Cycling Speed from Cadence and Gearing Calculator
Cycling Speed from Cadence and Gearing Calculator
The whole chain from pedal revolutions per minute to kilometres per hour, written out link by link: teeth to gear ratio, gear ratio to metres per crank revolution, metres per minute to km/h. Cycling’s quantity is speed, not pace, and this page says why.
Speed from a cadence and one gear
Cadence × development90 rpm in 53/19 on a 680 mm wheel — the wheel and gear from Sheldon Brown’s published gain-ratio example, at a common road cadence
Formula
development in metres = π × wheel diameter in metres × gear ratio
metres per minute = cadence in rpm × development
km/h = metres per minute × 60 ÷ 1000 = metres per minute × 0.06
mph = km/h × 1000 ÷ 1609.344
- 0.06 is exact
- sixty minutes in an hour over a thousand metres in a kilometre. Both are definitional, so the factor is 3/50 exactly and carries no rounding error at all. It is written out as 60 ÷ 1000 in the chain above so it cannot be read as a fitted coefficient
- 1609.344 is exact too
- the international yard and pound agreement of 1959 defines the yard as 0.9144 m exactly, which makes the mile 1609.344 m exactly. A conversion to mph is therefore exact arithmetic and not an approximation
- crank length is absent
- and that is deliberate. One crank revolution turns the chainring once whatever the crank’s length, so the distance travelled is untouched by it. What the crank length changes is how hard that revolution is to make, which is the gain ratio on the gear ratio and gain ratio calculator and is not a speed
- cycling’s quantity is speed
- not pace. A runner and a swimmer divide a time by a distance and get minutes per kilometre or seconds per 100 m, because their speed barely changes with the ground. A cyclist’s does: the same rider at the same cadence is doing 32 km/h on the flat and 9 km/h on a 10% climb in a different gear. So cycling quotes km/h, and the inputs that set it are the gear and the cadence rather than the clock
Worked example
90 rpm in 53/19 on a 680 mm wheel — the wheel and gear from Sheldon Brown's published gain-ratio example, at a common road cadence
The gear ratio is 53 ÷ 19 = 2.7895
The wheel circumference is π × 0.680 = 2.1363 m, so the development is 2.1363 × 2.7895 = 5.9591 m per crank revolution
90 crank revolutions a minute covers 90 × 5.9591 = 536.32 m a minute
536.32 × 0.06 = 32.18 km/h, which is 8.9387 m/s and 19.995 mph
Double the cadence to 180 rpm and the speed doubles exactly, to 64.36 km/h: speed is linear in cadence
Halve the sprocket to 9.5 teeth and the speed doubles again, because speed is linear in the gear ratio and the gear ratio is inverse in the sprocket
Set the cadence to zero and the speed is zero — a real answer, not a refusal
Set the sprocket or the wheel to zero and the panel shows nothing, because there is no gear to be in
Speed at 90 rpm, by gear, on a 678 mm wheel
| Gear | Gear ratio | Development | Speed | Speed | Wheel rpm |
|---|---|---|---|---|---|
| 34 × 28 | 1.2143 | 2.5864 m | 13.97 km/h | 8.68 mph | 109.3 |
| 39 × 25 | 1.5600 | 3.3228 m | 17.94 km/h | 11.15 mph | 140.4 |
| 50 × 19 | 2.6316 | 5.6053 m | 30.27 km/h | 18.81 mph | 236.8 |
| 53 × 19 | 2.7895 | 5.9416 m | 32.08 km/h | 19.94 mph | 251.1 |
| 53 × 14 | 3.7857 | 8.0636 m | 43.54 km/h | 27.06 mph | 340.7 |
| 53 × 11 | 4.8182 | 10.2627 m | 55.42 km/h | 34.44 mph | 433.6 |
The same gear at different cadences, and the unit chain
| Cadence | Metres per minute | km/h | m/s | mph |
|---|---|---|---|---|
| 60 rpm | 356.49 m | 21.39 km/h | 5.9416 | 13.29 mph |
| 80 rpm | 475.33 m | 28.52 km/h | 7.9221 | 17.72 mph |
| 90 rpm | 534.74 m | 32.08 km/h | 8.9124 | 19.94 mph |
| 100 rpm | 594.16 m | 35.65 km/h | 9.9026 | 22.15 mph |
| 120 rpm | 712.99 m | 42.78 km/h | 11.8832 | 26.58 mph |
From pedal revolutions to kilometres per hour, link by link
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.
Four measures are in circulation and they are not interchangeable. Gear ratio is chainring teeth divided by sprocket teeth, and it ignores the wheel, so it cannot compare a road bike with a 20-inch folder. Gear inches multiplies that ratio by the wheel diameter in inches and is an imperial relic: it is the diameter of the driving wheel a direct-drive high-wheel bicycle would need to be geared the same, which is why its numbers are in the seventies rather than anywhere meaningful. Development, or rollout, is the distance the bicycle travels in one crank revolution, wheel circumference times the ratio, in metres. Gain ratio is Sheldon Brown’s, and it is the only one of the four that is dimensionless and the only one that contains the crank length.
The chain this page computes has four links and none of them is approximate. The teeth give a gear ratio, chainring over sprocket. The gear ratio times the wheel circumference gives the development, which is how far the bicycle travels for one turn of the cranks. Cadence, in crank revolutions per minute, times the development gives metres per minute. And metres per minute times 60 and divided by 1000 gives kilometres per hour. The last factor is 0.06 exactly, because an hour has sixty minutes and a kilometre a thousand metres by definition, and the mile conversion is exact too: the international yard and pound agreement of 1959 fixes the yard at 0.9144 m, so a mile is 1609.344 m with nothing rounded.
Crank length does not appear on this page, and leaving it out is a decision rather than an oversight. One revolution of the cranks turns the chainring once however long the cranks are, so the distance covered does not depend on them at all. What the crank length changes is the leverage, and the measure that captures it is the gain ratio on the gear ratio and gain ratio calculator. A speed calculator that asked for crank length would be implying a dependency that is not there.
Cycling’s quantity is speed, and this is not a pace page. Running and swimming divide a time by a distance, because a runner or a swimmer covers ground at nearly the same rate for the whole of a race and the useful number is minutes per kilometre or seconds per 100 metres. A cyclist’s rate is not like that. It is set by the gear and the cadence and it swings enormously with the gradient and the wind: the same rider turning the same 90 rpm is doing 32 km/h on the flat in 53/19 and well under 10 km/h up a steep climb in 34/28. So the inputs that determine a cyclist’s speed are mechanical rather than temporal, and the output is km/h or mph. Where a cyclist does want a per-distance figure it is for a climb, and the measure is vertical metres per hour — which the climbing gradient and VAM calculator computes.
Two things to watch when you check this against your own bike computer. The first is the wheel: the computer uses the circumference it was configured with, and if that was a nominal figure from a tyre’s markings it is probably a little larger than the circle your loaded wheel actually rolls, so the computer reads slightly high. The wheel circumference and odometer calibration calculator works out how much. The second is the drivetrain: this page assumes the chain drives the wheel directly through one chainring and one sprocket, which is true of a derailleur bicycle and of a fixed wheel, and is not true of a hub gear or a gearbox, where an internal ratio sits in the chain and must be multiplied in.
Frequently asked questions
How do you work out speed from cadence and gearing?
Multiply the cadence in rpm by the development — the metres the bicycle travels per crank revolution, which is π times the wheel diameter in metres times the gear ratio — then multiply by 0.06 to turn metres per minute into km/h. At 90 rpm in 53/19 on a 680 mm wheel that is 90 × 5.9591 × 0.06 = 32.18 km/h.
Why is the conversion factor 0.06?
Because it is 60 ÷ 1000: sixty minutes in an hour, a thousand metres in a kilometre. Both are definitional, so the factor is exact and has no rounding error. The mph conversion is exact as well, dividing by 1609.344 metres to the mile.
Does crank length affect speed?
No. One turn of the cranks turns the chainring once whatever the crank’s length, so the bicycle covers the same distance. Crank length changes the leverage and therefore how hard the gear feels, which is what a gain ratio measures — it does not change the speed a given cadence in a given gear produces.
What cadence do I need for 30 km/h?
It depends entirely on the gear, which is why the calculator prints it as a row rather than a number. In 53/19 on a 680 mm wheel it is about 84 rpm; in 39/25 on the same wheel it is about 150 rpm, which is why nobody rides 30 km/h in that gear.
Why does cycling use speed where running uses pace?
Because a cyclist’s rate of travel is set by the gear and the cadence and varies hugely with the gradient, while a runner’s is nearly constant over a race. A pace in minutes per kilometre is a useful summary of a run and almost useless as a summary of a bike ride, so cycling quotes km/h or mph, and for climbing it quotes vertical metres per hour instead.
Related calculators
References
- Sheldon Brown. “Gain Ratios”, sheldonbrown.com/gain.html (read 15 Oct 2026; about 9,000 characters of which the article and its radius-ratio table are 5,000 to 6,000, and the table came through as readable TEXT). The source for gain ratio here. Two steps: “Find the radius ratio by dividing wheel radius by crank length”, done once per bicycle, then multiply by front teeth over rear. Of the answer: “This number is a pure ratio, the units cancel out”, so for each unit the pedal travels in its orbit the bicycle travels that many. BOTH published worked examples are reproduced through this site’s engine: a 700 x 30 road bike, 340 mm wheel radius, 170 mm cranks, radius ratio 2.0, 53/19 giving 5.58; and a mountain bike, 13 in radius, 6¾ in cranks, 46/16 giving 5.54. On the alternatives: “the handwriting is on the wall for all inch-based measurement systems”, and metres of development is “a bit more cumbersome” for needing a multiplication by π, “an irrational one, no less”.
- Wikipedia. ISO 5775 (read 15 Oct 2026; about 9,000 to 10,000 characters, designation table as readable TEXT). ISO 5775 was developed by the European Tyre and Rim Technical Organisation and is now managed by ISO; Part 1, “Bicycle tyres and rims: Part 1: Tyre designations and dimensions”, was last published August 2023 and Part 2, “Part 2: Rims”, March 2021. A clincher tyre carries its nominal section width and the nominal rim diameter in millimetres separated by a hyphen, so “32-597” is a 32 mm section on a 597 mm bead seat. Bead seat diameters: 622 mm (700C), 584 mm (650B, sold as 27.5 inch), 559 mm (26 inch mountain bike), 507 mm (24 inch), 406 mm (20 inch). The page warns that inch labels do not reliably indicate a bead seat diameter and that its own citations are to the superseded 1997 and 1996 editions, so a specific row should be checked against the standard.
- Wikipedia. Gear inches (read 15 Oct 2026; about 10,000 characters). Cited for the DEFINITION — “the diameter in inches of the drive wheel of a penny-farthing bicycle with equivalent (direct-drive) gearing” — and for the exact factor 0.0254π between gear inches and metres of development. NOT cited for any formula: the article says its measures are “calculated as follows” and the equations are ABSENT from the fetched text, so only its prose was used. Its own references include the UCI’s Part 2 Road Races regulations of 1 January 2023 and the German and Austrian federations’ road regulations on junior gear restrictions, none of which was read here.