How to estimate your one-rep max: Epley, Brzycki and five other formulas, worked through

The short version: take a set you pushed close to failure and run it through one of these.

Epley: 1RM = weight × (1 + reps ÷ 30)

Brzycki: 1RM = weight × 36 ÷ (37 − reps)

A set of 100 kg for 5 comes out at 116.7 kg with Epley and 112.5 kg with Brzycki. Both are reasonable answers. The rest of this page is about why they differ, which set to feed them, and when a formula stops being worth asking.

Which formulas estimate a one-rep max?

These are the seven you will meet in most calculators and validation studies. In each, w is the weight lifted and r is the number of reps.

They look different, but most of them encode the same idea: each extra rep you can do with a weight means your max is a few percent higher than that weight. Brzycki’s paper puts the anchor plainly: about 10 reps at roughly 75 percent of a maximal load. Epley lands on the same point.

What does each formula say about the same set?

Here is every formula applied to 100 kg. The formulas are proportional to the weight, so for 140 kg multiply a row by 1.4.

Three things stand out.

From 3 to 10 reps, the spread between the highest and lowest estimate stays under 10 kg on a 100 kg set. Epley and Brzycki meet exactly at 10 reps; below 10, Epley reads a little higher.

Past 10, the curves split. Brzycki and Lander accelerate, because their denominators shrink toward zero as reps climb. Lombardi and O’Conner flatten out. By 20 reps the same set implies anything from 135 kg to 212 kg, which is not an estimate any more.

At one rep, most of the formulas don’t return the weight you lifted. Epley says a 100 kg single means a 103.3 kg max. The sensible reading is to take a single at face value.

Why do the estimates drift past about 10 reps?

The clearest evidence comes from Reynolds, Gordon and Robergs (2006), who had 70 adults aged 18 to 69 test their 1, 5, 10 and 20 rep maxes on the bench press and a plate-loaded leg press. The load people could lift fell off nonlinearly as reps rose, 5-rep-max data predicted the true max best, and the authors concluded that no more than 10 repetitions should be used in linear equations to estimate a 1RM.

The second reason is that the relationship between reps and load is not the same on every lift. In Shimano and colleagues’ 2006 study, trained and untrained men did more reps on the back squat than on the bench press or arm curl at 60 percent of their max. The gap shrank at 80 and 90 percent. A formula fitted on one lift and applied to another is borrowing someone else’s curve, and the borrowing gets worse the lighter the load.

The third reason is that a long set tests something different. Twenty reps is as much a test of how well you tolerate fatigue as of how much force you can produce once. Two lifters with the same single can have very different 20-rep maxes.

The last one is about you, not the maths. Every formula assumes the set ended at or very near failure. If your set of five stopped with three reps left in the tank, the formula treats it as a five-rep max when that weight was really closer to an eight-rep max, and the estimate reads low.

Which formula should you use?

Honestly, the one you will use every time. An estimated max is most useful as a trend line, and any of the mainstream formulas applied the same way to similar sets will show the same trend. Switching between them week to week manufactures progress or regression that never happened.

Some habits that keep the number honest:

• Feed it sets of about 3 to 8 reps, taken close to failure. That is where the formulas agree most.
• Compare like with like. A 5-rep estimate this month against a 5-rep estimate last month means more than a 5-rep estimate against a 10-rep one.
• Use the heaviest working set of the session, not warm-ups or back-off sets.
• Treat the estimate for a lift you rarely train heavy, like a lateral raise, as a curiosity.

The same formulas work in reverse, for choosing a working weight from a known max:

Read it as a starting point. Given the Shimano result, expect the squat to allow more reps at a given percentage than the bench press or an arm curl, especially at lighter loads.

When should you test a true single?

When the exact number is what you need. A powerlifting meet is the obvious case. So is a program whose percentages are built on a tested max, or the end of a peaking block, when you have tapered and are fresh enough for the number to mean something.

It is a poor idea when you are stalled and want reassurance, at the end of a hard training week, or when you are coming back from a layoff. A single tested tired tells you less than a good set of five tested fresh.

If you do test one, the usual shape is a gradual warm-up through progressively heavier sets of fewer reps, then a small number of heavy single attempts with generous rest between them. Use safety arms or a spotter on anything that can pin you. And if you are working around an injury or a condition that affects heavy loading, get advice from a clinician or a coach who can see you lift before you go looking for a max.

What GymLogger X uses

GymLogger X uses Epley everywhere an estimated 1RM appears: the strength trend for each exercise, the rep-max table, and the plateau rule, which watches that trend. I picked it for the reason in the section above. It is one of the mainstream formulas, it agrees with Brzycki at 10 reps, and it is simple enough that you can check the app’s arithmetic yourself. There is no setting to switch formulas, on purpose.

A few details follow from the reasoning in this post:

• A logged single is its own 1RM. The app doesn’t run a single through the formula and hand you 103.3 kg for a 100 kg lift.
• The rep-max table on each exercise shows your best weight at 1, 3, 5, 8, 10 and 12 reps. Slots come from sets you actually lifted where possible, and any slot the app had to estimate is labelled as an estimate.
• Only a single you really did counts as an actual 1RM in that table. Until you log one, the 1RM slot shows an estimate, and the screen says so.

The plateau rule built on top of this is published in full on the app page, and the reasoning behind making the Apple Watch the logging surface is in the post on why GymLogger X exists. If you are still choosing an app, the guide to workout apps without a subscription compares the field by pricing model.