How this calculator works
A crank turn pulls the chain by the number of chainring teeth and turns the rear wheel by the same number of chain links divided by the cog teeth. That is the gear ratio. One revolution therefore moves the bike by the gear ratio times the wheel circumference. Cadence is crank revolutions per minute, so multiplying by cadence and dividing by 60 gives road speed. The wheel circumference here uses an estimate: the rim diameter plus twice the tyre width. Real tyres vary with casing, tread and pressure, and a loaded tyre compresses slightly, so the speed shown is a close guide rather than a measured value.
Formula
Wheel diameter = rim diameter + 2 x tyre width. Gear ratio = chainring teeth / cog teeth. Development = gear ratio x pi x wheel diameter. Speed = cadence / 60 x development. Gear inches = gear ratio x wheel diameter in inches. Working back, cadence = speed / development x 60.
Worked example
A 700c rim is 622 mm and a 25 mm tyre makes the wheel 672 mm across, with a circumference of 2.111 m. A 50-tooth chainring and 16-tooth cog give a ratio of 3.125 and development of 6.597 m per turn. At 90 rpm the speed is 1.5 turns per second x 6.597 m = 9.895 m/s, or 35.6 km/h. The same gear needs about 63 rpm to hold 25 km/h.
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Frequently asked questions
Why does the tyre size change the answer?
A larger outer diameter covers more ground per wheel turn, so the same cadence produces a higher speed. A 25 mm tyre on a 622 mm rim is about 50 mm larger across than the bare rim.
What cadence should I aim for?
Many riders settle between 80 and 100 rpm on flat roads, using a lower cadence for steep climbs and a higher one for sprints or descents. The right value depends on fitness, gearing and terrain rather than a single target.
Does this match my bike computer?
Close, but not exactly. Tyre pressure, load, tread and the way wheel size is measured all shift the true circumference by a few millimetres. Measure a loaded wheel by rolling it one turn and dividing the distance by pi if you need precision.