A bike speed and cadence calculator connects three quantities that are locked together by geometry: the gear you are in, how fast you turn the pedals, and how fast the bike goes. Fix any two and the third is determined. There is no physics in it beyond the size of your wheel — which is exactly why it is worth having, because it turns a vague sense of "this gear feels too big" into a number.
Arb Digital publishes a free tools library, and this page is deliberately narrow. Our bike gear ratio calculator tabulates every chainring and sprocket combination on a drivetrain in gear inches, development and gain ratio, and it never solves for a speed. This page does the opposite: one gear at a time, solved in either direction against a cadence or a speed. Use the other one to compare a whole drivetrain; use this one to answer a question about a specific gear.
What This Speed and Cadence Calculator Does
In its default direction it answers: in this gear, at this cadence, how fast am I going? Flip the selector and it answers the inverse: to hold this speed in this gear, what cadence would I have to turn?
Both come from the same chain of quantities. The gear ratio says how many wheel turns you get per crank turn. The wheel roll-out says how far the bike travels per wheel turn. Multiply those and you have development — the metres covered per crank revolution. Multiply that by cadence and you have speed.
Alongside the answer the page reports the development, the plain ratio, the speed in the opposite unit, and the cadence that would be required for a target speed you set — so the two directions are always visible at once rather than requiring a mode switch to compare.
There is also an optional slip allowance. Left at zero it gives the pure geometric answer, which is what most calculators show. Real tyres deform under torque and load, so measured speed is marginally lower than the geometry predicts, and the allowance lets you account for that if you are reconciling a calculation against a computer reading.
How to Use It
- Enter the actual gear. Not the biggest ring and smallest cog, but the one you were in when the question arose.
- Measure your roll-out. Mark the tyre, sit on the bike, roll one full wheel revolution, measure the ground. Tyre width, tread, pressure and your weight all move it.
- Use a cadence you can actually hold. The number is only useful if it corresponds to something sustainable, and a calculation at 130 rpm describes a sprint rather than a ride.
- Flip the mode to test a gear choice. If you know what speed a climb or a descent demands, solving backwards tells you immediately whether the gear you have is usable.
- Compare across a few cadences. The bars show the same gear at four cadences, which is often more informative than any single number.
The Formula: How Speed From Cadence Is Calculated
Gear ratio. ratio = chainring teeth ÷ sprocket teeth, which is wheel revolutions per crank revolution.
Development. development = ratio × wheel circumference, in metres per crank revolution. This is the same quantity Sheldon Brown's article on gain ratios as a new way to designate bicycle gears describes as the distance the bicycle moves with each revolution of the pedals.
Speed. speed = development × cadence gives metres per minute. Multiply by 60 and divide by 1,000 for kilometres per hour, or divide the metres per minute by 26.8224 for miles per hour, using the exact conversions in the SI units reference published by NIST.
Cadence from speed. Rearranged, cadence = speed in metres per minute ÷ development.
Worked example, matching the values this page loads with. A 50-tooth ring and an 11-tooth sprocket give a ratio of 50 ÷ 11 = 4.5455. With a 2,111 mm roll-out, development is 4.5455 × 2.111 = 9.596 metres per crank turn. At 90 rpm that is 9.596 × 90 = 863.6 metres per minute, which is 863.6 × 60 ÷ 1,000 = 51.82 km/h, or 32.20 mph. Solving backwards for a 35 km/h target: 35 km/h is 583.3 metres per minute, so the required cadence is 583.3 ÷ 9.596 = 60.8 rpm — which tells you immediately that 50 × 11 is far too big a gear for cruising at 35.
Why Cadence Is a Choice and Speed Is Not
The relationship on this page is linear and exact, which makes it easy to misread as a statement about effort. It is not.
Holding a speed requires a certain power output, set by aerodynamic drag, rolling resistance and gradient. That power can be delivered as a high force at a low cadence or a lower force at a high cadence, and the gear you choose decides which. The calculator tells you what combination produces a given speed; it says nothing about which combination you can sustain.
That trade-off has real physiological consequences. Low cadence means high pedal force, which loads the muscles more and recruits fast-twitch fibres sooner. High cadence means lower force but a higher metabolic and cardiovascular cost from the sheer number of contractions. Most riders self-select a cadence somewhere in the middle, and where that lands varies substantially between individuals and between disciplines — track, road, time trial and mountain biking all pull it in different directions.
The practical use of this calculator is not to find an optimal cadence. It is to check whether a gear exists that lets you ride at the speed you want at a cadence you like. If the answer comes out at 55 rpm or 120 rpm, the gearing is the problem.
Why Your Bike Computer Disagrees
Calculate a speed here, ride the same gear at the same cadence, and the computer will usually read slightly lower. Several things explain the gap.
Roll-out is not a constant. A tyre compresses under load and deforms further under drive torque, so the effective circumference is a little less than a free-rolling measurement, and it falls further as pressure drops or weight increases.
Cadence sensors average. A computer reports a smoothed figure over a few seconds, so a momentarily higher instantaneous cadence does not show.
Wheel sensors use a stored circumference. If that value was entered from a table rather than measured, every speed reading inherits the error — and so does every distance.
GPS is a different measurement entirely. A GPS speed comes from position over time, with its own error, and it will not match a wheel sensor exactly on a twisting road.
None of these are large. Together they typically account for one to three per cent, which is what the optional slip allowance on this page is for.
Choosing Gears for Real Situations
Solved backwards, this calculation answers most practical gearing questions faster than any amount of discussion.
Can I spin out on a descent? Enter your highest gear and a cadence you consider your ceiling — say 110 rpm — and read the speed. If it is below the speed of your regular descents, you are coasting rather than pedalling on them, and a larger top gear would help.
Is my bottom gear low enough? Enter your lowest gear and the slowest speed at which you can stay upright, perhaps 6 km/h, and read the cadence. If it comes out below about 60 rpm, that climb will be a grind rather than a spin.
What happens if I change one sprocket? Change the cog and watch the speed shift. It is the cheapest way to test a gearing change before buying anything.
For the wider ride picture, our cycling pace calculator covers pace and time over a route, the cycling calorie calculator estimates energy cost, and the e-bike range calculator handles battery range. The speed converter switches between units on its own.
Arb Digital builds fast, dependency-free calculators and interactive tools that load instantly, rank in search and keep visitors reading.
Browse the Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using a nominal wheel size instead of a measured roll-out — the error goes straight into the speed and into every distance a wheel sensor records.
- Reading the result as an effort level — the relationship is pure geometry, and the power needed to hold a speed depends on drag, gradient and rolling resistance, none of which appear here.
- Calculating at a cadence you cannot sustain — a figure at 130 rpm describes a sprint, not a ride.
- Expecting an exact match with a bike computer — tyre deformation, sensor smoothing and stored circumference values account for one to three per cent.
- Comparing gears between bikes by ratio alone — different wheel sizes make the same ratio a different gear, which is what development and gear inches exist to fix.
Related Free Tools From Arb Digital
The bike gear ratio calculator lays out the whole drivetrain in gear inches and development rather than solving one gear, and the gear ratio calculator covers mechanical gear trains and torque for machinery. The cycling pace calculator, cycling calorie calculator and e-bike range calculator cover pacing, energy and range, and the speed converter handles units. Everything else is in the free online tools hub.
Frequently Asked Questions
That page tabulates every chainring and sprocket combination on the drivetrain in gear inches, development and gain ratio, so you can compare a whole gearing setup. It never solves for a speed. This page takes one gear and solves it against a cadence or a target speed in either direction.
Multiply the chainring teeth by the wheel circumference and divide by the sprocket teeth to get development, the metres travelled per crank revolution. Multiply that by cadence for metres per minute, then by 60 and divided by 1,000 for kilometres per hour.
That is an individual question rather than an arithmetic one. Most riders self-select somewhere between 70 and 100 rpm on the flat, and the best figure varies with discipline, muscle characteristics and how long the effort lasts. What this calculator is good for is checking whether a gear exists that lets you ride the speed you want at a cadence you find comfortable.
Tyres compress under load and deform further under drive torque, so effective roll-out is slightly less than a free-rolling measurement. Cadence sensors also report a smoothed average, and a computer using a stored circumference from a table inherits that value's error. Together these usually account for one to three per cent.
Only if you can turn it at the same cadence, which is a question about power rather than gearing. A bigger gear at the same cadence is a higher speed and a higher power demand. If the power is not there, the cadence falls and the speed does not rise as much as the arithmetic suggests.
Enter your largest chainring with your smallest sprocket, set the cadence to the highest you can sustain in control, and read the speed. If that speed is below what you typically reach on descents, you are freewheeling rather than pedalling and a taller top gear would add something.
Yes, and it is why raw ratios are not comparable between bikes. The same 4.5 ratio on a 700c road wheel and on a smaller wheel produces meaningfully different speeds at the same cadence, because speed is proportional to circumference. That is exactly why cyclists quote development and gear inches rather than the ratio.
