Every 1RM estimator built into this calculator exploits the same empirical observation: the heavier the load relative to your true maximum, the fewer reps you can complete. A set of one rep is by definition your 1RM, a set of five sits in a predictable band below it, and a set of ten sits lower still. By fitting a curve to that load-versus-reps relationship using a single submaximal data point, the formulas project the load at which exactly one rep is possible. This calculator runs seven validated equations and, by default, averages them.
Epley (1985), 1RM = W × (1 + r/30), is the simplest arithmetically and tends to predict slightly higher numbers — a good fit for experienced lifters who maintain bar speed deep into a set. Brzycki (1993), 1RM = W ÷ (1.0278 − 0.0278 × r), tracks the linear region tightly for 1–10 reps and gives slightly conservative estimates favored by powerlifting coaches. Lander (1985) is structurally similar to Brzycki and is often paired with it. Lombardi (1989), 1RM = W × r^0.10, dampens the projection at higher rep counts. Mayhew (1992) and Wathan (1994) use exponential-decay terms that better fit performance past 10 reps, which is why the NSCA recommends them for moderate-rep work. O'Conner is a simple linear model useful as a quick sanity check.
From the averaged 1RM the calculator builds a Training Weights table by multiplying 1RM by 100%, 95%, 90%, 85%, 80%, 75%, 70%, and 65%, alongside the rep range each percentage typically supports (1 rep at 100%, about 4 reps at 90%, about 8 reps at 80%, and so on). It also derives a Rep Maxes grid for 1RM, 2RM, 3RM, 5RM, 8RM, 10RM, 12RM, and 15RM by applying the inverse Brzycki relationship — useful for setting last-set targets in 5/3/1, Texas Method, and Sheiko-style programs.
Accuracy is best at 1–5 reps, drops modestly out to 10 reps, and falls off sharply past 12 because muscular endurance, breathing, and pacing dominate over pure strength. The formulas also assume a set taken to or within one rep of failure; if you stop with three reps in reserve, every estimator will under-predict. Expect roughly ±5% error in the trained, fresh, well-rested case and wider error when fatigued, dehydrated, or for new lifters whose motor patterns aren't yet efficient at maximal loads.