What it estimates
The maximum weight you could lift for a single repetition, projected from a sub-maximal working set. The math comes from regression-fitted equations to historical lifting data, not from any muscle physiology principle. Three of these equations have stuck around because each works in a different rep range, and showing all three protects against the bias of any one.
Use 1RM estimates to:
- Prescribe load as a percentage of 1RM (a common programming approach)
- Track strength progress without retesting your 1RM every week
- Auto-fill RPE-based prescriptions in a coaching template
Formulas, no abstraction
Epley: 1RM = load × (1 + reps / 30)
Brzycki: 1RM = load / (1.0278 − 0.0278 × reps)
Lombardi: 1RM = load × reps^0.10
The calculator above runs all three and reports the median, which is the most robust single number when you don’t know which formula best fits your set. RIR is incorporated by adding the unfinished reps to the actual reps before applying the formula. So 100 kg × 5 reps with 2 RIR is treated as 100 kg × 7 reps for estimation purposes.
Worked example
A lifter benches 100 kg × 5 with 1 RIR (so they could have done 6).
Effective reps = 5 + 1 = 6
Epley: 100 × (1 + 6/30) = 100 × 1.20 = 120.0 kg
Brzycki: 100 / (1.0278 − 0.0278 × 6) = 100 / 0.861 = 116.2 kg
Lombardi: 100 × 6^0.10 = 100 × 1.196 = 119.6 kg
Median: 119.6 kg
That 119.6 figure becomes the projected 1RM. From there you can calculate RPE-based loads using the RPE calculator, which maps reps × RPE → percentage of 1RM.
Which formula fits which set
A common mistake is picking one formula and trusting it across all rep ranges. Each was fitted to slightly different data, and the accuracy degrades outside that range:
- Brzycki fits powerlifting-style 1-10 rep sets best. It overestimates above 10 because the denominator approaches zero as reps approach 36 (where it predicts an undefined 1RM). Don’t use it past 10 reps.
- Epley is the most general-purpose. Works reasonably across 1-15 reps. Tends to slightly overestimate at low reps (1-3) for strong lifters.
- Lombardi uses a power curve, which fits hypertrophy ranges (8-15 reps) better than the linear formulas. Underestimates at low reps.
For a 1-rep set, all three should agree closely; a 5-rep set will see ~3-5% spread; a 10-rep set will see 5-10% spread. The wider the spread, the less confident you should be in any single number.
Why a 3-formula median beats a single formula
LeSuer et al (1997) tested four prediction equations against actual 1RMs measured in 67 untrained subjects. No single formula was uniformly best; Brzycki was 5% closer for bench, Epley closer for squat. The honest implication is to display multiple formulas and let the trainer (or the median) decide.
This calculator follows the practical convention working strength coaches use: surface all three estimates, mark the median, let you eyeball which formula fits your set best.
Three-test PR protocol
For a more defensible 1RM, run a structured three-test protocol over 6-9 weeks instead of a single top set. We document the protocol in the three-test PR guide: test 1 at 5+ reps RPE 8, test 2 at 3 reps RPE 9, test 3 at 1 rep RPE 9-10. The three estimates triangulate to a confidence band, not a single point estimate.
When 1RM estimates fail
The estimates assume the trainee:
- Performed the set with sound technique
- Was rested (no major fatigue from previous sets)
- Was honest about reps left in the tank (the RIR input)
If any of these conditions break, the estimate inflates. A grinder rep at the end of a set that violated form added 5-15% to the estimate without adding 5-15% of true strength. Coaches use the RPE/RIR feedback channel for exactly this reason: the trainee says “felt like I had 0 left” and that’s the cap.
What this means inside Coach Sheet
In the Lifting Records tab, the e1RM column auto-calculates per main lift using the median of the three formulas with RIR adjustment. When you log “100 × 5 RIR 1” against a Bench Press row, the sheet writes 119.6 to the e1RM column without any manual recompute. The week-to-week e1RM trend becomes a chart in the Strength Progress tab, and stagnation flags fire when the trend flattens for 4+ weeks.
Sources
- [1]
- [2]
- [3]
- [4]