You can estimate it from a set of 10 reps or fewerStrong evidence
In 70 adults on the chest press and leg press, a 5-rep max predicted the one-rep max best, explaining 99% and 97% of the variation, against 96% and 92% from a 20-rep max; the authors advise that "no more than 10 repetitions should be used". In 103 women the formulas were more accurate with fewer than 10 reps to failure, and over the full range of 2 to 30 reps Brzycki's and Lander's formulas were out by 27% and 23% on average, with standard deviations of 102% and 71%. Validity was also higher with fewer reps in 69 college football players, and trained older adults predicted best from sets of 5 to 8.
Sources 1, 2, 22, 3
The formulas agree closely below 10 reps, and none is always bestStrong evidence
In 119 young adults, Lombardi's formula was the best for men's bench press and squat, Brzycki's and Lander's were among those that matched women's bench press, and none was accurate for men's arm curl. In 67 untrained students, only 2 of 7 formulas matched the tested bench press on average, and only 1 the squat. In 220 men of different training levels, Brzycki's was the most accurate of six with 10 reps or fewer, and the authors suggest that averaging two formulas may reduce the error. In 20 resistance-trained adults lifting 70% of their max, Epley's had the smallest error of three, and in 18 people with knee osteoarthritis the best formulas differed between the knee extension and the leg press.
Between 3 and 10 reps the seven formulas here differ by about 6 to 8% (our arithmetic), which is less than the error for one person. That's why the headline averages two and the rest are shown underneath.
Sources 4, 5, 7, 23, 6
For one person, the estimate can be 10% or more outEmerging evidence
In the 46 women who did 10 reps or fewer, the seven formulas here were out by 4% or less on average, but individual errors had standard deviations of about 9 to 11%: on bench presses averaging about 28 kg, roughly 3 kg either way for about two in three women (our arithmetic). In 119 young adults, the limits of agreement for the better formulas ran from about 2 to 4 kg either way on bench presses of 29 to 69 kg to about 10 kg either way on squats of about 117 kg. At worst, Brzycki's and Lander's formulas overestimated men's squat by about 14 kg on average.
Sources 2, 4
Some lifts and people run high or lowEmerging evidence
In 67 untrained students, every one of seven formulas underestimated the deadlift. In 51 adults averaging about 71 on 11 gym machines, every formula underestimated the tested max, with correlations of 0.77 to 0.90 for upper-body lifts and 0.60 to 0.80 for lower-body lifts.
People manage more reps on the leg press at the same percentage of their max: about 13 at 80%, against about 9 on the bench press. A formula reads those extra reps as a heavier max, so for someone who does the average leg press reps at 80%, Epley and Brzycki come out about 15 to 20% high; on the main table the same sum gives about 6%, and on the bench press about 2 to 3% (our arithmetic). Endurance runners also managed far more leg press reps at 70% of their max than weightlifters (39.9 against 17.9), so formulas may overestimate the max of people with an endurance background (our reading).
Sources 5, 8, 9, 10, 21
They still work after months of trainingEmerging evidence
In 103 women tested before and after 12 weeks of training, the formulas were more accurate with fewer than 10 reps both times. With 2 to 10 reps, 9 of the 14 formulas tested matched the tested max before training and 5 after, and the authors concluded that training didn't compromise the predictions. In 119 young adults tested before and after 16 weeks, the authors note that some formulas worked as well for trained people as for beginners.
Sources 2, 4
How many reps at each percentageStrong evidence
Across 269 studies of 7,289 people, people managed 9.8 reps on average at 80% of their max (a between-person standard deviation of 2.5), 4.9 at 90% and 14.8 at 70%. On the bench press it was 8.8 at 80%, and on the leg press 13.1. Sex, age and training status didn't clearly change the relationship. The traditional coaching chart is close at heavy loads and for the bench press, but lists fewer reps than people manage at lighter loads, most of all on the leg press.
Sources 9, 10
Reps in reserve are a rough guideEmerging evidence
In 12 studies with 414 people, people tended to underpredict their reps to failure, by 0.95 reps on average, and they judged better close to failure and in sets of 12 reps or fewer. In 141 trainees the prediction errors had a standard error of measurement of 2.6 to 3.4 reps, with a tendency to improve with experience. On the RIR-based effort scale, RPE 10 means no reps in reserve and RPE 9 means one; it was tested in experienced and novice squatters.
Sources 12, 24, 11
You don't need a true max to train wellStrong evidence
The American College of Sports Medicine (ACSM) says training to failure isn't necessary, that it may be inadvisable for older people, and that stopping 2 to 3 reps short gives enough effort. A properly run 1RM test is reliable (in 32 studies, repeat tests typically varied by about 4%), but loads take 2 to 3 practice sessions to settle, and the authors of one validation study say testing may not be prudent with joint discomfort or injuries.
Sources 25, 4, 26