Bike gear calculator

Gear inches, development, gain ratio and speed: what each number means

A bike gear is just a ratio: chainring teeth divided by sprocket teeth. A 50-tooth ring driving an 11-tooth sprocket turns the back wheel 4.55 times for each turn of the pedals. The four numbers in the chart turn that ratio into something you can feel on the road.

• Gear inches multiply the ratio by the wheel’s diameter in inches. It’s the old penny-farthing measure (the size of a directly driven wheel that would feel the same), and it’s still the most common way to compare gears. Big numbers are hard, fast gears; small numbers are for climbing.
• Metres of development multiply the ratio by the wheel’s circumference: how far the bike rolls for one turn of the cranks. It’s the European habit, and the easiest to picture.
• Gain ratio was proposed by Sheldon Brown. Divide the wheel’s radius by the crank length, then multiply by the gear ratio. Because it includes the crank, it tells you how far the bike travels for each unit of distance your foot moves round its circle, which makes riders on different crank lengths comparable. It has no units at all.
• Speed at cadence is development × pedal revolutions per minute × 60, in km/h, shown alongside mph.

A worked example

The chart above starts with a 50/34 chainset and an 11–32 cassette on a 700×28c wheel. The wheel is about 622 + 2 × 28 = 678 mm across, or 26.69 in, and 2,130 mm round. In 50×11 that gives 26.69 × 50 ÷ 11 = 121.3 gear inches and 2.130 × 50 ÷ 11 = 9.68 m of development. With 172.5 mm cranks the gain ratio is (339 ÷ 172.5) × 50 ÷ 11 = 8.93, and at 90 rpm you’d be doing 9.68 × 90 × 60 ÷ 1,000 = 52.3 km/h (32.5 mph). In the bottom gear, 34×32, the same sums give 28.4 gear inches and 12.2 km/h (7.6 mph).

Wheel size: why we start from the rim

Tyre markings such as “700C” or “26 inch” are names, not measurements. The reliable number is the ISO 5775 (ETRTO) bead seat diameter, moulded on the tyre as the second figure in a code like 28-622: 622 mm for 700C and 29er wheels, 584 mm for 650B and 27.5, 559 mm for 26-inch mountain bikes, 349 mm for a Brompton. As Sheldon Brown’s tyre sizing article puts it, a tyre’s outside radius is nominally the rim radius plus the tyre width, so the calculator takes the bead seat diameter plus twice the width.

That is an approximation. Real tyres measure a little wider or narrower than their label depending on the rim, knobs add height, and your weight squashes the tyre. For the most accurate chart, measure the roll-out and type it in:

1. Pump the tyres to your riding pressure and turn the wheel until the valve is at the bottom. Mark the tyre and the floor beside it.
2. Sit on the bike (lean on a wall) and roll forward in a straight line until the valve is at the bottom again.
3. Mark the floor and measure between the two marks in millimetres. Two or three runs, averaged, beat one.

The same number goes into a bike computer’s wheel setting, which is why a computer set to the wrong wheel size disagrees with the chart.

Comparing two setups: what does a smaller chainset change?

Tick “Compare with setup B” and the card lines up both setups gear by gear. With the example, swapping a 50/34 for a 46/33 on the same 11–32 cassette lowers the top gear by exactly 8% (46 ÷ 50) and the bottom gear by about 2.9% (33 ÷ 34). At 90 rpm you lose about 4 km/h off the top speed, and you would need about 98 rpm in 46×11 to match the 50×11 at 90. Whether that matters depends on how often you pedal flat out downhill. If you rarely use 50×11, the smaller jump between the rings and the slightly easier climbing gear may be worth more than the top end.

For a winter bike with mudguards and wider tyres, try the wheel box too. Going from 25 mm to 35 mm tyres on 700C wheels raises the wheel from 672 to 692 mm across, so every gear gets about 3% harder: a third of the jump from the 11 to the 12 sprocket.

Duplicate gears and cross-chaining

A double chainset with an 11-speed cassette offers 22 combinations, but nowhere near 22 different gears. Several pairs on the two rings land within a few percent of each other. In the example, 50×16 and 34×11 differ by only 1.1%. The card lists those near-duplicates (you choose how close counts) and gives the number of distinct gears left once the overlaps and the cross-chained corners are removed.

Cross-chaining means running the big ring with the largest sprockets, or the small ring with the smallest. The chain then runs at its steepest sideways angle, which makes it noisier, wears it faster and makes it more likely to rub the front derailleur. As a rule of thumb the card flags two sprockets at each end on cassettes of eight or more (one on shorter ones). It flags none on a single-ring (1x) bike, whose chainline is set for the middle of the cassette. Every flagged gear has a near-twin on the other ring with a straighter chain.

Common mistakes with gear calculators

• Treating 700C as 700 mm. A 700×23 and a 700×45 differ by 44 mm in diameter, which is a 6–7% difference in every gear.
• Mixing systems. Gear inches use the wheel diameter; development uses the circumference (π times as big, and in metres). Compare like with like.
• Comparing gain ratios across crank lengths without knowing it. Longer cranks lower the gain ratio for the same gear, which is the point of it: the same gear feels easier with longer levers.
• Counting cross-chained gears as usable range. They exist, but you’ll rarely want to use them.
• Trusting a cassette’s name. Two 11–32 cassettes can space their middle sprockets differently; type in your own.

Next, set your tire pressure for your weight and tyres, check your saddle height, or, if the days are short where you ride, see when the law wants your lights on. Planning a long day out? Summit Cabin works out hiking times if the route leaves the road, and Hilltop Cove gives the wind chill at descent speed.