Why three formulas give three answers
All of the common one-rep-max equations do the same thing: they fit a curve to the observed relationship between load and reps-to-failure, then extrapolate that curve back to a single rep. The curves were fitted to different populations. Epley worked from collegiate athletes, Brzycki from a physical-education testing context, Lombardi from a different dataset again. Each fit is reasonable inside the data it came from and each one drifts once you leave that range.
The result is that a set of 225 for five reps produces 262.5 lb under Epley, 253.1 lb under Brzycki and 264.3 lb under Lombardi. That is a spread of eleven pounds on an estimate near 260. At three reps the three converge to within about three pounds. At ten reps they are more than twenty pounds apart. The formulas are most trustworthy exactly where you least need them, and least trustworthy where people most want to use them.
| Set | Epley | Brzycki | Lombardi | Spread |
|---|---|---|---|---|
| 225 x 3 | 247.5 | 238.2 | 252.4 | 14.2 |
| 225 x 5 | 262.5 | 253.1 | 264.3 | 11.2 |
| 225 x 8 | 285.0 | 279.3 | 277.7 | 7.3 |
| 225 x 12 | 315.0 | 324.0 | 289.7 | 34.3 |
Note the shape of that last column. It narrows around eight reps because the three curves happen to cross there, then blows apart at twelve. Anyone quoting a single one-rep-max number without saying which equation produced it is discarding information that matters.
How the set has to be performed for the number to mean anything
Every one of these equations assumes the set was taken to or very near momentary failure with the same technique you would use on a maximal attempt. A set of eight that could have been eleven produces an estimate roughly twelve percent low. Reps that shorten in range as fatigue accumulates inflate the count and inflate the estimate. Bounced bench reps, cut squat depth and hitched deadlifts all report a strength you do not have under a judged single.
The practical consequence: log the reps in reserve alongside the set. A set of five with two reps left in the tank is not a five-rep max, and feeding it to a formula gives you a number that will fail you under the bar.
Programming off the percentage table
Most strength programmes prescribe load as a percentage of one rep max. A programme calling for five sets of three at eighty-five percent, against an estimated max of 260 lb, is 220 lb rounded to the plates. Many programmes deliberately calculate from a training max set at roughly ninety percent of the estimate, and the reason is precisely the spread in the table above. If your estimate came from the high formula and you programme directly off it, the fifth week of a linear progression is where the miss happens.
Recalculate from a fresh set every four to six weeks rather than carrying an old number forward. An estimate from a set you performed last week is worth more than a measured single from six months ago.
Risk, stated plainly
Maximal singles carry real risk. A missed squat or bench without a spotter or safety pins is the mechanism behind a large share of serious gym injuries, and the risk does not scale gently — the failure point on a true maximum arrives with no warning reps beforehand. Submaximal estimation exists so that most people never need to test. If you do test, that means a full warmup ramp, three to five minutes between attempts, safeties set at a height that will catch the bar, and a competent spotter who has been told what you intend to attempt. Novices get more useful information from a five-rep set than from a single, at a fraction of the exposure.
This page estimates a number. It does not prescribe training. What sets, what frequency and what progression suit you depends on your history, your recovery and any injury you are carrying, and none of that is visible from a weight and a rep count.
Related
For the conditioning side of a training week, heart rate zones covers intensity on the cardiovascular lifts, with the same caveat about population formulas standing in for individual measurement.
Questions people ask
Which formula should I use?
If you only want one, Epley for lower-body lifts and Brzycki for the bench press has modest support in the literature, and the difference is small enough at five reps or fewer that the choice rarely changes what you load. The more useful habit is to pick one equation and stay with it. A consistent estimate that is slightly biased still tracks your progress correctly, because the bias cancels when you compare this month to last month. Switching formulas between sessions manufactures gains and losses that never happened.
Can I use a set of twenty reps?
The calculator caps the input at fifteen and the reason is visible in the arithmetic. Brzycki divides by thirty-seven minus the rep count, so at twenty reps the denominator is seventeen and the multiplier reaches 2.1; at thirty reps it is 5.1, which is nonsense. Beyond about ten reps the set is testing muscular endurance and cardiovascular tolerance as much as maximal force production, and those qualities vary between people far more than maximal strength does. Use three to six reps if you want the estimate to mean something.
Does this work for machines and the Smith machine?
For tracking your own progress on a specific machine, yes — the load-rep relationship still holds and the estimate will move with you. For the bodyweight-multiple table, no. Those bands come from free-weight barbell lifts. A Smith machine removes the stabilisation demand and a leg press changes the movement entirely, so the numbers are not comparable and a machine total mapped onto the table will read one or two bands high.
My estimate went down. Did I lose strength?
Possibly, but check the set first. Estimated maxes are sensitive to how close to failure the set actually went, and proximity to failure is hard to judge consistently across sessions. Sleep, food, time of day and where you are in a training block all move a single set by several percent without any change in underlying strength. A drop across three or four consecutive sessions is a signal worth acting on; a single low estimate is noise.