How 1RM estimation works
Your one-rep max is the heaviest weight you can lift once with good form. Testing it directly is tiring and carries more risk, so lifters estimate it from a heavier set of several reps. Every formula assumes that the number of reps you can do falls in a predictable way as the weight rises. That is roughly true between about 2 and 10 reps, and less true beyond that.
Epley: 1RM = w × (1 + r ÷ 30)
Brzycki: 1RM = w × 36 ÷ (37 − r)
McGlothin: 1RM = 100 × w ÷ (101.3 − 2.67123 × r)
Lombardi: 1RM = w × r^0.10
Mayhew: 1RM = 100 × w ÷ (52.2 + 41.9 × e^(−0.055 × r))
w = weight lifted, r = reps completed
Worked example
You bench 100 kg for 5 clean reps.
Epley: 100 × (1 + 5 ÷ 30) = 100 × 1.1667 = 116.7 kg. Brzycki: 100 × 36 ÷ 32 = 112.5 kg. McGlothin: 10,000 ÷ (101.3 − 13.36) = 10,000 ÷ 87.94 = 113.7 kg. Lombardi: 5^0.1 = 1.1746, so 117.5 kg. Mayhew: e^(−0.275) = 0.7596, 41.9 × 0.7596 = 31.83, and 10,000 ÷ 84.03 = 119.0 kg. The average is 579.4 ÷ 5 = 115.9 kg.
A sensible first single to attempt in training is about 90 to 95% of that, 105 to 110 kg, rather than jumping straight at the estimate.
How accurate are the formulas?
The estimates are closest to a tested max when the set is heavy and short. Reynolds and colleagues (2006) found that predictions from lower-rep sets were more accurate than those from sets of 10 or 20 reps. Endurance-trained people often manage more reps at a given percentage, so formulas overestimate their max. Beginners improve so quickly that any estimate goes out of date in weeks.
The reps-at-percentage table uses a widely taught relationship from the NSCA's textbook Essentials of Strength Training and Conditioning. It is an average: some people will do more reps at 80%, some fewer, and it varies between lifts.
Testing a real max safely
Warm up thoroughly, use a spotter or safety bars, and stop a set when form breaks down. People with high blood pressure, heart disease, hernias, recent injuries or who are pregnant should check with a doctor before maximal lifting. Holding your breath under a heavy load raises blood pressure sharply.