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FitMetricLab

Strength Training

22 calculators

Strength calculators covering one-rep-max estimation, the coefficients that make lifts comparable across body weights and ages, loading arithmetic, and session structure.

Most of what follows depends on one estimate: a one-rep max inferred from a submaximal set. Several published formulas do that inference, and they disagree with each other in a way that grows with repetitions.

One-rep max formulas and where they separate

Epley, Brzycki, Lombardi, O'Conner and Wathen all convert a weight and a repetition count into an estimated single. At five repetitions they agree closely — 100 kg for 5 returns figures between about 112 and 118 kg across them. Past ten repetitions they diverge sharply, because the relationship between repetitions and load stops being close to linear and each formula handles the curve differently.

The practical consequence is that a set of 12 gives a much less reliable estimate than a set of 3, regardless of which formula is applied. Running several formulas on the same set shows the size of that uncertainty rather than hiding it behind one number.

RPE-to-percentage tables take a different route to the same place, mapping a rating of perceived exertion and a repetition count onto a percentage of maximum, which sidesteps the formula question but introduces the accuracy of the rating instead.

Comparison coefficients and loading arithmetic

Wilks, DOTS, IPF GL points and the Sinclair coefficient all exist to compare lifts across body weights, because absolute load scales with mass while relative strength does not. Each fits a different curve to a different competition dataset, so the same lifter can rank differently under each. The masters age coefficients add a second adjustment for age, derived from age-group performance data.

The loading calculators are arithmetic rather than estimation: plate calculators solve which plates make a target bar weight from a given set, warm-up sets divide a working load into a ramp, and intensity percentage converts between a percentage and an absolute load. Volume load and time under tension summarise what a session accumulated.

Common questions

Which one-rep max formula is most accurate?

No single formula is consistently closest, and the choice matters less than the repetition count behind it. All of them are fitted curves, and they agree within a few kilograms at three to five repetitions while diverging substantially past ten. A set of 3 at a known weight produces a more reliable estimate under any formula than a set of 15. The comparison tool runs five formulas on the same set so the spread is visible.

Why do Wilks and DOTS give different rankings?

They fit different curves to different datasets. Wilks was derived from earlier competition data using a fifth-order polynomial, while DOTS was fitted later to a different sample and behaves differently at the extremes of body weight, particularly for lighter and heavier lifters. IPF GL points uses another approach again. Each is internally consistent, so a comparison is only meaningful when everyone in it is scored under the same coefficient.

How many warm-up sets should come before a working set?

Warm-up protocols are usually described as a ramp of progressively heavier sets with falling repetitions, and published examples commonly use three to five steps between an empty bar and a working load. The calculator here divides a given target load into a ramp using a stated pattern of percentages rather than prescribing a number; the pattern it uses is shown alongside the result.

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