Gear Ratio Calculator

Gear ratio and speed formulas

This page uses the driven-to-driver tooth-count convention. It therefore reports a reduction ratio above 1 when the driven gear has more teeth than the driver.

Worked speed-reduction example

For z₁ = 20, z₂ = 40, and n₁ = 1200 rpm:

1. Ratio: i = 40 / 20 = 2, reported as 2:1.
2. Driven speed: |n₂| = 1200 × 20 / 40 = 600 rpm.
3. Classification: speed reduction.
4. Direction: opposite to the driver because this is one external mesh.

Worked overdrive example

For a 40-tooth driver, 20-tooth driven gear, and 1200 rpm input:

1. Ratio: i = 20 / 40 = 0.5, reported as 0.5:1.
2. Driven speed: |n₂| = 1200 × 40 / 20 = 2400 rpm.
3. Classification: overdrive or speed increase.
4. Direction remains opposite to the driver.

The engine retains full floating-point precision. Display rounding is applied after calculation and does not feed back into the formulas.

How to use the gear ratio calculator

Enter the whole-number teeth on the input and output gears, then enter the positive driver-speed magnitude in rpm. The calculator returns one explicit ratio convention, the driven speed, the speed relationship, and the rotation direction. The URL stores z1, z2, and n1 only as shareable state; all parameter combinations retain the same canonical page.

After calculating, you can transfer the tooth pair to the Gear Center Distance Calculator. That handoff uses module 2 only as a clearly identified editable starting value because tooth counts alone do not define pitch diameter or center distance.

Engineering scope and limitations

This V1 model covers one compatible external spur-gear pair with no slip. The gears must still share a compatible module or diametral pitch, pressure angle, tooth form, and operating geometry.

It does not model:

• internal gears, racks, idlers, compound trains, or multiple stages;
• planetary, worm, bevel, crossed-axis, chain, or belt transmissions;
• efficiency, friction, actual output torque, power loss, or thermal limits;
• bending or contact stress, surface durability, materials, quality grade, or life;
• backlash, profile shift, shaft and bearing deflection, alignment, or dynamic loads.

A low tooth count remains mathematically valid for the ratio, so the calculator issues an engineering warning instead of blocking the result. Undercut risk must be evaluated with the selected pressure angle, tooth system, and profile shift.