Most lifters who want to know their one-rep max never actually load the bar and go for a single all-out lift. It's not necessary, and for a lot of people it's not smart -- a true 1RM attempt means lifting at the edge of your technical limit, alone or with an untrained spotter, with no second chance if your form breaks down. Instead, you estimate it from a weight you can already lift for a few clean reps.
Where the estimate actually comes from
The math is older than most of the equipment in a modern gym. Two formulas dominate: Epley's, which is 1RM = weight x (1 + reps/30), and Brzycki's, which is 1RM = weight x 36 / (37 - reps). Plug in 100 kg for 5 reps and Epley gives you about 117 kg; Brzycki gives you about 112 kg. Neither number is "the" answer -- they're two slightly different curves fit to the same basic observation: as reps go up, the weight you can lift goes down in a fairly predictable way, at least for a while.
Both formulas were built from data on compound barbell lifts performed by trained lifters. That matters because the relationship between reps and load isn't universal -- it shifts with the exercise, your training history, and how close to failure you actually took the set.
Why the estimate gets shakier as reps climb
The formulas are most trustworthy in the 2-to-6 rep range and progressively less reliable past about 10 reps. At low reps, the set is short enough that fatigue and pacing barely factor in -- the weight you moved is a clean signal of your strength. At higher reps, things like muscular endurance, pacing strategy, and how much the bar slows down on the last couple reps start to matter more than raw strength, and the formulas don't account for any of that. A 20-rep set tells you much less about your actual 1RM than a 3-rep set does, even though both can be fed into the same equation.
This is also why two formulas can disagree more as rep count rises. At 3 reps they're usually close. At 12 reps, the gap between Epley's and Brzycki's output can be wide enough to change which plates you'd actually load.
Why anyone bothers calculating this at all
The practical reason lifters care about 1RM isn't bragging rights -- it's programming. Strength programs are commonly written as a percentage of your max: squat at 70% for volume work, 85% for a heavy top set, and so on. If you don't know your max, you can't calculate those numbers, and guessing wrong in either direction either stalls your progress or runs you into a weight you can't control with good form.
Because retesting a true max is fatiguing and risky, most lifters recalculate their estimated 1RM every few weeks from whatever working sets they're already doing, rather than scheduling a dedicated max-out day. A 5-rep set finished in a normal workout is enough data to update the number and adjust next week's percentages.
What this estimate won't tell you
An estimated 1RM is not a substitute for a tested one if you specifically need a verified number -- for a powerlifting meet, for example, where the number has to hold up under competition rules with a referee watching your depth and lockout. It's also just an estimate for barbell lifts with stable, well-grooved technique; it gets less meaningful for exercises where form breaks down unpredictably near failure, or for machines where the resistance curve doesn't behave like free weight.
For everyday programming, though, an estimate from a recent, honest set of 3-to-6 reps is close enough to plan the next several weeks of training around -- and it doesn't cost you a single all-out attempt to get it.
Plexto's One Rep Max Calculator takes a weight and rep count and returns an estimated max along with a full percentage chart from 50% to 100%, so you can read your training weights straight off it instead of doing the math by hand every session.