction automatically reflects your current capacity
• Speed: Prediction can be derived from normal warm-up sets, requiring no additional testing time
• Consistency: Less affected by motivation, pain tolerance, or subjective effort compared to reps-to-failure methods

How do these methods stack up against directly measured 1RM? Research provides clear guidance:

Rep-Based Equation Accuracy

A comprehensive comparison by LeSuer et al. (1997) tested seven prediction equations against actual 1RM in 67 trained subjects across the squat, bench press, and deadlift:

• All equations were reasonably accurate at 5 or fewer reps (prediction error ±3–5%)
• Accuracy degraded significantly at 10+ reps (prediction error ±8–15%)
• The Epley formula showed the best overall accuracy across exercises
• Bench press predictions were more accurate than squat or deadlift predictions across all formulas
• Individual prediction errors ranged from 0% to over 20%, even within the most accurate formulas

Velocity-Based Prediction Accuracy

Garcia-Ramos et al. (2018) systematically evaluated velocity-based 1RM prediction:

• The multi-point method (4+ loads) predicted 1RM within ±2–3% in the bench press and squat
• The two-point method achieved ±3–4% accuracy when using loads separated by at least 30% 1RM
• Using an individualized MVT improved accuracy by 1–2% compared to population-average MVT
• Velocity-based prediction was more consistent day-to-day than rep-based methods (lower coefficient of variation)

Head-to-Head Comparison

When directly compared, velocity-based 1RM prediction demonstrates several advantages:

• Similar overall accuracy to the best rep-based equations (±3–4% vs. ±3–5%)
• Better daily sensitivity — velocity-based estimates change with daily readiness, while rep-based estimates require a new test
• Lower fatigue cost — derived from submaximal warm-up sets rather than sets to failure
• More consistent — less influenced by subjective factors like motivation and pain tolerance

The key caveat: velocity-based prediction requires a device capable of measuring barbell velocity with sufficient accuracy (±0.03 m/s or better). With a lower-quality device, the prediction error can exceed that of simple rep-based equations.

Based on the evidence, here are practical recommendations for different training contexts:

For Individual Athletes with a VBT Device

Use velocity-based 1RM prediction as your primary method. Build your individual load-velocity profile over 2–3 weeks of training, determine your personal MVT for each main exercise, and let the system predict your daily 1RM from warm-up sets. Validate against a true 1RM test every 8–12 weeks.

For Individual Athletes Without a VBT Device

Use the Epley formula with sets of 3–5 reps for the best balance of accuracy and practicality. Avoid using sets above 8 reps for prediction. Test at least two different loads and average the predictions for improved accuracy.

For Coaches Managing Teams

If equipping every athlete with a VBT device, velocity-based prediction offers the most efficient and safest approach — no testing sessions needed, daily load adjustments possible. If using rep-based methods, standardize on the Epley formula and establish exercise-specific testing protocols to minimize inter-tester variability.

For Rehabilitation Settings

Velocity-based 1RM prediction is particularly valuable in rehabilitation where true maximal testing may be contraindicated. Using submaximal loads at known velocities allows clinicians to estimate strength capacity and track recovery without exposing healing tissues to maximal stress.

Combining Methods

Consider using velocity-based prediction for daily training decisions and rep-based estimation as a cross-check. If both methods agree within 3–5%, you can have high confidence in the estimate. If they diverge significantly, investigate why — it may indicate a measurement issue, unusual fatigue, or a need to update your load-velocity profile.

Common Pitfalls to Avoid

• Using high-rep sets for prediction: Above 10 reps, all prediction methods become unreliable. Keep test sets at 5 reps or fewer.
• Applying bench press equations to squats: Use exercise-specific data when available, or at minimum use a generalized formula like Epley rather than one developed for a specific exercise.
• Ignoring individual MVT: Population-average minimum velocity thresholds can differ from your personal threshold by ±0.05–0.10 m/s, which translates to 5–10% 1RM prediction error. Take time to establish your individual MVT.
• Testing when fatigued: Rep-based prediction requires maximal effort; if you are not fully recovered, the prediction will underestimate your true 1RM. Velocity-based prediction handles this better but still works best with genuine maximal intent on each rep.