Bike Speed Calculator: Gear Ratio to Speed

A bike speed calculator using gear ratio estimates how fast a bicycle travels from its wheel size, chainring and rear sprocket sizes, and pedaling cadence. Enter those measurements and the calculator returns estimated road speed in km/h and mph, assuming the wheel rolls without slipping.

Formula

The calculator uses the gear ratio to find wheel revolutions per minute, then multiplies by the wheel’s rolling circumference:

Speed (km/h) = cadence × (chainring teeth ÷ rear sprocket teeth) × π × wheel diameter (mm) × 60 ÷ 1,000,000

• Cadence is crank revolutions per minute (rpm).
• Chainring teeth is the number of teeth on the front chainring.
• Rear sprocket teeth is the number of teeth on the selected rear cog.
• Wheel diameter is the effective rolling diameter in millimetres. The circumference is approximated as π times diameter.
• Gear ratio is chainring teeth divided by rear sprocket teeth. It is dimensionless, shown as a ratio to one.
• The factor 60 converts minutes to hours, and 1,000,000 converts millimetres per hour to kilometres per hour.

To convert km/h to mph, multiply by 0.621371. The result is a theoretical speed, not a measurement of actual speed.

Worked Example

Using the calculator’s defaults—50 teeth at the front, 17 at the rear, a 700 mm wheel diameter, and 80 rpm:

1. Gear ratio = 50 ÷ 17 = 2.941176…, displayed as 2.94:1.
2. Wheel circumference ≈ π × 700 mm = 2,199.11 mm, or 2.19911 m.
3. Wheel revolutions per minute = 80 × (50 ÷ 17) = 235.2941 rpm.
4. Speed = 235.2941 × 2.19911 × 60 ÷ 1,000 = 31.045… km/h, displayed as 31.05 km/h.
5. In mph, 31.045… × 0.621371 = 19.29… mph, displayed as 19.29 mph.

Small differences can appear if you use a measured tire rollout instead of the diameter-based circumference approximation.

How Gear Ratio Becomes Speed

Each full crank revolution advances the chain by a length determined by the front chainring. The rear sprocket turns once for each corresponding length of chain that passes over it. For example, a 50-tooth chainring driving a 17-tooth sprocket turns the rear wheel about 50 ÷ 17, or 2.94 times, per crank revolution, assuming a conventional direct-drive bicycle hub.

At a fixed cadence, a larger front chainring or smaller rear sprocket raises the gear ratio and increases theoretical speed. A smaller front ring or larger rear cog lowers the ratio. But a higher ratio also requires more force at the pedals to accelerate or climb; it does not make a rider faster by itself. Real speed depends on how much power the rider can sustain and on conditions such as wind, gradient, tire pressure, and road surface.

Choosing Accurate Inputs

Count the teeth on the chainring and the rear cog actually being used. On a multi-speed bicycle, changing gears changes the rear sprocket value, so there is no single speed estimate for the whole bike. Cadence is crank rpm, not wheel rpm; a bike computer or cadence sensor may report it, or a rider can count crank revolutions for a timed interval.

Wheel labels such as 700C or 26 inches refer to tire and rim sizing conventions, not necessarily the exact outside diameter. Tire width and casing affect the mounted diameter. For a better estimate, measure rolling circumference directly: mark the tire and ground, roll the loaded bike straight for one full wheel revolution, and measure the distance. Convert that circumference into diameter by dividing by π if you want to use this calculator’s diameter input. Use millimetres: 2,100 mm is 2.1 m, not 2,100 m.

• Use teeth, not chainring or sprocket diameter.
• Enter cadence in rpm; do not enter seconds per crank revolution.
• Enter wheel diameter in millimetres, measured consistently with the mounted tire.
• For a more exact calculation, use the tire’s measured rolling circumference in place of π times diameter.

Interpreting the Estimate and Its Limits

The estimate assumes each crank turn produces the stated gear ratio and that the tire’s effective circumference stays constant. It does not account for wheel slip, tire deformation, drivetrain wear, shifting interruptions, or changes in cadence. It also cannot predict a rider’s sustainable pace. A speedometer or GPS device measures movement more directly; compare the calculator result with a steady, level-road reading to see whether your input assumptions are plausible.

Rounding matters most when comparing nearby setups. Tooth counts are whole numbers, while the effective wheel circumference is approximate. Treat results such as 31.05 km/h as a useful estimate, not precision to hundredths in real riding. In customary units, wheel diameter can be entered only after converting it to millimetres; the calculator reports mph alongside km/h for easier comparison.

Frequently Asked Questions

How do I calculate bike speed from cadence and gear ratio?
Multiply cadence in rpm by the gear ratio to get wheel rpm, then multiply by wheel circumference to get distance per minute. Convert that distance to km/h or mph. The calculator combines those steps.

Does a higher gear ratio always make me go faster?
It gives more wheel rotation per crank revolution, so it yields a higher theoretical speed at the same cadence. It does not guarantee a higher real speed because the rider must produce enough force and power to maintain that cadence.

What does a 50/17 gear ratio mean?
It means 50 chainring teeth divided by 17 rear sprocket teeth, or about 2.94 wheel revolutions per crank revolution on a conventional direct-drive setup.

Can I use wheel size marked on the tire?
Use it as a rough guide, but the printed size does not always equal the mounted tire’s exact outside diameter. A rolling-circumference measurement gives a more representative estimate.

Why is my actual speed different from the calculator?
Cadence, tire circumference, wind, slope, surface, tire pressure, and drivetrain losses can all differ from the assumptions. The formula estimates speed for the entered values; it does not measure road speed.

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in chainring | Chainring teeth | teeth | 50 | 1
in sprocket | Rear sprocket teeth | teeth | 17 | 1
in wheel | Wheel diameter | mm | 700 | 1
in cadence | Cadence | rpm | 80 | 0
out speed | Estimated speed | km/h | cadence * chainring / sprocket * pi * wheel / 1000000 * 60 | 2
out mph | Estimated speed | mph | speed * 0.621371 | 2
out ratio | Gear ratio | :1 | chainring / sprocket | 2