Climbing Gradient and VAM Calculator

Gradient both ways round — the road sign’s tangent and the along-the-road sine — with the angle in degrees, and VAM, the vertical metres climbed per hour. The relation from VAM to watts per kilogram is printed with the two sources it came from, and the altitude caveat is printed without a correction, because none was published.

Formula

The two gradient conventions, and how far apart they are

VAM as a rate, and the two relative-power figures

Vertical metres an hour, and the two ways to write a gradient

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.

Gradient looks simple and has two conventions hiding in it. The standard one, and the one a European road sign uses, is rise divided by the horizontal distance, expressed as a percentage — the tangent of the angle, so a 45-degree slope is 100% and not 71%. The other, rise divided by the distance along the road surface, follows the sine instead; the slope literature calls that one nonstandard. At road gradients the gap is small but it is not nothing: a 10% climb by the tangent is 9.95% by the sine, and a 20% one is 19.61%. This page prints both and the angle in degrees, because a bike computer measures distance travelled along the road while a sign measures the horizontal, and the two are answering slightly different questions.

VAM is the other half of the page and it is the more useful of the two. The letters stand for velocità ascensionale media, average ascent speed, and it is simply the vertical metres climbed per hour: height gained, divided by the time, scaled to an hour. The term was coined by the Italian physician and cycling coach Michele Ferrari. It works as a climbing measure for a reason worth stating — it throws away the horizontal entirely, so it does not care whether a climb is long and gentle or short and brutal, and two performances on different mountains can be set side by side. A speed in km/h cannot do that, because the same effort produces wildly different speeds on different gradients.

The relation from VAM to watts per kilogram, and how much to trust it. Two independent secondary sources give the same arithmetic in different notation, and the primary — Ferrari’s own article of 1 March 2003 on 53×12.com, which both cite — could not be read, the archive copy having been refused in the session these pages were researched. So it is printed as an empirical rule of thumb with two secondary attributions and not as anybody’s law. 220 Triathlon’s own verdict is that VAM is “a decent enough measure of power but it’s only a rough guide”, and its published worked example is reproduced here exactly: Alpe d’Huez at 7.9% with a VAM of 1,768 gives 1768 ÷ 279 = 6.34 W/kg.

Beside it is a second figure that is not empirical at all. Lifting a mass at a known vertical speed costs exactly g times that speed per kilogram, so with VAM in vertical metres per hour the relative power spent purely on lifting is VAM × 9.80665 ÷ 3600 — a divisor of 367.1 with the standard value of g, which is where the widely quoted 367 comes from, that figure corresponding to g = 9.81. This is a floor: the work gravity alone demands, with nothing for rolling resistance, drivetrain losses or air. The gap between the two rows is what the empirical relation is trying to account for, and at 7.9% it is about a quarter.

On altitude, this page prints the caveat and no correction. VAM falls with altitude for the same effort, because there is less oxygen to be had, so a climb finishing above 2,000 m is not directly comparable with one at sea level. What the sources read for this page actually publish on the point is very little: 220 Triathlon says only that “altitude will skew the figures” and contrasts a 10% climb from sea level with one beginning at 2,000 m, and Wikipedia’s article on VAM does not mention altitude at all. Neither publishes a correction factor. So none is applied here and none is invented, because a correction nobody published is a number this site would be making up. The same sources say wind, temperature and drafting matter little on a climb and less still above 8%, which is a useful thing to know and is also not a correction.

Two practical warnings about the inputs. The height gained is the summit altitude minus the altitude at the bottom, and it is not the “total ascent” or “elevation gain” a head unit reports for a whole ride, which sums every rise including those you then descend; using the latter on a rolling route will give a VAM that means nothing. And barometric and GPS altitude readings disagree, often by tens of metres over a long climb, so two riders’ VAM figures for the same climb can differ because of their devices rather than their legs. For the gearing and cadence that produce the speed up the hill, the cycling speed from cadence and gearing calculator and the gear ratio and gain ratio calculator; for a measured rather than an estimated watts-per-kilogram figure, the power to weight ratio 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. 220 Triathlon (Kelsey Media Ltd). “What is VAM?”, by the 220 Triathlon Team, published 3 November 2017, last modified 24 May 2022 (read 15 Oct 2026; about 35,000 characters, most of it navigation and related articles). The second, independent rendering of the same relation in different notation — “Watts per kg = VAM ÷ by (gradient factor x 100)” with “gradient factor = 2 + (% gradient ÷ 10)”, which is the same arithmetic as 200 + 10 × gradient — with “VAM = (metres of elevation gained x 60) ÷ by minutes taken to ride the climb” and the same attribution to Ferrari. ITS PUBLISHED WORKED EXAMPLE IS REPRODUCED through this site’s engine: Alpe d’Huez at 7.9%, a VAM of 1,768, giving 1768 ÷ 279 = 6.34 W/kg. On altitude it says only that “altitude will skew the figures”, contrasting a 10% climb from sea level with one starting at 2,000 m, and publishes NO correction — so neither does this page. It calls VAM “a decent enough measure of power but it’s only a rough guide”, and says wind, temperature and drafting have a negligible effect that falls further on gradients of 8% or more.
2. Wikipedia. VAM (bicycling) (read 15 Oct 2026; about 4,000 characters). The Italian velocità ascensionale media, average ascent speed, in vertical metres per hour, “coined by Italian physician and cycling coach Michele Ferrari”; VAM = metres ascended × 60 ÷ minutes taken. It gives the frictionless relation as W/kg equal to VAM divided by about 367, and the empirical one including friction and the bicycle’s mass as W/kg = VAM ÷ (200 + 10 × % grade). It attributes the origin to Michele Ferrari, “The rider’s performance: how to measure it?”, 53×12.com, 1 March 2003, archived 1 July 2003 — WHICH COULD NOT BE READ: the Internet Archive refused the request in this session before returning any content. Its other citations are a Strava support article (also refused) and four CyclingNews reports of 2003 to 2007. The page says NOTHING about altitude.
3. Wikipedia. Grade (slope) (read 15 Oct 2026; about 25,000 to 30,000 characters, BUT the formulas did NOT come through — the mathematical expressions are blank in the fetched text and only the surrounding prose was readable, so nothing numeric is taken from it). Cited for the two conventions and for which is standard: a percentage grade “is equivalent to the tangent of the angle of inclination times 100”, measured against the horizontal run, so a 45° slope is 100%; rise over the slope length is called nonstandard because it “follows the sine function rather than the tangent function”, making the same slope about 71%. It states that “In Europe, road gradients are expressed in signage as percentage”. The tangent-versus-sine figures on the climbing page are this site’s own arithmetic from those definitions, not quotations.