Gear Ratio Calculator
Enter the driver and driven tooth counts to find the gear ratio, output speed and output torque. Add an optional second (compound) stage with efficiency losses, or switch to reverse-solve mode to find the teeth you need to hit a target ratio.
Formula
Worked example
A 12-tooth driver turning a 36-tooth driven gear gives GR = 36 ÷ 12 = 3.000. At 1500 rpm the output spins at 1500 ÷ 3 = 500 rpm. With 10 N·m in at 97% efficiency, output torque = 10 × 3 × 0.97 = 29.1 N·m.
How the gear ratio is calculated
The gear ratio is the number of teeth on the driven (output) gear divided by the number of teeth on the driver (input) gear. Because meshing gears share the same tooth pitch, counting teeth is equivalent to comparing the gears pitch-circle diameters. A ratio greater than one means the driven gear is larger and turns more slowly than the driver, while a ratio less than one means it is smaller and turns faster. This single number captures everything about how the pair transforms rotation. When you add a second compound stage, the overall ratio is the product of the two stage ratios, not their sum.
Speed, torque and efficiency
Gears cannot create energy, so any speed they give up is repaid as torque, and vice versa. If the driven gear turns three times slower than the driver, it delivers close to three times the turning force, because mechanical power, the product of torque and rotational speed, is conserved across an ideal mesh. This inverse relationship is why low gears help a car accelerate from a stop and high gears let it cruise efficiently. Real gears lose a few percent per mesh to friction, so set the mesh efficiency (about 96 to 99 percent for spur gears, far lower for worm drives) and the calculator applies it to the output torque, raising the loss to the power of the number of meshes for a compound train.
Reverse-solving and gear trains
Switch to reverse-solve mode when you know the ratio you want and need to choose gears to reach it. Enter the driver teeth and a target ratio, and the calculator returns the whole number of driven teeth that gets closest, then recomputes the actual ratio those real gears produce. For chains of more than two gears, multiply the individual stage ratios together to get the overall ratio. Idler gears placed between a driver and driven gear do not change the magnitude of the ratio at all; they only reverse the direction of rotation, so designers add them purely to flip direction or bridge a gap.
Gear ratio outcomes at a glance
| Gear ratio | Type | Output speed | Output torque |
|---|---|---|---|
| Less than 1:1 | Overdrive | Faster | Lower |
| Exactly 1:1 | Direct drive | Unchanged | Unchanged |
| 2:1 | Reduction | Half | Double |
| Greater than 3:1 | High reduction | Much slower | Much higher |
How common ratios change output speed and torque relative to the input.
Frequently asked questions
Which gear is the driver and which is the driven?
The driver gear is connected to the power source (a motor or crank) and supplies the rotation. The driven gear receives that rotation through the mesh. The gear ratio is always the driven tooth count divided by the driver tooth count, so swapping which gear drives inverts the ratio.
Does a higher gear ratio mean more speed or more torque?
A higher ratio (above 1:1) means more torque and less speed at the output, it is a reduction. A ratio below 1:1 is an overdrive that gives more speed and less torque. Gears trade one for the other because they conserve power, not create it.
How do I find the gears for a ratio I already want?
Use reverse-solve mode. Enter the driver tooth count and your target ratio, and the calculator multiplies them to find the driven teeth needed, rounds to a whole number, and shows the actual ratio those real gears deliver. You can then nudge the driver count to land closer to the target.
How do idler gears and efficiency affect the result?
An idler gear sits between the driver and final driven gear and reverses rotation without changing the overall ratio, since its tooth count cancels out. Each mesh does lose a little power to friction, so the calculator applies the mesh efficiency you set to the output torque, compounding it once per mesh for multi-stage trains.