One-rep max formulas estimate your 1RM, the weight you can lift for exactly one clean rep, from a set of several reps. The most widely used are the formulas by Epley (1985) and Brzycki (1993). With them you do not have to test your max to plan with percentages.
The two formulas
Epley: 1RM = weight × (1 + reps ÷ 30)
Brzycki: 1RM = weight × 36 ÷ (37 - reps)
Both describe the same relationship: the heavier a weight is relative to your max, the fewer reps you can do. The one-rep max calculator shows the average of both formulas as its main result.
Example: You bench 100 kg for 5 clean reps. Epley gives 100 × (1 + 5 ÷ 30) = 116.7 kg, Brzycki 100 × 36 ÷ 32 = 112.5 kg. The average is about 114.6 kg. This is a worked example.
How accurate they are
The formulas are most reliable with 3 to 8 clean reps close to failure. Up to about 10 reps the two stay close together; beyond that they drift apart, because endurance and daily form play a bigger role. If the two results are far apart, the set had too many reps for a good estimate.
They work best for barbell compound lifts like squats, bench press or deadlifts. For isolation exercises and machines they are less reliable. How many reps someone can do at a given percentage also depends on the exercise, training experience and muscle fiber makeup. Treat the result as a starting point, not a measurement.