Bike Gearing Speed Calculator: Cadence to Speed

A bike gearing speed calculator estimates how fast a bicycle travels from its gear ratio, wheel circumference, and pedaling cadence. Enter the front and rear tooth counts, wheel circumference in millimetres, and cadence in revolutions per minute to get speed in kilometres per hour and miles per hour.

Formula

The calculator uses the selected gear ratio and the distance travelled for each wheel revolution to estimate speed:

Speed (km/h) = (front teeth ÷ rear teeth) × wheel circumference (mm) × cadence (rpm) × 60 ÷ 1,000,000.

• Front: number of teeth on the chainring the chain is using, in teeth.
• Rear: number of teeth on the sprocket the chain is using, in teeth.
• Wheel circumference: distance travelled in one wheel revolution, in millimetres.
• Cadence: crank revolutions per minute, or rpm.
• 60: converts minutes to hours; 1,000,000 converts millimetres to kilometres.

The other outputs convert kilometres per hour to miles per hour and calculate rollout: distance travelled for one complete crank revolution. For miles, the conversion is 1 mile = 1.609344 kilometres. The formula assumes the rear wheel turns once per wheel revolution and that the drivetrain has no slip.

Worked Example

Using the calculator’s defaults—50 teeth at the front, 17 at the rear, a 2,100 mm wheel circumference, and 90 rpm:

1. Gear ratio = 50 ÷ 17 = 2.941176…
2. Distance per crank revolution = 2.941176… × 2,100 mm = 6,176.47 mm, or 6.176 m.
3. Speed = 6,176.47 mm/revolution × 90 revolutions/minute × 60 minutes/hour ÷ 1,000,000 mm/km = 33.3529… km/h.
4. Rounded to two decimal places, speed is 33.35 km/h. In miles per hour, that is 33.3529… ÷ 1.609344 = 20.72 mph. Rollout rounded to three decimal places is 6.176 m.

What the Result Means

The answer is a theoretical speed at the cadence you entered, in the particular front and rear gear selected. A larger front chainring or smaller rear sprocket increases the gear ratio, so each crank revolution turns the wheel farther. At the same cadence, that means more speed. A smaller front ring or larger rear sprocket reduces the distance per crank turn and makes it easier to pedal uphill or accelerate at a low speed.

Cadence matters just as much as gear choice: if cadence doubles while the gear and wheel remain unchanged, the calculated speed doubles. This is a mathematical relationship, not a prediction that a rider can sustain that cadence or speed on a particular road. Wind, gradient, surface, tire pressure, load, and rider effort affect real-world speed but are not inputs to this calculation.

How to Measure Wheel Circumference

Wheel circumference is the distance the tire rolls in one complete turn. A nominal wheel size printed on a tire or described by a bicycle’s sizing system is not always an exact rolling circumference: tire width, tire model, pressure, and rim dimensions can change the actual measurement.

For a useful estimate, mark the tire and the ground at the same point, sit on the bike to compress the tire as it would be under riding load, and roll straight for one full wheel revolution. Measure the distance between the marks. If you measure in centimetres, multiply by 10 to enter millimetres; if you measure in inches, multiply by 25.4. Measuring over several wheel turns and dividing the total distance by the number of turns can reduce the effect of marking error.

When This Calculator Is Useful

• Compare gears: enter different chainring and sprocket tooth counts to see how much speed or rollout changes at the same cadence.
• Estimate cadence: if you know a speed and gear, rearrange the formula to estimate the cadence needed to achieve that speed.
• Understand gear range: compare the easiest and hardest available combinations to see how far a bike travels per crank revolution in each.
• Plan cadence-based riding: explore how changing cadence affects theoretical speed without changing gears.

To estimate cadence from a known speed, rearrange the equation: cadence (rpm) = speed (km/h) × 1,000,000 ÷ [(front ÷ rear) × circumference (mm) × 60]. The result remains an estimate if the speed, wheel circumference, or gear selection is approximate.

Common Errors and Limits

• Mixing units: the circumference field requires millimetres. Entering 2.1 for a 2.1 m circumference instead of 2,100 makes the result 1,000 times too low.
• Using the wrong teeth: count the chainring and rear sprocket currently engaged, not the total number of gears on the cassette.
• Confusing cadence with wheel rpm: cadence is crank turns per minute. The gear ratio converts crank rotations to wheel rotations.
• Assuming a precise real-world speed: displayed decimals reflect arithmetic, not measurement accuracy. An approximate circumference or cadence cannot support a more precise practical estimate.
• Ignoring drivetrain setup: the formula describes a conventional chain-driven bicycle. It does not model drivetrain losses, unusual transmission systems, tire deformation, or wheel slip.

Gear ratio alone does not tell you how fast a bike will go: cadence and wheel circumference are also required. Nor does a higher gear automatically make a rider faster. It increases distance per pedal revolution, but may be harder to turn; the speed achieved depends on whether the rider can maintain the needed cadence and effort.

Frequently Asked Questions

How do I calculate bike speed from gearing and cadence?
Divide the front chainring teeth by the rear sprocket teeth, multiply by wheel circumference and cadence, then convert units. With circumference in millimetres, multiply by 60 and divide by 1,000,000 to get km/h.

What wheel circumference should I enter?
Enter the measured rolling distance for one wheel revolution in millimetres. A direct roll-out measurement is generally more useful than relying on a nominal wheel diameter or size label.

Does a bigger chainring make a bike faster?
At the same rear sprocket, wheel circumference, and cadence, a bigger chainring raises the calculated speed because it increases the gear ratio. It does not guarantee a higher actual speed, since it can also make the pedals harder to turn.

Why does my actual speed differ from the calculator?
The result assumes a known, steady cadence and wheel circumference. Measurement errors and changing cadence matter, while wind, slope, rolling resistance, and rider power affect actual speed but are outside the formula.

Can I calculate cadence from speed and gearing?
Yes. Rearrange the formula to solve for cadence, using speed in km/h, circumference in millimetres, and the same front and rear tooth counts. The result estimates cadence for that speed and gear.

Related

• 1 Mile Time Calculator: Pace, Speed, and Finish Time
• 10 Mile Marathon Time Calculator and Pace Formula
• Bike Cadence Calculator

in front | Front chainring teeth | teeth | 50 | 0
in rear | Rear sprocket teeth | teeth | 17 | 0
in wheel | Wheel circumference | mm | 2100 | 0
in cadence | Cadence | rpm | 90 | 0
out speed | Speed | km/h | front / rear * wheel * cadence * 60 / 1000000 | 2
out mph | Speed | mph | speed / 1.609344 | 2
out rollout | Distance per crank revolution | m | front / rear * wheel / 1000 | 3