Estimating your 1RM from reps: how wrong are the formulas

You hit eight reps with 100 kg, type it into a calculator and it hands back a 1RM of 125 kg. The question nobody asks is the obvious one: how close is that number? The short answer is that the estimate holds up well at low reps and starts missing badly as soon as you go past five or six.

Where the formulas come from

Every popular formula does the same job. It takes a load and a rep count and assumes the relationship between them follows one shared curve for everybody. One divides the reps by 30 and adds that as a percentage, another uses a fraction with 37 on the bottom, a third runs on logarithms.

They share an origin too. All of them were fitted to averages taken from groups of lifters, which means they describe the average well and describe you only as far as you sit near it. Feed the same set into two different formulas and the answers can sit 5 to 10 kg apart.

What we know reliably

Error grows with reps. The evidence here is consistent, whichever formula gets tested. Estimating from a set of 3 to 5 reps, you are typically out by 2 to 5 per cent, so 2 to 5 kg on a 100 kg lift. At 10 reps the error usually climbs to 5 to 10 per cent, and for some lifters further than that. Beyond 12 to 15 reps you are no longer estimating, you are guessing.

The set has to end at or very near failure. The maths assumes you stopped because you could not do another rep. Stop two reps early and the whole calculation shifts down, more than most people expect.

The spread between people is huge. At 70 per cent of a true max, one lifter stops at eight or nine reps while another grinds out more than twenty, with similar technique and similar training age. That is not measurement noise, it is real biology, the same reason two people on the same programme progress differently.

The exercise changes the relationship. At the same percentage, legs usually allow more reps than upper body, and machines allow more than free weights. In the deadlift the rep count at high percentages is unusually low, because grip, back position and technique give out well before the legs do. One percentage chart cannot cover every lift in your programme.

Even a tested 1RM is not a fixed number. Test the same lifter twice a few days apart and the result moves by a few per cent either way. You are comparing an estimate against a target that wobbles on its own.

What is likely but not settled

Which formula suits whom is unresolved. Different formulas land closer on different lifts and different experience levels, but there is no clean rule telling you which one to pick.

It is likely that each lifter has a fairly stable personal rep profile, so if you get 14 reps at 70 per cent today, you will get roughly the same two months from now. That fits everything else we know, but it is poorly researched over longer stretches and across different training blocks.

Differences in fast and slow muscle fibres are a plausible explanation for why one lifter manages twenty reps and another eight. The reasoning is sound, but direct evidence in ordinary gym-goers is thin, so treat it as likely rather than proven.

Estimating from bar speed is promising, because it measures something real instead of assuming a curve. Even so, the speed profile has to be built for each lifter individually, and a few kilos of error remain.

What gets repeated wrongly

That the calculator gives you a number. It gives you the middle of a range. Other popular gym tools fail the same way that watches and treadmills miss on calorie estimates: the output looks precise because it has decimals, while underneath it is an average built from other people.

That the percentage chart is a rule. Eighty per cent meaning eight reps is an average, not a law. For you, 80 per cent might be five reps or twelve.

That you can actually lift your estimated max. A true single is partly a skill: bracing, the walkout, staying calm under a heavy bar. Lifters with little experience of heavy singles often lift less than the formula predicts even when the muscle is ready. Some of that gap comes from expectation, which is covered in the piece on placebo in training.

That a rising estimated max proves rising strength. If you estimated from five reps last month and twelve this month, you also changed the size of the error. Compare like with like.

What this means for your training

• Estimate from a set of 3 to 5 reps taken to failure or one rep short of it. That is where the formulas are at their best.
• Keep the conditions the same: same exercise, similar rest before the set, similar time of day, same shoes and kit.
• Write the result down as a range, say 120 to 130 kg, rather than a single figure.
• Repeat the test every 4 to 6 weeks, not every week.
• Build your own chart. Record how many reps you genuinely get at 80 and 85 per cent in each main lift. That chart beats any formula for you.
• For higher rep work, programme by effort and reps in reserve instead of raw percentages.

There is a part of this that has nothing to do with maths. Sleeping under six hours, sitting in a steep calorie deficit and turning up dehydrated will all drag down both your daily max and the reps you manage. In a deficit it is normal for the estimate to drop a few per cent without any muscle being lost, so do not rebuild your whole programme around one bad test day.

When to see a doctor

Max testing means a short but sharp spike in blood pressure. If straining brings on chest pain, strong dizziness, breathlessness or faintness, stop and get checked. The same goes for sharp joint pain that lingers after the session, for uncontrolled high blood pressure, recent surgery and pregnancy. If you already have knee pain in the squat, sort that out before you go anywhere near a heavy test.

In short

• Up to 5 reps, formulas miss by roughly 2 to 5 per cent; at 10 reps it is 5 to 10 per cent or more.
• The set must end at or right beside failure, or the calculation is meaningless.
• Reps at a given percentage vary enormously between people and between lifts.
• Treat the estimate as a range and keep your own rep chart for each exercise.