Projections
Pelaris projects two results you have not actually done: the one-rep max implied by a hard multi-rep set, and the race time implied by a strong run at a different distance. Both are labelled as estimates, both come from published work, and both have a range outside which we do not project at all. Here is the maths, and the fence around it.
The formula
1RM = weight × (1 + reps ÷ 30)
Known as the Epley formula. A single rep returns the weight you lifted, because at one rep the estimate and the result are the same number.
Now the honest part, because it shapes how we cite this. Epley’s original is a poundage chart from a self-published training manual in 1985. There is no peer-reviewed derivation to link and no stable page to point you at, and rather than dress up a citation that does not exist, we anchor on the claim the app actually makes: that a one-rep max can be estimated well from a hard multi-rep set, without you ever having to test one.
That claim has real evidence behind it. Reynolds, Gordon and Robergs tested exactly this question in the Journal of Strength and Conditioning Research in 2006, and concluded that dynamic muscular strength can be accurately estimated from multiple repetition testing. It is the closest topical match to what Pelaris does, and it comes with a caveat we carry through into the product.
Ten reps or fewer is where a projection earns its keep. Reynolds and colleagues advise staying at or under ten repetitions, and the reason is intuitive once you have done a set of twenty. Past that point you are measuring how long you hold form and how much discomfort you tolerate as much as you are measuring maximal strength. A projection off a hard set of five is worth far more than one off a set of twenty, and the app treats both as estimates regardless.
How hard the set was matters as much as how many reps it ran. That is why Pelaris asks you to rate effort in reps in reserve rather than assuming every set was taken to the limit, and it is also how automatic PR detection knows which sets are worth reading in the first place.
The formula
t2 = t1 × (d2 ÷ d1)1.06
Riegel’s power law. Your known time over one distance, scaled to a target distance by the ratio between them, raised to a fatigue exponent of 1.06.
Peter Riegel published this in American Scientist in 1981, after fitting a curve to athletic world records spanning 100 metres out to 100 miles. The exponent is the whole idea. If humans held pace perfectly as distance grew, it would be 1.0 and doubling the distance would exactly double the time. It is 1.06, which is the mathematics of fatigue: every doubling costs you slightly more than double, and 1.06 is how much more.
In practice this is the question every runner asks after a good race. You have just run a strong 10k and you want to know what it means for a half marathon. Riegel answers it, and Pelaris does the arithmetic from the efforts already in your log rather than asking you to find a calculator.
The guard rail: half to double, and no further. Pelaris only projects to distances between half and double the effort it read. A strong 5k will project a 10k. It will not project a marathon. The further you extrapolate a power law, the more it leans on things your run never tested, particularly fuelling and the specific endurance a much longer race demands. Keeping projections inside the half-to-double band keeps them inside the range where your actual result still has something to say. Run a half marathon and the marathon projection comes into range.
The same principle applies to how the projection is built into your training. A projected time is a planning input, not a promise, and the methodology your program runs on decides what to do with it. If you want to close the gap between projection and result, the honest answer is usually specific endurance and a well-executed taper, not a different formula.
Every projection in Pelaris carries a label that says it is calculated. It appears as a secondary line beneath the number it supports, never dressed up as something you achieved. And the moment a tested result exists for that lift or that distance, the tested result takes the headline and the projection steps back to a supporting role.
That ordering is not decoration. A projection is a well-founded inference from something you did, and something you did is always the better evidence. Keeping the hierarchy visible is what lets a projection be useful without ever being misleading, and it is the same standard applied to every calculated number across the app, from a VO2max estimate to a body ratio read from a scan.
Two sources carry the projections above. Both were checked by hand against a live page. The full shelf of sixteen sits on the science hub.
Your projected 1RM is read off a hard multi-rep set, and this study is the evidence that a max can be estimated well without you ever having to test one.
Reynolds, J.M., Gordon, T.J. & Robergs, R.A. "Prediction of one repetition maximum strength from multiple repetition maximum testing and anthropometry." Journal of Strength and Conditioning Research, 2006;20(3):584-592. doi:10.1519/R-15304.1
View the sourceWhen a strong run at one distance hints at your time over another, that is Riegel's power law, drawn from world records from 100 metres out to 100 miles.
Riegel, P.S. "Athletic records and human endurance." American Scientist, 1981;69(3):285-290.
View the sourceGood at low rep counts, and less so as the reps climb. Reynolds, Gordon and Robergs concluded that a one-rep max can be accurately estimated from multiple repetition testing, and advised staying at or under ten repetitions. Pelaris uses the Epley formula, weight multiplied by one plus reps divided by thirty. A projection read off a hard triple or a hard set of five is a solid working number. One read off a set of twenty is a rough guide, because at that rep count you are measuring endurance and discomfort tolerance as much as maximal strength.
Epley: weight multiplied by one plus reps divided by thirty. A single rep returns the weight you lifted, because at one rep the estimate and the result are the same thing. Pelaris records every projection as an estimate, tagged with the method used, so a calculated number is never mistaken for a tested one.
No, and that is precisely the point of the projection. A true max test is heavy, taxing, and needs a good day plus a safe setup. The evidence says you can get a trustworthy number from a hard set you were going to do anyway. If you do choose to test one, Pelaris will use your tested result as the headline and step the projection back to a supporting line.
Riegel’s power law: your projected time equals your known time multiplied by the ratio of the two distances raised to the power of 1.06. Peter Riegel derived that fatigue exponent from world records spanning 100 metres to 100 miles, published in American Scientist in 1981, and it remains the standard way to scale a race result from one distance to another.
Because we only project between half and double the distance of the effort we read, and a marathon is more than eight times a 5k. Extrapolating a power law that far leans on assumptions the run never tested, particularly fuelling and the specific endurance a much longer race demands. Holding projections inside the half-to-double range keeps them within the span where your actual result still says something. Run a half marathon and a marathon projection comes into range.
Never. Projections are labelled as estimates and shown as a secondary line. The moment you have a tested result for a lift or a distance, that result takes the headline and the projection moves out of the way. A number you actually achieved always outranks a number we worked out for you.
Log the session you were going to do anyway. Pelaris reads the projections off it, labels them honestly, and steps them aside the moment you test the real thing.
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Pelaris gives AI-assisted general training information. It is not medical advice, it does not diagnose anything, and it is not a substitute for a doctor or a qualified health professional.