# Bicycle Physics Calculator - Gears, Power & Speed, Climbs, Self-Stability, Braking > Bike physics: gear ratios and speed per cadence, power vs speed with rolling, aero and gradient, climb times and W/kg, Whipple self-stability, braking limits. - URL: https://qilingtools.com/en/physics/bicycle - Category: Physics Tools (https://qilingtools.com/en/physics) - Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education) - Last updated: 2026-10-29 - Price: Free, no sign-up - Privacy: Runs locally in the browser; files are never uploaded One page for the physics of a bicycle. Enter chainring and cassette teeth to get every ratio, the distance per crank turn and the speed at several cadences, with duplicates and cross-chain combinations flagged. The power tab converts between watts and speed using rolling resistance, aerodynamic drag, gradient and drivetrain loss; the climbing tab estimates times on famous climbs; the stability tab uses the Whipple benchmark bicycle of Meijaard et al. to find the hands-free stable speed range; and the braking tab shows the skid and pitch-over limits. ## How to use 1. In Gears & cadence pick a drivetrain or type the teeth, choose a tyre and cadence, and click a row to shift the animated bike 2. In Power & speed set mass, position, surface, grade and wind, then solve speed from power or power from speed 3. In Climbing pick a climb and a power-to-weight ratio to see the time and VAM 4. In Self-stability adjust head angle, fork offset and speed to see the eigenvalues and the hands-off lean response 5. In Braking set the centre-of-mass position and friction to compare front, rear and combined braking ## Features - Gear ratio, development, gear inches and speeds at several cadences, with duplicates and cross-chaining flagged - Gear chart plus a side-view animation with turning cranks, chain and wheels - Power model with rolling resistance, aero drag (position CdA, drafting), gradient and drivetrain loss, with a power breakdown - Climb times and VAM for famous climbs such as Alpe d’Huez and Mont Ventoux - Linearized Whipple bicycle: eigenvalues vs speed, weave and capsize speeds, animated lean response - Braking: skid and pitch-over limits for front, rear and both brakes, with stopping distance ## FAQ ### Why are there fewer usable gears than rings × cogs? Many big-ring and small-ring combinations give nearly the same ratio, for example 50×21 ≈ 34×14. These duplicates (flagged when within 3%) add no new ratios, and the cross-chained combinations bend the chain badly. A 2×12 road groupset ends up with roughly 15 distinct gears, which is one reason single-ring drivetrains with wide cassettes are popular on gravel and mountain bikes. ### Why does riding a little faster take so much more effort? Air drag grows roughly with the square of speed, so the power to overcome it grows with the cube. Above about 30 km/h on the flat, more than 80% of your power goes into pushing air aside, and 10% more speed needs about 33% more power. Reducing drag by tucking down, using aero bars or drafting pays off more than a little extra strength. Uphill the speed is low, drag matters less and power-to-weight decides. ### Why can a bicycle balance itself without a rider steering? When the bike starts to fall to one side, the front wheel steers into the fall and brings the wheels back under the frame. This comes from the steering geometry (trail and steer-axis tilt) and the front wheel’s gyroscopic effect. The linearized Whipple model captures both: too slow and the correction comes too late, giving a growing wobble (weave); too fast and it is too weak, so the bike slowly topples (capsize). The benchmark bike is self-stable between about 4.3 and 6.0 m/s. ### Does more trail always mean more stability? Trail is the distance from where the steering axis meets the ground back to the tyre contact point; it makes the front wheel self-centre like a caster. More trail generally gives calmer steering, but self-stability also depends on head angle, mass distribution and front-wheel inertia, so more is not always better. Researchers have even built a self-stable bicycle with zero trail and no gyroscopic effect. Changing the head angle and fork offset in the tool shows the stable range shifting or vanishing. ### Can the front brake alone throw me over the bars? Hard braking shifts weight to the front wheel, so the front brake can stop you far harder than the rear. On dry roads its limit is usually not skidding but pitching over: at a deceleration of g × b/h (b is the horizontal distance from the centre of mass to the front contact, h its height) the rear wheel lifts. That is about 0.5–0.6 g for a typical road bike. Sliding your body back and staying low raises the limit; on slippery roads the tyre skids first. ## Related tools - [Unit Converter](https://qilingtools.com/en/math/unit): Free online unit converter: length, area, volume, weight, temperature, time, speed, data, pressure, energy and angle — one value converts every unit at once. - [Vector Calculator](https://qilingtools.com/en/math/vector): Free online vector calculator for 2D and 3D: addition, scalar multiples, dot and cross products, magnitude, angle, unit vector and projections, with checks. - [Significant Figures Calculator](https://qilingtools.com/en/math/significant-figures): Free online sig fig calculator: count significant figures digit by digit, round to N sig figs or decimals with six rounding modes, and compute by sig fig rules. - [Tone Generator](https://qilingtools.com/en/audio/tone-generator): Free online tone generator: sine, square, sawtooth and triangle waves from 1 to 20,000 Hz, a note picker, sweeps, white/pink/brown noise and a WAV download. - [Audio Spectrogram](https://qilingtools.com/en/audio/spectrogram): Free online spectrogram generator: see time, frequency and level from a Hann-windowed STFT, with FFT size, log axis, dB range and colour maps. 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