Gear ratio calculator for gear trains, belts, chains and bicycles
This gear ratio calculator turns tooth counts or pulley diameters into the numbers you actually need: the overall ratio, the output speed in rpm, the output torque after losses, and the power at both ends. It handles simple pairs and compound trains of up to six stages — the kind found in gearboxes, winches, clocks and robot drives — as well as V-belt and flat-belt drives, roller-chain sprockets and bicycle gearing with gear inches, development and gain ratio.
Every result is explained with its formula, and an SVG schematic shows the train. The calculation runs in your browser.
How to use the Gear Ratio Calculator
- Choose the Drive type: gear train, belt & pulleys, chain & sprockets or bicycle.
- For a gear train, enter the driver and driven teeth of each stage and press Add stage for a compound train (the driven gear of one stage shares a shaft with the driver of the next). Tick the idler option if idler gears are present and you do not want direction reversals counted.
- For belts enter the pulley diameters, for chains the sprocket teeth and chain pitch, for bicycles the chainring, cog, wheel size, crank length and cadence. A centre distance is optional and adds belt length or chain links.
- Enter the Input speed, Input torque and the Efficiency per stage (about 98% for spur gears, 95–97% for V-belts, 97–98% for chains).
- Read the ratio, output rpm, torque, power and efficiency, the direction of rotation and the detail rows with the formulas; copy the summary or download the schematic.
Gear Ratio Calculator features
Compound trains up to six stages
Ratios multiply stage by stage; the tool shows each stage ratio, the product and the number of direction reversals.
Torque, speed and power
Output speed = input ÷ ratio; output torque = input × ratio × efficiency; power in and out are compared so losses are explicit.
Belt drive geometry
Ratio from diameters, belt speed, open-belt pitch length from the centre distance and the wrap angle on the small pulley with a slip warning below 120°.
Chain drive sizing
Pitch diameters from p / sin(180°/T), chain speed and the chain length in pitches rounded up to an even number of links for ANSI #35–#80 and motorcycle/bicycle pitches.
Bicycle gearing
Gear inches, development in metres, Sheldon Brown’s gain ratio and road speed at your cadence for common wheel sizes or a custom diameter.
Gear ratio formulas
For two meshing gears the ratio is the number of teeth on the driven gear divided by the number on the driver: i = T₂ / T₁. Because meshing teeth move at the same pitch-line speed, the speeds are inversely proportional, n₂ = n₁ / i, and the torques are directly proportional, τ₂ = τ₁ × i × η, where η is the efficiency. A ratio greater than 1 is a reduction (slower, stronger); less than 1 is an overdrive.
In a compound train the ratios of the stages multiply: a 12→36 stage (3:1) followed by a 10→40 stage (4:1) gives 12:1, so 1,500 rpm becomes 125 rpm and 10 N·m becomes 120 N·m before losses. In a simple train with idler gears in between, only the first and last gears set the ratio; the idlers change the direction and the centre distance but cancel out of the arithmetic.
| Drive | Ratio | Notes |
|---|---|---|
| Spur / helical gears | T₂ / T₁ | each external mesh reverses the direction |
| Belt and pulleys | D₂ / D₁ | same direction; allow 1–3% creep for V-belts |
| Chain and sprockets | T₂ / T₁ | same direction; no slip |
| Worm and wheel | T_wheel / starts | a single-start worm on a 40-tooth wheel gives 40:1 |
| Bicycle | chainring / cog | ratio > 1 is a speed increase; gear inches = wheel Ø × ratio |
Worked examples
For the torque side of a drive design — bolt tightening, lever arms and power conversion — see the torque calculator; the speed calculator and unit converter help with rpm, m/s and imperial units.
- Single reduction: a 12-tooth pinion driving a 36-tooth gear gives 36/12 = 3:1. At 1,500 rpm and 10 N·m input the output runs at 500 rpm with 30 N·m (29.4 N·m at 98% efficiency) and turns the opposite way.
- Belt drive: a 100 mm motor pulley and a 250 mm driven pulley 400 mm apart give 2.5:1, a belt pitch length of about 1,364 mm and a 158° wrap on the small pulley.
- Chain: a 17-tooth front and 45-tooth rear sprocket on 12.7 mm (½″) chain give 2.65:1; at 600 mm centres the chain needs 125.9 pitches, so fit 126 links.
- Bicycle: a 50-tooth chainring with a 25-tooth cog on a 27″ wheel is 54 gear inches, 4.31 m of development per pedal turn and about 23 km/h at 90 rpm.
Choosing tooth counts
Keep pinions above about 17 teeth for standard 20° involute gears to avoid undercutting, keep single-stage ratios below roughly 6:1 for spur gears (10:1 for helical) and split larger reductions across stages. Where possible choose coprime tooth counts (a hunting tooth) so that the same pairs of teeth do not mesh every revolution. For timing belts and chains the same rule applies to sprocket teeth, and the chain should have an even number of links so a half link is not needed.
Gear Ratio Calculator FAQ
How do I calculate a gear ratio from teeth?
Divide the driven gear’s teeth by the driver’s teeth. A 12-tooth driver and 36-tooth driven gear give 36 ÷ 12 = 3:1, meaning the output turns once for every three turns of the input and carries three times the torque (minus losses).
How does a compound gear train change the ratio?
Multiply the stage ratios. 3:1 followed by 4:1 is 12:1. Add stages in the calculator and the overall ratio, output rpm and torque update automatically.
Does an idler gear change the ratio?
No. An idler between two gears only reverses the direction and bridges the gap; the ratio depends on the first and last gears alone. Tick the idler option so the direction report ignores those reversals.
What efficiency should I use?
Typical per-stage figures are 97–99% for spur and helical gears, 95–97% for V-belts, 97–98% for roller chains and only 50–90% for worm drives depending on the ratio and lubrication.
What are gear inches on a bicycle?
The diameter of the imaginary direct-drive wheel that would give the same distance per pedal turn: wheel diameter × chainring ÷ cog. 54 gear inches is a moderate gear; multiply by π × 0.0254 to get development in metres.