Gear Ratio Calculator

Enter the teeth on the driver gear and the driven gear and this calculator returns the gear ratio in decimal and simplified form, the output speed from your input RPM, and the output torque with an efficiency allowance for friction. A 20-tooth driver turning a 60-tooth driven gear is a 3:1 reduction: the output shaft turns once for every three input turns, at one third the speed and roughly three times the torque.

Quick Answer

How to use the gear ratio calculator

Count the teeth on both gears, type the two counts in, and click Calculate Ratio. The speed and torque fields are optional extras on top of the ratio itself.

1. Enter the driver teeth: the gear on the power source (motor shaft, crank, engine output). If you are counting teeth on a sprocket or a timing pulley instead of a gear, the same count works, because the ratio math is identical.
2. Enter the driven teeth: the gear that the driver turns. Getting these two backwards is the most common gear ratio mistake there is; it inverts the answer, turning a 3:1 reduction into a 0.333:1 overdrive.
3. Add input RPM if you want output speed: the tool divides it by the ratio. On a vehicle, the same two-count method is how an axle ratio calculator treats the ring and pinion in the differential.
4. Add input torque and efficiency if you want output torque: torque comes back in whatever unit you typed in. Efficiency defaults to 95% if you leave it blank, and it must sit between 0 and 100 or the tool stops with a message.
5. Read the classification line: the results label the pair a reduction, an overdrive or direct drive, and spell out the full arithmetic in the detail line so you can check each step.

One honest quirk: the tool accepts fractional tooth counts (20.5 teeth) and computes the decimal ratio from the numbers as typed, but the simplified ratio is built from whole teeth, rounded first. Real gears have whole teeth, so enter whole counts and the two forms always agree. Copy my results puts the ratio, simplified form and classification on your clipboard; Reset restores the 20-tooth and 60-tooth worked example.

The three formulas behind the results

Every result in this calculator comes from three short formulas. The ratio itself needs nothing but the two tooth counts.

The simplified ratio is the same fraction reduced by the greatest common divisor of the two counts: 60 and 20 share a divisor of 20, so 60:20 simplifies to 3:1, printed here as driven: driver to match the main result. The physics underneath is conservation of energy, the same principle the gear entry in Encyclopaedia Britannica’s technology coverage describes: meshing teeth force the two shafts to trade speed against torque, and the ratio is the exchange rate. Because pitch diameter grows in direct proportion to tooth count for gears of the same module, the ratio from diameters, RPM or torque is the same number; teeth are just the easiest version to count. The reference text for this whole field is Machinery’s Handbook from Industrial Press, which tabulates gear geometry and train calculations in far more depth than any single-pair tool.

Worked example: 20 teeth driving 60 teeth at 3,000 RPM

The range of results below is the exact output of the pre-filled calculator: a small motor pinion driving a gear three times its size, with 50 Nm of input torque and a 95% efficiency allowance.

Three more runs show the shape of the trade-off. Swap the gears (60 driving 20) and the ratio becomes 0.333: 1, an overdrive: the same 3,000 RPM input leaves at 9,000.0 RPM, and 50 units of torque shrink to 15.83 at 95% efficiency. Equal 20-tooth gears give 1.000: 1 direct drive, 3,000 RPM in and out. A 17-tooth driver with a 43-tooth driven gear, a pair with no common divisor, gives 2.529: 1 with the simplified form left as 43: 17, and 395.3 RPM out from 1,000 RPM in. For chain drives rather than meshing gears, the sprocket counts feed straight into this tool, and the chain length calculator then works out how much chain that pair needs; belt drives pair the same ratio thinking with the belt distance calculator for centre distances.

Reduction, overdrive and direct drive

A ratio above 1:1 is a reduction: the output turns slower and pulls harder. A ratio below 1:1 is overdrive: the output turns faster and pulls weaker. Exactly 1:1 is direct drive, where the pair changes direction and shaft position but neither speed nor torque.

Reductions do the heavy work in machines: winches, conveyor drives, robot joints, bicycle climbing gears and the low gears of a gearbox all sit well above 1:1, often between 3:1 and 100:1 once several stages are stacked. Overdrive lives at the other end of a transmission, where a cruising gear below 1:1 lets the engine loaf at highway speed; the progression through a gearbox from deep reduction to overdrive is the subject of Britannica’s transmission engineering article. The practical limit for one spur pair is roughly 6:1 to 10:1, because the pinion gets too small to cut cleanly and the gear gets too large to package; beyond that, designers stack stages, which the next section covers.

Why the efficiency field only touches torque

Efficiency trims the torque result because friction in the mesh eats force, not turns. The two shafts are locked together by the teeth, so the speed ratio holds exactly; what friction takes shows up as heat and as torque that never reaches the output shaft.

A clean, well-lubricated spur or helical mesh typically returns 95 to 99% per stage in reference data such as the KHK Gear Knowledge library from gear manufacturer Kohara Gear Industry, while worm drives can drop far lower, sometimes under 70%, because their teeth slide instead of roll. This tool defaults to 95% when the field is blank, which is a fair planning number for one spur pair. Two things to keep straight: the allowance applies once, to this single pair, so a three-stage box needs the per-stage figure multiplied through (0.95 three times is about 86% overall); and the tool silently ignores a zero or negative RPM or torque instead of erroring, so a missing speed row in the results usually means the field was blank or not positive. Course material such as MIT OpenCourseWare’s Design and Manufacturing I works through the same trade-offs with full gear-train design problems.

Compound trains and idler gears

A compound train puts two gears on one shared shaft so the output of the first stage becomes the input of the second, and the overall ratio is the product of the stage ratios. A 2:1 stage followed by a 3:1 stage gives 6:1 overall, which is how winches and robot gearboxes reach 50:1 or 100:1 without a single enormous gear.

This calculator handles one pair at a time, so run each stage separately and multiply the ratios yourself; the output RPM of stage one is the input RPM of stage two, and the efficiency allowance compounds the same way. An idler gear, a single gear placed between driver and driven purely to bridge distance or flip direction, changes nothing about the ratio: the overall figure still depends only on the first and last gears, a point the gear reference material collected by Boston Gear’s engineering tools library states in the same form. Direction does flip with each mesh, though: one mesh reverses rotation, two meshes restore it, which matters when the output must turn the same way as the input.

What competing calculators miss

Six tools dominate this keyword, and each leaves a specific gap:

• Omni Calculator: the polished incumbent, with a reverse mode that finds a missing tooth count and mechanical advantage. Gap: no efficiency allowance anywhere, so its torque figures are the ideal frictionless numbers, and the page is built for physics students rather than someone sizing a drive.
• Rivcut: genuinely broader, with up to three stages, per-stage efficiency and power in and out. Gap: it is a machining vendor’s lead-in, the three-stage form is heavy for a single-pair check, and there is no simplified ratio.
• Firgelli: mode-based (teeth, RPM or torque starting points), speed reduction and torque increase percentages. Gap: a linear-actuator storefront tool where the modes hide fields until you guess the right starting point, and again no simplified fraction.
• Softonic Tools: a three-step wizard with clean reduction and overdrive wording. Gap: the wizard forces one question per screen for a four-number job, and there is no torque or efficiency input at all.
• WuTools: fast, with the same four formulas written out. Gap: ideal torque only, no efficiency, no classification line, and nothing on compound trains or idlers.
• Turn2Engineering: the deepest of the group, multi-stage and vehicle speed included. Gap: built for vehicle gearing, so the simple pair check a robotics or conveyor user needs is buried under automotive inputs.
• The gap this page fills: the single-pair job done completely in one pass: decimal and simplified ratio in the correct driven: driver order, a named classification, output RPM, and output torque with an honest efficiency allowance, plus the compound and idler arithmetic in prose for when one pair is not the whole machine.

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