Cycling Cadence, Gear & Speed Calculator
A bike's forward speed is set by three things: pedalling cadence (rpm), gear ratio (chainring teeth ÷ cog teeth), and rolling circumference (wheel + tyre). Enter all three and the tool reports (1) speed in km/h and mph; (2) the gear ratio; (3) gain ratio — metres travelled per pedal stroke (European convention); (4) gear inches — the equivalent direct-drive wheel diameter (US / penny-farthing legacy). Wheel size comes from a preset list (700×23c…650b, 29er, 27.5″, 26″, 20″ folder) or a custom rollout. Useful for road, MTB, TT and singlespeed riders picking gearing, dialling cadence, or comparing setups.
Check values: cadence, sprocket teeth and rollout must all be > 0; ratio must be sensible.
Speed (km/h)
—
km/h
Speed (mph)
—
mph
Gear ratio (chainring / cog)
—
Distance per pedal stroke (gain ratio)
—
m / pedal stroke
Gear inches
—
″
Formula
gear ratio = chainring_teeth / cog_teeth rollout per stroke (gain ratio, m) = gear ratio × wheel circumference (m) gear inches = (circumference mm / π / 25.4) × gear ratio speed (m/min) = cadence × rollout per stroke speed (km/h) = speed (m/min) × 60 / 1000 speed (mph) = km/h ÷ 1.609344
- · **Rolling circumference includes the tyre and rider-weight squish**. ISO charts are only approximate — low pressure or wide-flange tyres can drop 5–15 mm. The most accurate value comes from your bike computer's auto-calibration (Garmin, Wahoo) or a roll-out test (chalk mark, one revolution, tape-measure distance).
- · **Cadence ranges**: (1) road pros 85–95 rpm (Froome holds 90+ even climbing); (2) MTB 60–80 rpm with technical burst; (3) TT / triathlon 85–95 rpm sustained; (4) track sprint 130–170 rpm; (5) commuter 70–80 rpm. **Low cadence + heavy gear = muscle fatigue fast; high cadence + light gear = cardiovascular fatigue fast** — well-trained riders work both.
- · **Gear inches** (19 c. US / UK legacy, the penny-farthing equivalent wheel size): (1) road high 100+″ (50×11 ≈ 122″); (2) mid 70–80″ (38×13 ≈ 77″); (3) climb 30–40″ (30×28 ≈ 28″); (4) granny < 20″ for 20 %+ grades. **Gain ratio** (metric): 5–10 m / stroke for road cruise, 3–5 m climbing, 2–3 m off-road technical.
- · **Choosing a ratio**: (1) **target speed at your habitual cadence** sets the ideal ratio — pick the chainring/cog combo closest to it; (2) **best chainline is straight** — big-to-small or small-to-big creates cross-chain drag and chain wear; (3) **range** matters — 11-speed road 11–28 / 11–34, gravel 11–42, MTB 10–52; bigger jumps make finding the sweet spot harder.
- · **Power vs speed** (flat, no wind, no draft): power ∝ velocity³ — aerodynamic drag dominates. **Doubling speed needs 8× power**. Going 30 → 35 km/h costs (35/30)³ ≈ 1.59× the power of holding 30 km/h — far more than the linear cadence × ratio relationship would suggest.
- · **References**: (1) Sheldon Brown's Gear Calculator — the canonical reference — https://sheldonbrown.com/gears/; (2) Continental Tyre rolling-circumference chart, 2023 ed.; (3) Shimano Tech Bulletin 2023 — gear inches conversion; (4) Wattbike Atom science guide — cadence efficiency curves; (5) Allen & Coggan, "Training and Racing with a Power Meter", 3rd ed.
Frequently asked
Same speed — is higher cadence + lighter gear or lower cadence + heavier gear better?
**Short answer**: high cadence taxes the cardiovascular system but spares the legs; low cadence taxes the legs but is easier on the heart. **Research**: Coyle et al. (1991) and Lucia et al. (2001) found road pros habitually spin 90–105 rpm while club riders sit at 70–80 rpm — pros choose the higher cadence specifically to spare the quads for climbs and attacks. **Practical**: (a) **flat steady riding**: 80–90 rpm matched with the right gear minimises drag; (b) **climbing 8 %+**: keep 90 rpm by shifting to a much lighter gear (30 × 28 = 0.86 ratio); (c) **time trial**: lock in 90+ rpm at the biggest gear you can hold aero; (d) **beginners**: build the 80+ rpm habit first, then add gear — going up in cadence is harder than going up in gear. **Rule of thumb**: if climbing wipes out your legs your cadence is too low; if your heart explodes but the legs are still fresh, it's too high.
Gear inches or gain ratio — which should I quote?
Both express the same ratio — pick by audience. (1) **Gear inches** (the equivalent direct-drive wheel diameter): US, UK, vintage cycling magazines and Sheldon Brown use this — it descends from 1880s penny-farthing terminology where the front-wheel diameter literally equalled gear ratio × rear-wheel diameter. **Typical values**: road high gear 100+″, TT 110–130″, climbing 25–40″. (2) **Gain ratio** (metres per pedal stroke): continental Europe, Eurobike publications, metric users. **Typical values**: 8–11 m on the road, 4–6 m climbing. **Sheldon Brown actually recommends gain ratio** because the unit *is* the real distance, but gear inches remain the lingua franca of English-speaking bike shops. **Pick whichever your riding buddies use** — don't invent a third standard.
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