Normalised Power and Intensity Factor Explainer

What Normalised Power is for, why the fourth power pulls it above a ride’s average, and why this site computes no figure for it. The algorithm is published free by its own proprietor — the obstacle is that it needs the whole second-by-second power trace and this engine holds no time series at all.

The four published steps, and what each one needs

What a summary screen is and is not enough for

A published algorithm this engine cannot run, and the one it can

This page is about cycling. Two different kinds of number appear in this category and they are not sourced the same way. A regulation — a minimum bicycle weight, a gear rollout limit for a junior rider — is published by a body for a period, and every one quoted here is printed with that body and that edition, because the Union Cycliste Internationale and the national federations revise them. A definition — a gear ratio, a circumference, a rate of climb — belongs to nobody and is the same everywhere, and where this page relies on one it says whose published wording it took it from.

What Normalised Power is trying to do. A bike ride is not a steady effort. Power swings from nothing on a descent to several hundred watts out of a corner, and a plain average of all that understates how hard the ride was, because the body does not recover from a hard minute the way an arithmetic mean assumes. The metric is an attempt to produce the single steady wattage that would have cost about the same, and its proprietor describes it as “an estimate of the power that you could have maintained for the same physiological ‘cost’” if the output had been constant.

Why the fourth power. Raising each thirty-second average to the fourth power before averaging and then undoing it with a fourth root is a weighting: it makes the hard stretches count for far more than the easy ones. A consequence worth stating plainly, because it is the thing readers most often get backwards — the result can never be below the ride’s plain mean. Variation can only push it up. A flat time trial at constant watts sits almost exactly on its average; a criterium sits well above it. Nothing read for this page explains why the exponent is four rather than three or five, and this page does not guess.

This site computes no Normalised Power figure, and the reason is worth stating precisely because it is not the usual one. The algorithm is published free, by its own proprietor: TrainingPeaks’ blog sets out four steps — “Calculate the rolling average power with a window size of 30 seconds”, “take this value to the fourth power”, “Calculate the average of values from the previous step”, “Take the fourth root of the average” — and attributes them to Coggan’s book. Nothing is being withheld. The obstacle is that those four steps need the whole power trace, second by second, and the calculator engine on this site is a numeric expression evaluator with no arrays, no loops and no time series: it can hold the numbers a head unit prints on a summary screen and nothing longer. A figure built from a ride’s average power alone would not be a Normalised Power, it would be a fourth quantity wearing a trademarked name.

The names are owned, and that is a separate matter from the arithmetic. Normalized Power, Intensity Factor and Training Stress Score all carry a registered-trademark mark on TrainingPeaks’ own pages, and Polar’s V650 manual states that “NORMALIZED POWER®, INTENSITY FACTOR® and TRAINING STRESS SCORE® … are trademarks of TrainingPeaks, LLC and are used with the permission”. A trademark covers a name, not a calculation, so the arithmetic is nobody’s property — but it does mean that a number this site produced and called by one of those names would be making a claim about whose metric it was. This page names them to explain them and computes none of them.

So the position here has three parts, which get run together everywhere else. The algorithm is published and free. The names are registered and licensed. And no formula for Training Stress Score was read at all — the proprietor’s explanatory article gives none and Polar’s licensed manual gives none — which is a “could not establish” finding rather than an “encumbered” one, a weaker and a different claim, recorded that way on purpose. No Training Stress Score is computed here.

The number this page cannot look up for you, it asks you for. The calculator engine has no table interpolation of any kind, and a curve fitted to stand in for a published table is worst at its extremes, which is exactly where an answer changes anything. Anyone who needs this calculation already has the figure, printed on the thing this page is about, so that figure is the input and the arithmetic done on it is honest.

What this site does compute on this subject, and where. Intensity Factor is one division — its proprietor’s own definition is “the ratio of the normalized power as described above to your threshold power” — and two numbers off a summary screen are enough for it, so the FTP and power zones calculator does it, with your Normalised Power as the input and the twenty-minute FTP convention taken apart rather than assumed. For the watts-per-kilogram side of the same figures, the power to weight ratio calculator; for a climb turned into an estimated relative power from a rate of ascent instead of a measurement, the climbing gradient and VAM calculator.

Where the line runs between this page and the health section: health owns the athlete’s body, this category owns the bike and the ride. A heart rate is measured in the rider, so a heart-rate training zone is health’s work, at the target heart-rate zones calculator, and so is aerobic capacity, at the VO2 max calculator. A watt is measured at the cranks by a strain gauge in the bicycle and would read the same if something other than a person were turning them, so power, and everything built on it, is here. Nothing on this page prescribes a wattage, an interval, a heart rate or anything to eat, and nothing here is a physiological measurement or a medical claim.

Frequently asked questions

Related calculators

References

1. TrainingPeaks. “Normalized Power”, byline “By Tom Epton”, the TrainingPeaks blog, published 17 March 2022, “Updated October 15, 2024” (read 15 Oct 2026; about 25,000 characters). THE DECISIVE SOURCING FINDING OF THIS BATCH: the proprietor of the metric publishes the algorithm, free, in four numbered steps, quoted here in full because the explainer rests on them. “Calculate the rolling average power with a window size of 30 seconds.” “Take each value from step one and take this value to the fourth power (multiply this number by itself four times).” “Calculate the average of values from the previous step.” “Take the fourth root of the average from the previous step — this value gives us the normalized power.” It attributes the calculation to Andy Coggan’s Training and Racing with a Power Meter and writes the metric as “Normalized Power®” and “NP®”. So nothing is withheld and nothing had to be reconstructed; what stops this site computing it is that the four steps need a second-by-second power trace and this engine has no arrays and no loops.
2. TrainingPeaks. “Normalized Power, Intensity Factor and Training Stress Score”, byline “By Dr. Andrew Coggan, Ph.D.”, published 10 February 2016, “Updated May 11, 2026” (read 15 Oct 2026; about 14,000 characters; the intensity ranges and the TSS scale came through as readable bulleted lists, and NO FORMULA was readable anywhere on the page). The proprietor’s own explanatory article, notably less forthcoming than its blog above: it calls the method “a special algorithm” which “is somewhat complicated” and gives no steps. It does define intensity factor exactly — “IF is simply the ratio of the normalized power as described above to your threshold power” — which is the one quantity here a summary screen’s figures are enough to compute. On training stress score it gives NO formula: only that TSS “takes into account both the intensity (i.e., IF) and the duration of each training session” and that it is modelled after Dr Eric Bannister’s heart-rate TRIMPS. THAT IS WHY NO TSS IS COMPUTED IN THIS BATCH — not a licence, but no formula read from its own proprietor. Its heading prints all three marks with a registered symbol: “Normalized Power® , Intensity Factor® , and Training Stress Score®”.
3. Polar Electro. “Advanced power metrics”, the Polar V650 user manual, support.polar.com (read 15 Oct 2026; about 7,000 to 8,000 characters, most of it navigation). Read for the trademark position and quoted for it, because a licensee’s own notice is better evidence than an inference from a ® symbol. It states that “NORMALIZED POWER®, INTENSITY FACTOR® and TRAINING STRESS SCORE® … are trademarks of TrainingPeaks, LLC and are used with the permission”. It defines normalised power as providing “a better measure of the true physiological demands of a given training session”, intensity factor as “the ratio of the normalized power to your threshold power”, and training stress score as quantifying “the overall training load based on your power data”, and warns that “Polar training load and TRAINING STRESS SCORE cannot be compared”. It publishes no formula for any of the three. So the position this batch reports is specific: the arithmetic of normalised power is PUBLISHED and free, the NAMES are registered and licensed, and the training stress score formula was not read at all.
4. “Reliability of the Functional Threshold Power in Competitive Cyclists”, DOI 10.1055/a-1018-1965, accepted 11 September 2019, published online 17 January 2020; the search result’s own page title gives the citation as Int J Sports Med 2020; 41(03): 175–181 (read 15 Oct 2026; about 40,000 characters, Table 1 as text with the layout flattened, reference list appearing twice). THE AUTHOR LIST DID NOT COME THROUGH in either of two fetches — the Authors section was empty on both — so no author is named here. It defines FTP as the highest power a cyclist can hold in a quasi-steady state without fatigue for about sixty minutes, and states that because that test is so long “it was suggested that the FTP might be determined as 95% of the mean PO in a 20-min TT (FTP20)”, crediting that to Allen and Coggan’s Training and Racing with a Power Meter, 2nd edition, 2010. It describes FTP as an input to training stress score and intensity factor, again crediting Allen and Coggan, and does not mention normalised power at all.