The Math Behind the Bench Press Percentile Calculator

Full Methodology

This calculator estimates bench press percentiles by modeling the entire adult population as a combination of lifters and non-lifters, then fitting a normal distribution to the resulting data.

1. Population Split

Based on CDC data:

35% of men lift weights regularly
25% of women lift weights regularly

2. Average Bench Press by Group

Non-lifters: Men = 119 lbs, Women = 55 lbs
Lifters: Men = 220 lbs, Women = 104 lbs

3. Weighted Population Average

Men: 119 × 0.65 + 220 × 0.35 = 155 lbs  
Women: 55 × 0.75 + 104 × 0.25 = 65 lbs

4. Average Bodyweight

Men: 190 lbs
Women: 160 lbs

5. Relative Strength (Lift ÷ Bodyweight)

Men: 155 / 190 = 0.82  
Women: 65 / 160 = 0.41

6. Bodyweight Standard Deviation

Estimated from NHANES percentiles using:

SD ≈ (95th percentile − 5th percentile) / 3.29

Men: (284 − 136) / 3.29 ≈ 45 lbs  
Women: (263 − 110) / 3.29 ≈ 47 lbs

7. Non-Lifter Strength Variability

Men: 0.82 × 45 ≈ 37 lbs  
Women: 0.41 × 47 ≈ 19 lbs

8. Lifter Strength Variability

Derived from strength percentiles:

Men: (370 − 119) / 3.29 ≈ 75 lbs  
Women: (198 − 55) / 3.29 ≈ 43 lbs

9. Combined Standard Deviation

Men: 37 × 0.65 + 75 × 0.35 ≈ 50 lbs  
Women: 19 × 0.75 + 43 × 0.25 ≈ 25 lbs

10. Final Distributions

Men: mean = 155 lbs, std dev = 50 lbs
Women: mean = 65 lbs, std dev = 25 lbs

11. Relative Strength Distribution

Men: std = 50 / 190 ≈ 0.26  
Women: std = 25 / 160 ≈ 0.16

12. Percentile Calculation

Percentiles are computed using a normal distribution:

z = (value − mean) / standard deviation  
percentile = CDF(z)