How the Epley, Brzycki, and Lombardi 1RM formulas work
Epley (1985) uses a linear relationship: 1RM = w × (1 + reps/30). Every additional rep adds about 3.3% of the weight to the max estimate. Brzycki (1993) uses a hyperbolic fit: 1RM = w × 36 / (37 - reps), which caps sensibly as reps climb. Lombardi uses a power-law: 1RM = w × reps^0.10, which is gentle at low rep counts and most accurate for 1-5 reps. All three formulas were fit to real powerlifting data and agree within about 5% for sets of 3-8.