Epley and Brzycki Disagree: When It Actually Matters

Run the same set through two one-rep-max formulas and you get two answers. This bothers people more than it should — but the pattern of the disagreement is genuinely informative, and worth understanding before you pick a number to build a training block on.

They cross at exactly ten reps

Take 100kg and vary the rep count. Here is what the two formulas project, from the same functions behind the One-Rep Max Calculator:

Reps	Epley	Brzycki	Difference
1	100.00	100.00	—
2	106.67	102.86	Epley +3.81
3	110.00	105.88	Epley +4.12
4	113.33	109.09	Epley +4.24
5	116.67	112.50	Epley +4.17
6	120.00	116.13	Epley +3.87
7	123.33	120.00	Epley +3.33
8	126.67	124.14	Epley +2.53
9	130.00	128.57	Epley +1.43
10	133.33	133.33	identical
11	136.67	138.46	Brzycki +1.79
12	140.00	144.00	Brzycki +4.00

The gap widens to about 4.2kg around four reps, closes to nothing at exactly ten, and then reverses. Below ten reps Epley is the more generous formula; above ten, Brzycki is. That crossover is a property of the two equations, not a coincidence of these numbers — it happens at ten reps whatever weight you start from.

Why the shapes differ

Epley is linear. Every rep adds the same fixed fraction — one thirtieth — of the weight lifted. Ten reps means a projected max of one-third above the working weight, twenty reps means two-thirds above, and the line keeps climbing at a constant rate forever.

Brzycki is a ratio with reps in the denominator: 36 ÷ (37 − reps). That behaves gently in the low rep ranges and then accelerates hard, because the denominator is shrinking toward zero. At 20 reps it projects 2.12× the weight lifted. At 30 reps, 5.14×. At 35 reps, 18×. At 36 reps it claims your max is 36 times what you just lifted, and at 37 the formula divides by zero and ceases to exist.

That is why the calculator refuses rep counts above 12. It is not excessive caution — it is the point past which one of the two formulas is visibly departing from reality.

Which one should you use?

In the range where either is trustworthy — roughly one to six reps — the honest answer is that the difference is smaller than the noise in your own performance. Four kilos on a 115kg projection is about three and a half percent. Your actual strength moves more than that between a good night's sleep and a bad one.

So rather than picking a winner:

• Use the average for programming. The calculator returns it alongside both. It is not more scientific, but it stops you unconsciously selecting whichever formula flatters you today, which is the real failure mode.
• Use the same formula every time. Consistency matters far more than which of the two you chose. Switching formulas between blocks introduces a step change in your working weights that has nothing to do with training.
• Treat a wide gap as a signal to test lower. If you are estimating from sets of ten and the formulas disagree, redo it from a set of four. Both formulas are more reliable there, and they will agree more closely.

The error that dwarfs the formula choice

All of the above concerns a discrepancy of a few percent. Meanwhile, miscounting reps — stopping a set two reps short of genuine failure, or counting a rep that a spotter helped with — shifts the projection by considerably more.

A set of 5 that was really a comfortable set of 5-with-3-left projects a max around 116kg by Epley. Taken to the point where a sixth rep genuinely would not have moved, the same lifter might have done 8, projecting 127kg. That is a ten percent swing from rep honesty alone, against three percent from formula choice.

Worry about the reps. The formula is the smaller problem.

From estimate to bar

Once you have a number you trust, the Rep-Max Percentage Calculator converts it into working weights for each rep target, and the Rep-Max Plate Chart shows the plates each of those weights actually needs. Both invert the same Epley relationship the max estimate uses, so a weight you feed in comes back out unchanged — a consistency worth having when the whole point is comparing this block against the last one.

Other formulas you will run into

Epley and Brzycki are the two most widely implemented, but they are not the only ones, and knowing the landscape helps when two apps give you different answers.

Lombardi uses a power relationship rather than a linear or ratio one. O'Conner is a simpler linear variant that tends to be conservative. Mayhew and Wathen use exponential terms and were fitted against particular populations. Several coaching systems also use published percentage tables rather than a formula at all, which amounts to the same thing with the arithmetic done in advance.

They differ mainly in the mid and upper rep ranges. At three to five reps, all of them cluster within a few percent, which is the practical argument for not agonising over the choice: in the range where you should be estimating, they largely agree.

A worked comparison at a real training weight

Abstract percentages are easy to dismiss, so here it is in kilos. A lifter benches 92.5kg for four reps.

• Epley: 92.5 × (1 + 4/30) = 104.83kg
• Brzycki: 92.5 × 36/33 = 100.91kg
• Average: 102.87kg

Just under four kilos between the two. Now consider what that does downstream. Programming sets of five at around 85% gives 89.1kg from the Epley figure and 85.8kg from the Brzycki one — a 3.3kg difference in the working weight, which is between one and two plate increments.

That is not nothing. It is also comfortably inside the range that a good night's sleep, a decent warm-up, or a well-timed coffee moves your performance. Which is the honest way to hold it: the choice matters enough to be consistent about, and not enough to lose an evening over.

The one rule that actually matters

Pick one and stay with it for at least a full training block, ideally longer.

The reason is comparability. Your log's purpose is to tell you whether this month beat last month. If you estimated with Brzycki in January and Epley in March, part of the improvement you are looking at is a change of formula, and you have no way to separate it from the real progress. A step change of three or four percent, arriving on the day you switched apps, will look exactly like a training effect.

The same applies to switching between the average and a single formula. Consistency is worth more than the small accuracy differences between the options — and the average has the practical advantage of being the harder number to unconsciously game, since you cannot pick the flattering one after seeing both.