Four rules we hold ourselves to
- Name the equation. If a page prints a number, it says which published formula produced it and what the alternatives return.
- Show the spread. Where several accepted formulas exist, we run all of them and report the range. The disagreement between them is information, not noise to be hidden.
- State where it breaks. Every equation was fitted on a particular population over a particular range. Each page says where its own answer stops being dependable.
- Stay out of medicine. No BMI categories, no health thresholds, no diagnosis. These are training and planning numbers.
One-rep max
Seven published regressions, all applied to every set you enter: Epley (1985), Brzycki (1993), Lombardi (1989), O'Conner (1989), Wathan (1994), Lander (1985) and Mayhew (1992). They were derived from submaximal and maximal lifts by trained lifters, mostly in college athletic populations, between the 1970s and the 1990s. We report the median of all seven as the headline, because no published comparison has established a winner across lifts, populations and rep ranges, and a median is robust to any one of them being a poor fit for you.
Two deliberate behaviours. At one rep the answer is the weight itself — Epley's equation at r=1 returns 1.033w, which would tell someone who just lifted a true single that their max is 3% higher than the bar they lifted. And above ten reps the page says the estimate is unreliable, because every one of the seven drifts up there and they do not drift together. The pre-built pages stop at ten reps for the same reason.
Full comparison: seven one-rep max formulas, compared.
Where the one-rep max estimate breaks down
This is the canonical account. Every one of the 216 pre-built pages under the one-rep max calculator links here rather than restating it, so there is one place to correct if any of it turns out to be wrong.
The set has to have been close to failure. Every one of the seven equations takes reps-to-failure as its input, not reps performed. A set you stopped three reps short and a set that genuinely pinned you produce the same number on this page and very different truths. So does a bounced rep, a half squat, or a bench press with the hips off the bench: the equations cannot see technique, and they will happily convert a bad rep into a confident-looking estimate.
They were fitted on sets of two to ten reps. Outside that band all seven extrapolate, and they do not extrapolate together — Brzycki flattens as reps climb while Epley keeps rising, so the disagreement between them widens exactly where you have least reason to trust any of them. That is why the pre-built pages stop at ten reps, and why a set of twelve or fifteen is better re-tested than converted.
Strong, experienced lifters are under-estimated. A trained lifter typically holds a higher percentage of their max for a given rep count than the regression average, so the estimate reads low for them and closer to correct for a novice. The same effect runs the other way for lifts with a long range of motion and a large fatigue cost, which is part of why deadlift estimates from high-rep sets are the least reliable of the four main lifts.
The equations disagree, and that is the useful part. The spread printed on every page — typically 5 to 10% — is the honest width of the answer. We report the median of the seven rather than picking one, because no published comparison has established a winner across lifts, populations and rep ranges. Where the spread is wide, believe the lower end.
Programming from an estimated max
Percentages, not absolute weights, are how training programmes are written. A heavy triple sits near 90 to 92% of max, working sets of five near 85%, sets of eight near 75%, and volume work near 70%. Round every one of those to a weight you can actually load: the precision these formulas imply does not survive contact with a plate rack, and a 5 lb rounding error is smaller than the disagreement between the equations themselves.
Never attempt an estimated max cold. Treat the number as a planning input. If you want to test a true single, build up to it over several weeks, warm up thoroughly on the day, take small jumps near the top, and set safety bars or use a spotter. This is a training estimate, not medical advice, and it is not a substitute for a coach who can actually see the bar move.
Sleep cycles
A cycle is modelled at 90 minutes and sleep onset at 14 minutes, both population averages. Bedtime plus onset gives the start of the first cycle; each option is that moment plus a whole number of cycles. There is no physiology in this — it is arithmetic on a clock, and we say so rather than implying the site knows something about your sleep architecture.
The arithmetic runs on wall-clock minutes, not on timestamps, which is why the answers stay correct across a daylight-saving change: an alarm is a wall-clock time on both sides of the clock change. Real cycles run roughly 70 to 120 minutes and lengthen through the night, so the sixth boundary is a far looser target than the first. The sleep cycle calculator lets you change the 90 if it is not your number, and this guide explains where the figure came from.
BMR and maintenance calories
Three equations, shown side by side:
- Mifflin-St Jeor (1990) — the headline figure. Best validation record in the general population.
- Harris-Benedict, Roza-Shizgal revision (1984) — runs a little higher; still widely used.
- Katch-McArdle (1996) — appears only when you enter a body-fat percentage, because it is driven by lean mass. Feeding it a guessed lean mass would manufacture a fourth number carrying no extra information, so we do not.
Maintenance is BMR multiplied by an activity factor from 1.2 to 1.9. That multiplier is the largest single source of error in the answer, larger than the choice of equation: most people select one level too high. The three formulas typically span about 4%; your activity estimate can be out by 15%.
Cutting and bulking targets are maintenance minus or plus a deficit, and the weekly rate converts at 7,700 kcal per kilogram of fat — the familiar 3,500 kcal per pound. Using 7,000 kcal per kilogram, which is the pound figure with the unit swapped, overstates weekly loss by about 10%; it is the most common arithmetic error in this category. The cut rate is capped at 1% of bodyweight a week, because a flat 800 kcal deficit means something entirely different to a 110 kg person and a 55 kg one.
Detail: Mifflin-St Jeor vs Harris-Benedict vs Katch-McArdle.
Body composition
Body fat uses the US Navy circumference method (Hodgdon & Beckett, 1984), in its original inch-based logarithmic form. Its published standard error against hydrostatic weighing is about ±3 percentage points, so the result panel shows the band, not only the point estimate. Where the measurements cannot produce an answer — a waist at or below neck circumference — the page says which measurement to check rather than printing a number.
Lean body mass runs Boer (1984), James (1976) and Hume (1966), plus the direct calculation from a measured body-fat percentage whenever one is supplied. That direct row beats all three estimates and the page says so.
FFMI is fat-free mass divided by height in metres squared. Normalised FFMI adds 6.1 × (1.8 − your height in metres) so that lifters of different heights can be compared; at exactly 1.80 m the two are identical. Many sites print one and label it the other. Both are shown here, labelled.
Protein targets use 1.6–2.2 g per kg for people doing resistance training, taking the top of the range when cutting. Ranges for endurance training and for not training are lower and less well evidenced, and are marked as such.
Rounding, units and why sites disagree
Answers are rounded half-up at the last step. Where a published table rounds an intermediate value — BMR to a whole calorie before the activity multiplier, for instance — we round in the same order, which is why our maintenance figure can differ by one calorie from a site that carries the fraction through. Metric is used internally everywhere; imperial input is converted once, at the edge, never half-way through a formula. The exception is the Navy body-fat equation, which is defined on inches, so centimetres are converted to inches and fed to the original.
If another site gives you a different answer, it is almost always one of three things: a different equation, a different rounding order, or a different activity multiplier. It is rarely a bug in either site. That is precisely why every page here names its equation.
How the numbers are tested
Each formula is implemented once, in one file. A separate test suite carries an independent implementation of the same published equations and re-derives every pre-computed answer that ships in the HTML: all 216 cells of the one-rep-max table, all 48 rows of the sleep-cycle table, every worked example on every calculator page, and the rendered answer on all 312 generated pages. The build does not ship if any of them disagree.
If you find a number that is wrong, that is the most serious bug this site can have. Tell us and it gets checked against the source equation the same day.