How One-Rep-Max Formulas Work

Your one-rep max (1RM) is the heaviest weight you can lift exactly once with good form. Actually testing it is the most dangerous way to find out — maxing out taxes joints and technique and leaves nothing in the tank for training. Instead, lift a submaximal weight for several reps and let a 40-year-old formula estimate the max you never had to attempt.

The core idea: reps predict max

Lift a weight for two reps and you could clearly have done one slightly heavier. Lift it for ten and you could have gone much heavier. The relationship between reps completed at a given weight and the true 1RM is smooth enough to model, and different researchers fitted curves to it. The most famous is Epley's:

1RM = weight × (1 + reps / 30)

Each additional rep adds about 1/30 — 3.3% — to the estimated max. Squat 100 kg for 5 reps and Epley predicts 100 × (1 + 5/30) = 116.67 kg. That's the whole trick: the set did the measuring, the arithmetic did the maxing.

Four formulas, one question

The calculator carries four estimates. Watch them on the same 100 kg × 5 set:

Epley (1985):    1RM = W × (1 + R/30)          → 116.67 kg
Brzycki (1993):  1RM = W × 36 / (37 − R)        → 112.50 kg
Lombardi (1989): 1RM = W × R^0.1                → 117.46 kg
Lander (1985):   1RM = 100 × W / (101.3 − 2.67123 × R) → 113.71 kg

All four are exact by construction at one rep (Epley, Brzycki, and Lombardi return the lifted weight itself; Lander sits within about 1% of it), and they drift apart as reps climb, because they weight the fatigue effect differently. Epley and Lombardi are the optimists, Brzycki the conservative one, and the gap between highest and lowest grows from a rounding error at 3 reps to 4–5% at 10–12 reps. For 100 kg × 6 the spread is already visible: Epley 120 vs Brzycki 115.2.

The percentage table: programming from a max

Estimating the max is half the tool's job; the other half is turning it into training weights. Programs are written in percentages of 1RM, and the calculator derives its table from the inverse of the Brzycki relationship:

% of 1RM for R reps = (37 − R) / 36

So 5 reps ≈ 88.9% of max, 8 reps ≈ 80.6%, 10 reps ≈ 75%, 12 reps ≈ 69.4%, 15 reps ≈ 61.1%. Applied to our estimated 116.67 kg: sets of 8 should land near 94 kg, sets of 12 near 81 kg. That's how "I got 100 for 5" becomes "do 4 × 8 at 94" — the table does the translating, and you never touch a true max to get there.

Which formula, and when to trust it

Below about 5 reps the formulas agree so closely that the choice barely matters — take the average, or Epley, and move on. Beyond 10 reps, treat any 1RM estimate skeptically: light-weight, high-rep sets to exhaustion stop predicting maximal strength well, because muscular endurance, local fatigue, and pacing start to dominate the outcome. A 225 lb × 6 set gives 270.0 lb by Epley but 261.29 lb by Brzycki — a 9 lb disagreement that widens further at 12 and 15 reps. The calculator caps input at 20 reps for exactly this reason. Rule of thumb: estimate from sets of 3–6, where strength itself is still the main variable being tested.

From estimate to program

Standard strength programming maps percentages to goals: roughly 85% of 1RM and above for low-rep maximal strength work (sets of 1–5), the 67–85% band for the 6–12 rep hypertrophy range, and below that for muscular-endurance sets. Re-estimate your 1RM every few weeks from a fresh hard set — as the estimate climbs, the percentages climb with it, and progression becomes arithmetic instead of guesswork. Strength work also has a place in the wider energy picture: lifting burns through a MET-based estimate (the calculator's weight-lifting activity runs at 6.0 METs), though conditioning cardio is a cleaner tool for the deficit math described in How a Calorie Deficit Works.

Try it yourself

The One Rep Max Calculator runs all four formulas on any weight-and-reps input and builds the full percentage table from your result. The Calories Burned Calculator estimates the energy cost of a lifting session, and the Pace Calculator handles the running side of a combined program — pace zones for the cardio days, percentage table for the barbell days.