Guides
1RM Formulas Explained
Seven formulas, one barbell, seven different answers. You lift 100 kg for 8 reps and one formula tells you your max is 120 kg while another says 128 kg. This guide shows you every formula, works each one out on the same set, and helps you pick the one number you will actually train with.
No login, no app to install. Read the formulas, compare the results, and use the number with confidence in your next session.
Outline
What You Will Learn in This Guide
- What Is a 1RM Formula?
- The Seven Formulas at a Glance
- Epley (1985)
- Brzycki (1993)
- Lander (1985)
- Lombardi (1989)
- Mayhew (1992)
- O’Conner (1989)
- Wathan (1994)
- All Seven Formulas, Side by Side
- Why the Formulas Disagree
- How to Pick One Formula and Stick With It
- From a Formula to a Training Plan
- Frequently Asked Questions About 1RM Formulas
The basics
What Is a 1RM Formula?
Your one-rep max, or 1RM, is the heaviest weight you can lift once with good form. Testing it directly is the most accurate way to find it, but a true max test is tiring, it needs a spotter, and it eats a whole training day. A 1RM formula gives you a shortcut: you take a normal working set, plug the weight and the reps into a simple equation, and the formula estimates your max. If you want the full step-by-step process for testing and estimating, start with our guide on how to calculate your 1RM.
Every formula on this page does the same job in a different way. Each one was built from a different group of lifters, in a different decade, by fitting a curve to real test data. That is why they disagree: they are seven different best guesses, not seven ways of measuring the same fact. Your job is not to find the one true formula. It is to understand what each one assumes, see how far apart they land on your own lifts, and then choose one and use it the same way every time.
One rule runs through this whole guide: a formula is only as good as the set you feed it. Use a recent set, from a lift you know well, done with full range of motion and no grinding cheat reps. A sloppy set in gives you a fantasy number out.
The short version
The Seven Formulas at a Glance
Here is the whole guide on one table. Every formula below takes the same two inputs, the weight you lifted and the reps you did, and returns your estimated 1RM. If you already know your weight and reps and just want the answer, our rep range to 1RM converter runs all seven of them for you at once.
| Formula | Year | Equation | Best for |
|---|---|---|---|
| Epley | 1985 | 1RM = weight × (1 + reps ÷ 30) | Simple, all-purpose estimates |
| Brzycki | 1993 | 1RM = weight × 36 ÷ (37 − reps) | Low-rep sets, 1 to 6 reps |
| Lander | 1985 | 1RM = weight ÷ (1.013 − 0.0267123 × reps) | Moderate reps, 4 to 10 reps |
| Lombardi | 1989 | 1RM = weight × reps0.10 | Quick mental estimates |
| Mayhew | 1992 | 1RM = weight × 100 ÷ (52.2 + 41.9 × e−0.055 × reps) | Moderate to higher reps |
| O’Conner | 1989 | 1RM = weight × (1 + 0.025 × reps) | The simplest rule of thumb |
| Wathan | 1994 | 1RM = weight × 100 ÷ (48.8 + 53.8 × e−0.075 × reps) | Moderate to higher reps |
You do not need to memorize these equations. Read the next seven sections once, see how each one behaves on the same 100 kg set of 8 reps, and the differences will stick. Then pick one formula and stop shopping around.
Formula 1 of 7
Epley (1985)
The formula: 1RM = weight × (1 + reps ÷ 30)
How it works
Epley is the most widely used 1RM formula in the world, and the default in most calculators. It assumes your strength drops in a straight line as reps climb: every extra rep costs you the same slice of your max. That straight-line assumption makes it easy to use and easy to remember, and it holds up well for sets of 1 to 10 reps. It was published by Boyd Epley in 1985, and forty years later it is still the first formula most coaches reach for.
Worked example: 100 kg for 8 reps
You squat 100 kg for 8 reps. Divide 8 by 30 to get 0.267, add 1 to get 1.267, and multiply by 100 kg. That gives you 126.7 kg. In other words, Epley says your 8-rep set was about 78.9% of your max.
Result: Epley estimates your 1RM at 126.7 kg from 100 kg for 8 reps.
Formula 2 of 7
Brzycki (1993)
The formula: 1RM = weight × 36 ÷ (37 − reps)
How it works
Brzycki, published by Matt Brzycki in 1993, is the formula most textbooks print next to Epley. It uses a curve instead of a straight line: as reps climb, each extra rep costs you a little more. The formula breaks down past about 10 reps, because at 37 reps the denominator hits zero, so it is really a low-rep formula. If your sets are mostly 1 to 6 reps, Brzycki is a strong choice.
Worked example: 100 kg for 8 reps
You squat 100 kg for 8 reps. Subtract 8 from 37 to get 29, divide 36 by 29 to get 1.241, and multiply by 100 kg. That gives you 124.1 kg. Brzycki sits 2.6 kg below Epley on this set, which tells you the two formulas already disagree by a full plate-load on a heavy squat.
Result: Brzycki estimates your 1RM at 124.1 kg from 100 kg for 8 reps.
Formula 3 of 7
Lander (1985)
The formula: 1RM = weight ÷ (1.013 − 0.0267123 × reps)
How it works
Lander, published in 1985, works backwards from a percentage chart. Instead of multiplying your weight up, it divides your weight by the percentage of your max that a given rep count represents. The constant 0.0267123 is the slope of that chart, fitted to real lifters. Lander behaves a lot like Epley in the middle rep ranges, which is why you will often see the two numbers within a kilogram or two of each other.
Worked example: 100 kg for 8 reps
You squat 100 kg for 8 reps. Multiply 0.0267123 by 8 to get 0.2137, subtract that from 1.013 to get 0.7993, and divide 100 kg by 0.7993. That gives you 125.1 kg, right between Epley and Brzycki.
Result: Lander estimates your 1RM at 125.1 kg from 100 kg for 8 reps.
Formula 4 of 7
Lombardi (1989)
The formula: 1RM = weight × reps0.10
How it works
Lombardi, published in 1989, is the simplest formula on this page to explain: your max grows with reps raised to the power of 0.10. It is a power curve, which means it rises fast at first and then flattens out. That shape makes Lombardi the most conservative formula at higher reps, and the easiest one to estimate in your head if you remember that 8 raised to 0.10 is about 1.23.
Worked example: 100 kg for 8 reps
You squat 100 kg for 8 reps. Raise 8 to the power of 0.10 to get 1.231, and multiply by 100 kg. That gives you 123.1 kg, the second-lowest estimate of the seven on this set.
Result: Lombardi estimates your 1RM at 123.1 kg from 100 kg for 8 reps.
Formula 5 of 7
Mayhew (1992)
The formula: 1RM = weight × 100 ÷ (52.2 + 41.9 × e−0.055 × reps)
How it works
Mayhew, published in 1992, is an exponential formula built from a large sample of college football players. The e in the equation is Euler’s number, about 2.718, and the formula uses it to model how quickly strength falls off as reps climb. Because it was fitted to trained athletes doing moderate to high reps, Mayhew tends to hold up better than Epley or Brzycki once you pass 8 reps.
Worked example: 100 kg for 8 reps
You squat 100 kg for 8 reps. The exponent is minus 0.055 times 8, which is minus 0.44, and e to that power is 0.644. Multiply 41.9 by 0.644 to get 27.0, add 52.2 to get 79.2, and divide 10,000 by 79.2. That gives you 126.3 kg, almost identical to Epley on this set.
Result: Mayhew estimates your 1RM at 126.3 kg from 100 kg for 8 reps.
Formula 6 of 7
O’Conner (1989)
The formula: 1RM = weight × (1 + 0.025 × reps)
How it works
O’Conner, published in 1989, is the simplest formula here: add 2.5% of your max for every rep you did. No exponents, no division by a curve, just one easy rule you can do in your head between sets. That simplicity is also its weakness. A fixed 2.5% per rep underestimates your max on higher-rep sets, because real strength does not fall off in such a tidy straight line.
Worked example: 100 kg for 8 reps
You squat 100 kg for 8 reps. Multiply 0.025 by 8 to get 0.20, add 1 to get 1.20, and multiply by 100 kg. That gives you 120.0 kg, the lowest estimate of all seven. If you use O’Conner, know that it is conservative: it will tell you a smaller max than the other formulas on the same set.
Result: O’Conner estimates your 1RM at 120.0 kg from 100 kg for 8 reps.
Formula 7 of 7
Wathan (1994)
The formula: 1RM = weight × 100 ÷ (48.8 + 53.8 × e−0.075 × reps)
How it works
Wathan, published in 1994, is the youngest formula on this page and the twin of Mayhew: same exponential shape, different constants, fitted to a different group of lifters. The steeper exponent means Wathan’s curve bends more sharply, which is why it gives the highest estimate of the seven on an 8-rep set. If you train in the 6 to 12 rep range and want a formula built for it, Wathan is worth your attention.
Worked example: 100 kg for 8 reps
You squat 100 kg for 8 reps. The exponent is minus 0.075 times 8, which is minus 0.60, and e to that power is 0.549. Multiply 53.8 by 0.549 to get 29.5, add 48.8 to get 78.3, and divide 10,000 by 78.3. That gives you 127.7 kg, the highest estimate of the seven.
Result: Wathan estimates your 1RM at 127.7 kg from 100 kg for 8 reps.
Compare
All Seven Formulas, Side by Side
Here is the same set, 100 kg for 8 reps, run through every formula. The spread is 7.7 kg, from 120.0 kg (O’Conner) to 127.7 kg (Wathan), and the average of all seven is 124.7 kg. That average is a useful anchor: if one formula gives you a number far from it, ask why before you trust it.
| Formula | Estimated 1RM | Your set as % of 1RM | vs the average |
|---|---|---|---|
| Epley | 126.7 kg | 78.9% | +2.0 kg |
| Brzycki | 124.1 kg | 80.6% | -0.6 kg |
| Lander | 125.1 kg | 79.9% | +0.4 kg |
| Lombardi | 123.1 kg | 81.2% | -1.6 kg |
| Mayhew | 126.3 kg | 79.2% | +1.6 kg |
| O’Conner | 120.0 kg | 83.3% | -4.7 kg |
| Wathan | 127.7 kg | 78.3% | +3.0 kg |
| Average of all seven | 124.7 kg | 80.2% | 0.0 kg |
Now look at what happens when the reps climb. The table below runs the same 100 kg through every formula at 4, 8, 10, and 12 reps, and shows the gap between the highest and lowest answer each time.
| Reps with 100 kg | Lowest estimate | Highest estimate | Spread | Spread as % of average |
|---|---|---|---|---|
| 4 reps | 109.1 kg | 116.5 kg | 7.4 kg | 6.6% |
| 8 reps | 120.0 kg | 127.7 kg | 7.7 kg | 6.2% |
| 10 reps | 125.0 kg | 134.7 kg | 9.7 kg | 7.4% |
| 12 reps | 128.2 kg | 144.4 kg | 16.2 kg | 11.8% |
The pattern is clear: at 4 reps the formulas sit within 7.4 kg of each other, and at 12 reps the gap has more than doubled to 16.2 kg. The agreement is actually tightest around 5 to 6 reps, where the spread drops to about 5.5 percent, and it widens again past 10 reps. That is why every coach tells you to estimate from low-rep sets. A formula is a good guess at 5 reps and a rough guess at 12. If you want a deeper look at how reps translate into percentages, our rep range to 1RM converter shows the full chart.
The science
Why the Formulas Disagree
The formulas disagree because they were built from different lifters. Epley worked with college athletes in the 1980s. Mayhew and Wathan fitted their curves to football players. Brzycki pooled published studies. Different lifters, different lifts, different decades, and each curve fits its own data a little better than anyone else’s. When you use a formula, you are borrowing someone else’s lifters and hoping they are like you.
Rep range is the biggest driver of the gap, and the pattern surprises most lifters. The formulas agree most around 5 to 6 reps, where the spread is only about 5.5 percent. They fan out at both ends: at 1 to 3 reps the spread is 7 to 9 percent, because the curves were never anchored at a true single, and past 10 reps it passes 10 percent and keeps climbing. At 15 reps the gap reaches nearly 22 percent. Past 8 reps, endurance, technique, and conditioning start to matter as much as strength, and the formulas split apart. A lifter with great conditioning will do more reps at a given percentage than a lifter without it, and no formula can see that from weight and reps alone.
| Rep range | How much the formulas agree | What to do |
|---|---|---|
| 1 to 3 reps | Spread of about 7 to 9% | Still useful, because the input is near-maximal, but check the number against a heavier set. |
| 4 to 6 reps | Spread of about 5 to 6% | The sweet spot. The formulas agree most here, so estimate from sets in this range whenever you can. |
| 7 to 10 reps | Spread of about 6 to 7% | Useful, but treat the number as a range, not a fact. |
| 11 reps or more | Spread over 10%, up to 22% at 15 reps | Do not plan heavy training from this. Test a heavier set first. |
Your own lifting style matters too. If you grind slow reps, your 8-rep set is closer to your max than the formulas assume, so they will overestimate you. If you move the bar fast and stop with gas left in the tank, they will underestimate you. That is where RPE training helps: rating how hard a set felt tells you how close to your limit you really were, and that context makes any formula smarter.
Your decision
How to Pick One Formula and Stick With It
Here is the honest answer: for most lifters, the best formula is the one you will use consistently. The difference between Epley and Brzycki on a normal set is 2 to 3 kg, which is less than a normal day-to-day swing in your strength. Switching formulas every week creates fake progress and fake plateaus. Picking one and using it for a whole training block gives you clean, comparable numbers.
- Want the simplest default? Use Epley. It is the most common formula in calculators and apps, so your numbers will match what most tools show you.
- Mostly training heavy, 1 to 6 reps? Use Brzycki. It was built for low reps and stays honest there.
- Mostly training in the 8 to 12 rep range? Use Mayhew or Wathan. Their exponential curves were fitted to exactly that kind of lifting.
- Want a number in your head between sets? Use O’Conner. Add 2.5% per rep. Just remember it runs conservative, so your real max is probably a little higher.
- Already using a calculator or app? Find out which formula it uses and match it. Mixing formulas between your log and your calculator is the one mistake that quietly ruins your data.
Once you pick, lock it in for at least 8 to 12 weeks. Log your estimated max the same way every session, and watch the trend instead of any single number. If your estimate climbs 5 kg over a block, you got stronger, no matter which formula produced the number. And if you want to see where your numbers sit against other lifters, check our strength standards guide after you have a solid estimate.
Put it to work
From a Formula to a Training Plan
A max estimate only matters when you turn it into weights on the bar. That is what percentage-based training does: you take your estimated 1RM and multiply it by a percentage for the day. Using the average estimate from our example, 124.7 kg, your training weights look like this.
| Training zone | Percentage | Weight from a 124.7 kg max | What it is for |
|---|---|---|---|
| Technique and speed | 70% | 87.3 kg | Warm-ups, speed work, deload weeks |
| Volume and hypertrophy | 80% | 99.8 kg | Your bread-and-butter working sets |
| Heavy strength | 85% | 106.0 kg | Top sets in a strength block |
| Near-max strength | 90% | 112.2 kg | Heavy singles and peaking work |
Round to the nearest plate you can actually load: 87 kg becomes 87.5 kg, 100 kg stays 100 kg, 106 kg becomes 105 kg, and 112 kg becomes 112.5 kg. Small rounding never matters; using a different formula every week does. If you want the full system behind these percentages, read our guide on strength training fundamentals, which covers progressive overload, volume, and intensity in detail.
One last habit ties it all together. Every time you estimate a max, compare it with how the set actually felt. If 80% moved like a warm-up, your estimate is probably low. If 85% buried you, it is probably high. Over a few weeks, your feel and your formula will agree, and that is when your training numbers start meaning something. You can also cross-check with your Wilks score to see how your total strength compares across bodyweights.
Questions
Frequently Asked Questions About 1RM Formulas
What is the most accurate 1RM formula?
There is no single winner. Epley and Brzycki are the most studied and the most used, and for sets of 1 to 6 reps the formulas land within about 5 percent of your true max. The honest answer is that the most accurate formula is the one you use on a good low-rep set, and then stick with for the whole training block.
Which 1RM formula should I use?
Use Epley if you want the standard default that most calculators use. Use Brzycki if you mostly train heavy, in the 1 to 6 rep range. Use Mayhew or Wathan if you mostly train in the 8 to 12 rep range. Whichever you pick, use it the same way for at least 8 to 12 weeks so your numbers stay comparable.
Why do 1RM formulas give different results?
Because each formula was fitted to a different group of lifters, in a different decade, using a different curve shape. Epley uses a straight line, Brzycki uses a curve, and Mayhew and Wathan use exponential curves. On a 100 kg set of 8 reps they range from 120.0 kg to 127.7 kg, and that gap grows as reps climb.
How many reps should I use to estimate my 1RM?
Use a set of 1 to 6 reps for the best estimate. Sets of 7 to 10 reps still work, but treat the number as a range rather than a fact. Avoid estimating from sets above 10 reps, because the formulas spread more than 10 percent apart there and conditioning starts to matter as much as strength.
Can I use a 1RM formula for any lift?
Formulas work best for heavy barbell lifts like the squat, bench press, and deadlift, where strength is the main limit. They are less reliable for machines, isolation moves, and lifts where technique or balance fails before strength does. For those lifts, track your rep progress directly instead of estimating a max.
Are 1RM formulas accurate for beginners?
They give a rough guide, not a precise number. Beginners gain strength fast, their technique changes week to week, and a hard set for a beginner is often limited by coordination rather than muscle. Use the estimate to pick training weights, retest every few weeks, and expect the number to move quickly.
What is the difference between Epley and Brzycki?
Epley multiplies your weight by 1 plus reps divided by 30, while Brzycki multiplies it by 36 divided by 37 minus reps. On 100 kg for 8 reps, Epley gives 126.7 kg and Brzycki gives 124.1 kg. Epley is simpler and more common, Brzycki is a little more conservative at low reps, and both are fine as long as you use one consistently.
Should I test my real 1RM or trust a formula?
Use a formula for day-to-day programming and test your real max only when you need it, such as before a competition or at the end of a training block. A true max test is tiring and needs a spotter, while a formula lets you estimate from a normal working set and keep training the next day.