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Gear Ratio Calculator

Work out what a pair of gears does to your speed and torque, and how far apart to mount them.

Inputs

The gear the power comes from.

The gear the power goes to.

Results

Gear ratio

—

Written as driven : driving.

In lowest terms

—

Wheel speed

—

Relative to motor speed.

Wheel torque

—

Relative to motor torque.

Center distance

—in

How far apart to mount the two shafts.

That is this many holes apart

—

When you would use this

  1. Our drive is too slow and we want to know what to change.

    Try a different pair here. The speed multiplier tells you what you gain, and the torque multiplier tells you what you give up. There is no pair that improves both.

  2. We cannot get the gears to mesh properly.

    Check the centre distance and whether it lands on a whole number of holes. If it does not, the two gears are from different families and cannot mount on standard holes at all, however you angle the plate.

  3. Our motors keep stalling on the lift.

    More reduction means more torque at the output. Try a taller ratio here, then check it against the stall calculator to see whether it brings you back inside a safe fraction of stall.

How this is calculated

A gear pair trades speed for torque. Nothing is gained on balance. Whatever you multiply the torque by, you divide the speed by.

ratio = driven teeth ÷ driving teeth speed = motor speed ÷ ratio torque = motor torque × ratio

A reduction (ratio above 1) gives a slower, stronger drive that's harder to push around. An overdrive (ratio below 1) gives a faster drive with less pushing power. Neither one is correct. It depends on whether your game is won by speed or by contact.

Where to mount them

VEX spur gears are 24 diametral pitch, so a gear's pitch diameter in inches is its tooth count divided by 24. Two gears mesh when their shafts sit half the sum of those diameters apart:

center distance = (driving teeth + driven teeth) ÷ 48 inches

Because VEX structure has holes every 0.5", that distance has to land on the grid. It always does. Every standard VEX spur gear pair lands exactly on a hole. The four sizes are 12, 36, 60 and 84, all multiples of 12 offset the same way, so any pair sums to a multiple of 24 and the center distance works out to a whole number of holes. You can't pick a legal VEX spur pair that won't mesh on standard holes.

Direction

Two meshing gears turn in opposite directions. If that's a problem, put a third gear between them. An idler flips the direction back without touching the ratio, because its tooth count cancels out of the sum.

Sources & assumptions

Tooth counts are VEX's four published spur gear sizes. The 24 diametral pitch figure is derived rather than published: it's the value consistent with both VEX's gear dimensions and the 0.5" hole spacing, and it reproduces the center distances teams measure in practice.

Assumes a simple two-gear external mesh. Compound gear trains, where two gears lock on one shaft, multiply their ratios together. Run each stage through this calculator and multiply the results.

Save this run, and compare

Keeps what is on screen so you can change something and see both sides of the change. Saved in this browser only, never uploaded.

Save this as evidence

Collects what you entered, what came out, how it was worked out, and anything the tool flagged, with a timestamp and a version so someone else can reproduce it.

This is evidence, not a notebook entry. It deliberately does not write your problem statement, your reasoning, or your conclusion, because under RECF rules an Engineering Notebook has to be the students' own work and no tool may generate or organise its content. Take the numbers, decide what matters, and write it yourself.