About

Miscalculating gear development leads to poor cadence zones, premature fatigue, and suboptimal race pacing. This calculator derives cycling speed from three mechanical inputs: N_front (chainring teeth), N_rear (cog teeth), and RPM (pedal cadence), combined with true wheel circumference computed from ETRTO bead seat diameter and tire cross-section. It outputs speed in both km/h and mph, gear development in meters, Sheldon Brown's gain ratio (a crank-length-normalized metric superior to gear inches), and skid patch count for fixed-gear setups. The tool assumes zero drivetrain loss and no tire deformation under load. Real-world speed will be 2 - 5% lower due to chain friction, tire slip, and wind resistance.

Pro tip: optimal road cadence sits between 80 - 100 RPM. Track sprinters peak above 130 RPM. If your calculated speed at target cadence doesn't match your GPS data, check actual tire circumference with a roll-out test rather than relying on nominal sizing.

Formulas

Cycling speed is a direct function of gear development and pedal cadence. Gear development represents the distance the bicycle travels per one full crank revolution.

G = N_frontN_rear

C = π × (D_BSD + 2 × W_tire)

Dev = G × C

v = Dev × RPM × 601000

Gain ratio normalizes development against crank arm radius, providing a dimensionless comparison across different crank lengths:

GR = Dev2 × π × L_crank

Skid patch count determines the number of distinct contact points on a fixed-gear tire before the pattern repeats:

SP = N_rearGCD(N_front, N_rear)

Where G = gear ratio, N_front = chainring teeth, N_rear = cog teeth, C = wheel circumference m, D_BSD = bead seat diameter mm, W_tire = tire cross-section width mm, Dev = development m, v = speed km/h, RPM = cadence rev/min, GR = gain ratio (dimensionless), L_crank = crank length m, SP = skid patches.

Reference Data

Tire Designation	ETRTO	BSD mm	Approx. Circumference mm	Typical Use
700 × 23c	23-622	622	2098	Road racing
700 × 25c	25-622	622	2111	Road all-round
700 × 28c	28-622	622	2136	Endurance road
700 × 32c	32-622	622	2155	Gravel / touring
700 × 38c	38-622	622	2180	Light gravel
700 × 40c	40-622	622	2200	Gravel racing
700 × 45c	45-622	622	2242	Adventure / bikepacking
650b × 47c	47-584	584	2130	Gravel alternative
26 × 1.95″	50-559	559	2070	MTB cross-country
26 × 2.1″	54-559	559	2090	MTB trail
26 × 2.35″	60-559	559	2130	MTB all-mountain
27.5 × 2.1″	54-584	584	2168	MTB trail 650b
27.5 × 2.35″	60-584	584	2210	MTB enduro 650b
27.5 × 2.6″	66-584	584	2260	MTB plus 650b
29 × 2.1″	54-622	622	2288	MTB 29er XC
29 × 2.25″	57-622	622	2310	MTB 29er trail
29 × 2.4″	61-622	622	2340	MTB 29er enduro
20 × 1.75″	47-406	406	1570	BMX / folding
16 × 1.5″	40-305	305	1210	Folding / kids
Track tubular 700c	22-622	622	2086	Velodrome

Frequently Asked Questions

This calculator assumes zero drivetrain loss, no tire deformation, and no aerodynamic drag. Real-world chain and bearing friction typically costs 2-5% efficiency. Tire pressure and load compress the contact patch, reducing effective rolling radius by 1-3 mm. Wind resistance grows with the square of velocity. A roll-out test (marking the ground, rolling one full crank revolution, measuring the distance) gives your true development value.

Gain ratio, developed by Sheldon Brown, divides gear development by the pedal circle circumference (2 × π × crank length). This produces a dimensionless number representing how many meters the bike travels per meter of pedal travel. Unlike gear inches, it accounts for crank arm length differences. A gain ratio of 5.0 means the wheel travels 5 meters for every 1 meter the pedal moves. Road bikes typically range from 2.5 (low) to 8.5 (high). Values below 2.0 indicate extremely easy spinning gears; above 9.0 indicates very heavy time-trial gears.

Wider tires increase wheel circumference. Switching from a 700×23c (circumference ≈ 2098 mm) to a 700×32c (≈ 2155 mm) adds about 57 mm per revolution. At 90 RPM in a 50/17 gear, this difference translates to roughly 0.9 km/h. The ETRTO-based circumference formula used here (π × (BSD + 2 × tire width)) approximates mounted tire diameter. Actual circumference varies with tire brand, pressure (higher pressure = slightly smaller), and rider weight.

Skid patches only apply to fixed-gear (track) bicycles. The count equals N_rear ÷ GCD(N_front, N_rear). A 48/17 combination gives 17 ÷ GCD(48,17) = 17 ÷ 1 = 17 skid patches - excellent tire longevity. A 48/16 gives 16 ÷ GCD(48,16) = 16 ÷ 16 = 1 patch - the tire wears through at one spot. If you skid with both feet (ambidextrous skidding), multiply the count by 2. Prime-number cog teeth (17, 19) generally maximize skid patches.

Recreational cycling: 60-75 RPM. Road endurance: 80-95 RPM. Road racing / criteriums: 90-105 RPM. Time trials: 95-110 RPM. Track sprinting: 110-140+ RPM. Mountain biking: 70-90 RPM (terrain dependent). Higher cadence reduces torque per stroke, sparing muscular glycogen at the cost of cardiovascular load. Lower cadence demands more force per pedal stroke, fatiguing Type II muscle fibers faster. Select gearing that keeps you within your target RPM range at expected speeds.

Crank length changes lever arm, not gear ratio or development. However, it changes the gain ratio. Moving from 172.5 mm to 170 mm cranks increases gain ratio by about 1.5% for the same chainring and cog - meaning each pedal stroke feels slightly harder but covers more distance per unit of pedal travel. Shorter cranks also allow higher cadence due to reduced hip angle requirement. The effect is measurable but modest; a 5 mm change in crank length produces roughly the same gain ratio shift as changing one tooth on the rear cog.