A bike gear ratio calculator tabulates every chainring and sprocket combination on a drivetrain and expresses each one in the units cyclists actually use — gear inches, development metres and gain ratio — so you can see the whole range at once, spot the duplicated gears and judge the size of the jumps between them.
Arb Digital publishes a free tools library, and two boundaries here are worth stating explicitly. Our gear ratio calculator is a mechanical engineering tool: tooth counts or diameters across up to three gear stages, returning overall ratio, output speed and output torque for a gearbox or machine drive. Bicycle gearing is a different job. A bike's output is not a shaft speed but a road speed, which depends on wheel size, and the conventional bicycle units — gear inches and development — exist precisely because a raw ratio tells a cyclist nothing without the wheel. This page is bicycle-specific and says nothing about torque.
The second boundary is with our own bike speed and cadence calculator. That one solves a single pair: one gear, one cadence, one speed, in either direction. This page never solves for a speed. It tabulates the whole gear range so you can compare a drivetrain against itself or against another. If you want to know how fast one gear goes at 90 rpm, that is the other tool.
What This Bike Gear Calculator Does
It takes three inputs — chainrings, sprockets and wheel roll-out — and produces the full grid of combinations in whichever unit you select.
Gear inches is the traditional English-speaking unit and is the diameter, in inches, that a direct-drive penny-farthing wheel would need to be in order to travel the same distance per pedal revolution. Typical road bike gears run from the low thirties to about 120.
Development is the metric equivalent: the distance in metres the bike travels for one full turn of the cranks. Typical values run from about 2.5 to nearly 10 metres.
Gain ratio is Sheldon Brown's dimensionless system, which divides wheel radius by crank length before applying the sprocket ratio, so it accounts for the leverage your cranks give you. It is the only one of the three that changes if you fit different length cranks.
Alongside the table the page reports the range, the largest percentage step between adjacent gears, and how many genuinely distinct gears remain once near-duplicates are collapsed.
How to Use It
- List every sprocket, not just the ends. A cassette described as 11-28 has nine sprockets in between, and the steps between them are the whole point.
- Measure your roll-out rather than looking it up. Tyre width, tread depth, pressure and rider weight all change the effective circumference, and a table value can be a couple of per cent out.
- Pick the unit your riding group uses. Gear inches and development describe exactly the same thing; only the number differs.
- Set the duplicate threshold to something honest. Three per cent is roughly the smallest difference a rider notices under load. Anything closer than that is the same gear reached two ways.
- Compare setups by their bottom gear first. The lowest number decides what you can climb, and it is the change most people actually need.
The Formula: How Bicycle Gearing Is Calculated
Plain ratio. ratio = chainring teeth ÷ sprocket teeth. This is how many turns the rear wheel makes per turn of the cranks, and on its own it is not comparable between bikes with different wheels.
Gear inches. gear inches = ratio × wheel diameter in inches, where diameter is derived from your measured roll-out as circumference ÷ π, converted at 25.4 mm per inch. As Sheldon Brown's bicycle glossary entry for gear inches puts it, the figure is the equivalent diameter of the drive wheel on a high-wheel bicycle.
Development. development = ratio × wheel circumference in metres. Since gear inches uses diameter and development uses circumference, the two differ by a factor of π and a unit conversion, and they carry exactly the same information.
Gain ratio. gain = (wheel radius ÷ crank length) × ratio, both lengths in the same unit. Brown's article introducing gain ratios as a new way to designate bicycle gears argues that it is the only system giving a true value for relative leverage across bikes with different wheel and crank sizes, because it is the distance the bike travels for each unit the pedal travels in its orbit. All the unit conversions follow the definitions published by NIST in its SI units material.
Worked example, matching the values this page loads with. A 2,111 mm roll-out gives a wheel diameter of 2,111 ÷ π = 671.9 mm, which is 26.45 inches. The top gear, 50 × 11, has a ratio of 4.545, so gear inches are 4.545 × 26.45 = 120.2, and development is 4.545 × 2.111 = 9.60 m. The bottom gear, 34 × 28, has a ratio of 1.214, giving 32.1 gear inches and 2.56 m. The range is 120.2 ÷ 32.1 = 3.74 to one, and with 172.5 mm cranks the gain ratio of the top gear is (335.9 ÷ 172.5) × 4.545 = 8.85.
Why a 22-Speed Does Not Have 22 Gears
A double chainring and an eleven-sprocket cassette is sold as a 22-speed, and it never has twenty-two distinct gears.
The reason is that both chainrings sweep overlapping ranges. In the default setup, 50 × 21 gives a ratio of 2.381 and 34 × 14 gives 2.429 — a difference of two per cent, which no rider can feel. Across the whole grid, a typical road double duplicates enough combinations that the genuinely distinct count often falls to fourteen or sixteen.
That is not a design flaw. The overlap is what makes the front shift usable: it means you can change chainring mid-climb and find a similar gear rather than an enormous jump. But it does mean the marketing number and the useful number are different, and the duplicate-flagging on this page is there to show you which.
It also explains the rise of one-by drivetrains. A single ring with a very wide cassette gives fewer nominal speeds but almost no duplication, so a nominal 12-speed can offer more distinct gears than a nominal 22-speed — at the cost of much larger steps between them.
Range and Steps Are Two Different Problems
Every gearing decision is a trade-off between how wide the range is and how closely spaced the gears are, and you cannot improve both without adding sprockets.
Range is the ratio of the highest gear to the lowest, and it decides what terrain you can cover. A 3.7 range is a typical road double. A gravel or mountain setup with a wide one-by cassette often exceeds 5. Range is what you need for steep climbs and fast descents on the same ride.
Step size is the percentage jump between adjacent gears, and it decides whether you can hold a comfortable cadence. Steps of five to eight per cent feel smooth; steps above fifteen per cent force a noticeable change in effort or cadence at every shift, which matters most when riding hard in a group on flat ground.
With a fixed number of sprockets, widening the range necessarily widens the steps. This is the entire reason racing cassettes are close-ratio and touring cassettes are not, and why adding sprockets — going from ten to eleven to twelve — is worth paying for even when the range does not change.
Cross-Chaining and the Gears You Should Not Use
The table shows every mathematically possible combination, and a few of them should not be ridden.
Running the large chainring with the largest sprocket, or the small ring with the smallest, puts a severe lateral angle on the chain. That increases friction, accelerates wear on both chain and sprockets, and on some setups causes the chain to rub the front derailleur cage. The gears at those extremes are also almost always duplicated elsewhere in the grid at a better chain line, so nothing is lost by avoiding them.
The practical rule most riders use is to stay off the two or three largest sprockets when in the big ring and the two or three smallest when in the small ring. If you find yourself needing a cross-chained gear regularly, the gearing is wrong for the terrain rather than the shifting being wrong.
If you want to see what any single one of these gears does at a given cadence, the bike speed and cadence calculator handles that. For the effort side of a ride, our cycling calorie calculator, cycling pace calculator and e-bike range calculator cover energy, pacing and battery range.
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
- Comparing raw ratios between bikes with different wheels — a 2.5 ratio on a 700c wheel and on a 26-inch wheel are different gears, which is exactly why gear inches exists.
- Using a nominal tyre circumference — width, tread, pressure and rider weight all change roll-out, and a measured figure is worth the two minutes it takes.
- Counting the marketing speed count as distinct gears — overlapping chainrings duplicate a large fraction of the grid.
- Optimising range while ignoring step size — a wide range on a fixed sprocket count means bigger jumps, and jumps are what you feel on every shift.
- Planning to use the cross-chained extremes — they wear the drivetrain, and they duplicate gears available at a better chain line.
- Changing the chainring when the problem is the cassette — the bottom gear is usually easier and cheaper to lower at the back.
Related Free Tools From Arb Digital
The bike speed and cadence calculator solves one gear, one cadence and one speed rather than tabulating the range, and the gear ratio calculator handles mechanical gear trains, output speed and torque for machinery rather than bicycles. The cycling pace calculator, cycling calorie calculator and e-bike range calculator cover the rest of a ride. Everything else is in the free online tools hub.
Frequently Asked Questions
That tool is for mechanical gear trains: tooth counts or diameters across up to three stages, returning overall ratio, output speed and output torque for a gearbox or machine. Bicycle gearing is a different job, because a bike's output is road speed rather than shaft speed and therefore depends on wheel size. This page works in gear inches, development and gain ratio, and says nothing about torque.
That one solves a single pair — one gear, one cadence, one speed — in either direction. This page never solves for a speed. It tabulates every chainring and sprocket combination on the drivetrain so you can compare the whole range, find the duplicates and measure the steps.
The diameter in inches that a direct-drive penny-farthing wheel would need in order to travel the same distance per pedal revolution as your geared bike. It is the chainring divided by the sprocket, multiplied by the wheel diameter. Typical road gears run from the low thirties to about 120.
Development is the distance in metres the bike travels for one full turn of the cranks. It uses wheel circumference where gear inches uses diameter, so the two differ only by a factor of pi and a unit conversion, and they carry identical information. Typical values run from about 2.5 to nearly 10 metres.
Because both chainrings sweep overlapping ranges, so many combinations land within a couple of per cent of each other and are effectively the same gear. A typical road double often has only fourteen to sixteen genuinely distinct gears. The overlap is deliberate — it is what makes a front shift find a usable gear rather than an enormous jump.
Mark the tyre and the ground, sit on the bike at your normal pressure, roll forward exactly one wheel revolution, and measure between the marks. That accounts for tyre width, tread and the compression under your weight, all of which a lookup table misses by a per cent or two.
It divides wheel radius by crank length and multiplies by the sprocket ratio, giving a dimensionless number that says how far the bike travels for each unit the pedal travels in its orbit. It is the only one of the three systems that accounts for crank length, so it is the fair way to compare bikes with different cranks or wheel sizes.
