Bicycle Gear Speed Calculator and Gear Ratio Guide

A bicycle gear speed calculator estimates how fast a bike travels at a chosen cadence in a particular gear. Enter wheel circumference, front and rear tooth counts, and cadence; the calculator returns speed in kilometres per hour and miles per hour, plus the gear ratio and distance travelled per crank revolution.

Formula

For a conventional chain-driven bicycle, the front chainring turns the rear wheel through the ratio of front teeth to rear sprocket teeth. At a given cadence, speed is the wheel’s distance per revolution multiplied by wheel revolutions per minute, then converted to distance per hour.

• Gear ratio: G = F / R, where F is front chainring teeth and R is rear sprocket teeth. This is a unitless ratio.
• Distance per crank revolution: D = C × F / R, where C is rolling wheel circumference in metres. D is metres per crank revolution.
• Speed: V = C × (F / R) × N × 60 / 1,000, where N is cadence in revolutions per minute (rpm). V is kilometres per hour (km/h).
• Miles per hour: V_mph = V / 1.609344. One international mile is exactly 1.609344 kilometres.

The calculator’s circumference input is in metres, so use a measured metric value or convert inches by multiplying by 0.0254. Tooth counts and cadence are entered as numbers; cadence is crank revolutions per minute, not pedal strokes per minute for one leg.

Worked Example

Using the calculator’s defaults—C = 2.105 m, F = 50 teeth, R = 17 teeth, and N = 90 rpm:

1. Gear ratio: 50 / 17 = 2.9412, which displays as 2.94.
2. Distance per crank revolution: 2.105 × 50 / 17 = 6.1912 m, which displays as 6.19 m.
3. Wheel revolutions per minute: 90 × 50 / 17 = 264.7059 rpm.
4. Speed: 2.105 × 50 / 17 × 90 × 60 / 1,000 = 22.2882 km/h, which displays as 22.29 km/h.
5. Convert to miles per hour: 22.2882 / 1.609344 = 13.8529 mph, which displays as 13.85 mph.

These are theoretical speeds for steady cadence and wheel rotation. They describe the gear’s mathematical relationship, not a promise that a rider can maintain that pace on the road.

How to Use the Calculator

• Find the front chainring count. Count the teeth on the chainring connected to the crank. A two- or three-chainring bike has a separate value for each ring.
• Find the rear sprocket count. Count teeth on the selected sprocket, or check reliable component specifications. The smallest rear sprocket generally gives a higher gear; the largest gives a lower gear.
• Enter wheel circumference. The most useful value is the actual rolling circumference with the tyre at riding pressure and the rider’s weight on the bike. A nominal wheel size is only an approximation.
• Enter cadence. Use the crank’s revolutions per minute. For example, 80 rpm means the crank makes 80 full turns in one minute.

Change one input at a time to compare combinations. At the same cadence and wheel size, a larger front ring raises speed, while a larger rear sprocket lowers it. Doubling cadence doubles the calculated speed, provided the gear and wheel remain unchanged.

Getting an Accurate Wheel Circumference

Tyre labels and wheel-size names do not uniquely determine rolling circumference. Tyre width, construction, pressure, rim dimensions, and load all affect the effective distance per wheel turn. For a practical measurement, mark the tyre and ground at the contact point, sit on the bike with help if needed, roll one complete wheel revolution in a straight line, and measure the distance between the marks. Repeat for consistency. Measure in millimetres if convenient, then divide by 1,000 to enter metres.

If you cannot measure, use a published circumference value for the precise tyre and wheel combination as a starting estimate. A circumference error of 1% produces about a 1% speed error. The calculator’s default of 2.105 m is a plausible example, not a universal value for every bicycle.

Reading Gear Ratios and Comparing Gears

A ratio above 1 means the wheel turns more than once per crank revolution in a simple chain drive; below 1, it turns less than once. For example, a 50-tooth chainring with a 25-tooth sprocket has a 2.00 ratio. A 34-tooth chainring with a 34-tooth sprocket has a 1.00 ratio. With the same wheel and cadence, the first setup travels twice as far per crank turn as the second.

Gear inches and development are other ways to compare bicycle gearing. Gear inches are commonly calculated from wheel diameter multiplied by the gear ratio, with diameter expressed in inches. Development is distance travelled per crank revolution, as calculated here. These figures help compare gearing across wheel sizes: two bikes with the same tooth ratio can have different development if their rolling circumferences differ. Gear inches are a comparison convention, not a direct speed measurement; cadence is still needed to calculate speed.

Limits and Common Mistakes

• Confusing cadence with wheel rpm: Cadence describes crank rotation. Multiply it by the gear ratio to estimate wheel rpm.
• Reversing the tooth counts: Use front teeth divided by rear teeth. Reversing them predicts the wrong direction of the gearing effect.
• Mixing units: The calculator expects circumference in metres. Entering millimetres without conversion makes the result 1,000 times too large; entering inches as metres also gives a major error.
• Expecting road speed: Wind, slope, acceleration, tyre deformation, drivetrain condition, and rider effort affect actual speed. The formula does not model them.
• Rounding intermediate values: Keep the full circumference and tooth-count calculation until the final display. Rounding the ratio early can slightly change the result.

The calculation applies to a conventional chain-and-sprocket drive. Internal-gear hubs and continuously variable transmissions need their internal ratios to be included; front and rear tooth counts alone may not describe the selected gear. It also estimates speed without accounting for gear shifting under load or mechanical losses.

Frequently Asked Questions

How fast is a bicycle in a particular gear?
It depends on wheel circumference, front and rear tooth counts, and cadence. Enter those values to calculate theoretical speed; changing cadence or either sprocket changes the result.

What is a good bicycle cadence for this calculation?
There is no single cadence that applies to every rider or situation. Use the cadence you want to evaluate, or measure your own while riding; the calculator converts any entered rpm into an estimated speed.

Does a larger front chainring make a bike faster?
At the same rear sprocket and cadence, yes: it increases distance travelled per crank revolution. It does not guarantee a higher real-world speed, which also depends on the rider, terrain, and conditions.

How do I calculate bicycle speed without a calculator?
Multiply wheel circumference in metres by front teeth divided by rear teeth, then by cadence in rpm and 60; divide by 1,000 for km/h. Divide km/h by 1.609344 for mph.

Why does my calculated speed differ from my cycling computer?
The computer may use a different wheel circumference, while actual cadence or speed may vary during the ride. Check the computer’s circumference setting and compare measurements on a steady, level stretch; the calculator gives an estimate for the exact inputs you provide.

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in c | Wheel circumference | m | 2.105 | 0
in f | Front chainring teeth | teeth | 50 | 0
in r | Rear sprocket teeth | teeth | 17 | 0
in n | Cadence | rpm | 90 | 0
out k | Speed | km/h | c * f / r * n * 60 / 1000 | 2
out m | Speed | mph | c * f / r * n * 60 / 1000 / 1.609344 | 2
out g | Gear ratio | ratio | f / r | 2
out d | Distance per crank revolution | m/rev | c * f / r | 2