Engineering · Mechanical Engineering · Machine Elements
Bike Gear Ratio Calculator
Calculate bicycle gear ratio, gain ratio, and development (rollout) from chainring, sprocket, wheel diameter, and crank arm length.
Calculator
Formula
T_front = number of teeth on the front chainring; T_rear = number of teeth on the rear sprocket; D_wheel = outer wheel diameter in metres (including tyre); R_wheel = wheel radius in metres; L_crank = crank arm length in metres. Gear Ratio is dimensionless, Development is metres travelled per pedal revolution, and Gain Ratio is a dimensionless number comparing wheel radius to crank arm radius — independent of wheel size.
Source: Sheldon Brown, 'Gain Ratios — A New Way to Designate Bicycle Gears', sheldonbrown.com, 1999; ANSI/ASME B29.1 roller chain standard for pitch reference.
How it works
The gear ratio is the simplest metric: divide the number of front chainring teeth by the number of rear sprocket teeth. A 50-tooth chainring paired with a 17-tooth sprocket gives a gear ratio of 2.94, meaning the rear wheel rotates 2.94 times per pedal revolution.
The development (or rollout) converts the gear ratio into real-world distance per pedal stroke by multiplying by the wheel circumference (π × diameter). This is the most practically useful number: a development of 8.22 m means the bike travels 8.22 metres forward for every complete pedal revolution.
The gain ratio, introduced by Sheldon Brown, refines this further by dividing the wheel radius by the crank arm length, producing a dimensionless number comparable across different wheel sizes. A gain ratio above 6 is suitable for flat sprinting; below 2 is typical for steep climbs. Road speed is derived by multiplying development by cadence (rev/min) and converting to km/h or mph.
Worked example
Setup: A road cyclist uses a 50-tooth chainring, a 17-tooth sprocket, a 700c tyre with an outer diameter of 668 mm, and 172.5 mm crank arms, pedalling at 90 rpm.
Step 1 — Gear Ratio: 50 ÷ 17 = 2.94
Step 2 — Development: 2.94 × π × 0.668 m = 2.94 × 2.098 = 6.17 m/rev
Step 3 — Gain Ratio: (50 ÷ 17) × (0.334 ÷ 0.1725) = 2.941 × 1.936 = 5.69
Step 4 — Speed: 6.17 m/rev × 90 rpm × 60 min/h ÷ 1000 = 33.3 km/h (20.7 mph)
Limitations & notes
The wheel outer diameter must include the inflated tyre. Standard values are approximately 668 mm for 700c × 23 mm tyres and 559 mm for 26-inch MTB tyres; actual diameter varies with tyre brand, pressure, and load. The calculator assumes a single-speed or fixed-gear drivetrain per calculation — for multi-speed bikes, run one calculation per gear combination of interest. Chain efficiency losses (typically 1–3%) and drivetrain flex are not modelled. Speed results assume a perfectly flat surface with no wheel slip.
Frequently asked questions
What is a good gear ratio for climbing?
A gear ratio below 1.0 (e.g. 34-tooth chainring with a 36-tooth sprocket = 0.94) is excellent for steep climbs, giving a gain ratio of roughly 2–3. Many gravel and mountain bikes use compact or sub-compact chainrings paired with wide-range cassettes to achieve ratios in the 0.7–1.2 range for technical terrain.
What is the difference between gear ratio and development?
Gear ratio is a pure mechanical number — it tells you how many times the rear wheel rotates per pedal turn. Development (rollout) translates that into metres travelled per pedal revolution by factoring in wheel size. Two bikes with the same gear ratio but different wheel diameters will travel different distances per pedal stroke; development captures this difference.
Why is gain ratio more useful than gear ratio or development?
Gain ratio also accounts for crank arm length, making it a true measure of mechanical advantage. A tall rider using 175 mm cranks and a short rider using 165 mm cranks will experience the same gear ratio differently because their lever arm is different. Gain ratio normalises for this, allowing valid comparisons across bikes of different wheel sizes and crank lengths.
What outer diameter should I enter for my wheel?
Measure the fully-inflated tyre from ground contact to the opposite tread surface, or use a standard reference: 700c × 23 mm ≈ 668 mm, 700c × 28 mm ≈ 678 mm, 700c × 40 mm ≈ 700 mm, 26 × 2.1" MTB ≈ 676 mm, 29 × 2.2" MTB ≈ 740 mm. Sheldon Brown's tyre size chart provides detailed lookup values.
How many teeth should I choose for my rear sprocket to hit a target speed?
Rearrange the development formula: T_rear = T_front × π × D_wheel ÷ Development_target. For example, if you want 8 m/rev with a 50-tooth chainring on a 668 mm wheel: T_rear = 50 × π × 0.668 ÷ 8 ≈ 13.1, so use a 13-tooth sprocket. You can iterate with this calculator by changing rear teeth until the development output matches your target.
Does cadence affect gear ratio or development?
No — gear ratio and development are purely mechanical properties of the chainring, sprocket, and wheel size. Cadence only affects speed. Higher cadence with the same gear multiplies your speed proportionally: doubling cadence from 60 to 120 rpm doubles your speed without changing the gear mechanics.
Last updated: 2025-01-30 · Formula verified against primary sources.