Gear Ratio Calculator
Gear ratio = driven teeth ÷ driving teeth. Enter the teeth for up to three stages and the gear ratio calculator gives the overall ratio, the output speed and the output torque.
Gear ratio
- Gear ratio 36/12 × 40/15 = 8. In a compound train the stage ratios multiply.
- 8:1
- Output speed 1,800 rpm ÷ 8. A reduction: the output turns slower than the input.
- 225 rpm
- Output torque 10 × 8, ideal: speed is traded for torque one for one, so power in equals power out.
- 80
- Output direction Each external gear mesh reverses the direction of rotation. An idler gear between two gears reverses it again without changing the ratio.
- same as the input
| Stage | Driving teeth | Driven teeth | Stage ratio | Speed after this stage (rpm) |
|---|---|---|---|---|
| 1 | 12 | 36 | 3:1 | 600 |
| 2 | 15 | 40 | 2.667:1 | 225 |
- The ratio here is driven over driving, so a number above 1 is a reduction. Some catalogs write it the other way up; 3:1 and 1:3 describe the same pair read from opposite ends.
- Belt and chain drives follow the same arithmetic, with pulley diameters or sprocket teeth in place of gear teeth.
How the Gear Ratio Calculator works
A gear ratio is the number of teeth on the driven gear divided by the number on the driving gear. A 12-tooth gear turning a 36-tooth gear is a 3:1 ratio: the driving gear goes around three times for each turn of the driven one. The output turns three times slower and, with no losses, with three times the torque. Speed is traded for torque one for one, so the power is the same on both sides.
Gear trains multiply. When two gears share a shaft, the second stage starts from the first stage's output, and the overall ratio is the product of the stage ratios. The default example is a two-stage train: 12 teeth driving 36, then 15 teeth driving 40 on the same shaft. That is 3 × 2.6667 = 8:1 overall. A motor at 1,800 rpm comes out at 225 rpm, and 10 units of input torque come out as 80. Each external mesh reverses the direction of rotation, so after two stages the output turns the same way as the input.
Real gears lose some power to friction at each mesh. Enter an efficiency per mesh and the calculator multiplies it through the stages: at 95% per mesh, two meshes pass 90.25% of the power, and the 80 units of torque become 72.2. The speed is unchanged, because the teeth cannot slip. The efficiency of a particular gearset depends on its type, finish and lubrication, so this calculator takes it as an input rather than assuming one.
For a car or truck the same arithmetic runs from the engine to the road. The transmission gear and the axle ratio (the final drive) multiply into an overall ratio, and the tire turns that into road speed. Engine rpm = mph × 63,360 ÷ (60 × π × tire diameter) × transmission ratio × axle ratio. 63,360 is the number of inches in a mile, and 63,360 ÷ (60 × π) = 336.14, which is where the shop rule rpm = mph × ratio × 336 ÷ tire diameter comes from.
A worked example: a 265/70R17 tire is 31.61 inches tall, because its sidewall is 70% of 265 mm, 185.5 mm or 7.30 inches, twice over plus the 17-inch wheel. At 65 mph it turns 691.28 times a minute. With 3.73 axle gears in direct drive (1.00), the engine turns 2,578 rpm. In a 0.70 overdrive it is 1,805 rpm. Switch to taller 33-inch tires and the same gears give 2,470 rpm in direct drive, which is why a bigger tire is often paired with a numerically higher axle ratio to restore the original engine speed.
Choosing the speed mode runs the other way: from an engine speed to the road speed it gives in a gear. At 2,500 rpm on the same 265/70R17 tires, 3.73 gears and direct drive give 63.0 mph.
Gear Ratio Calculator FAQ
How do you calculate a gear ratio?
Divide the driven gear's teeth by the driving gear's teeth. A 12-tooth gear driving a 36-tooth gear is 36 ÷ 12 = 3, written 3:1. For a train of gears, multiply the ratios of each stage.
What does a gear ratio do to speed and torque?
The output speed is the input speed divided by the ratio, and the output torque is the input torque multiplied by it, less friction losses. An 8:1 train turns 1,800 rpm into 225 rpm and 10 units of torque into 80.
How do you calculate RPM from gear ratio and tire size?
RPM = mph × axle ratio × transmission ratio × 336.14 ÷ tire diameter in inches. A 31.61-inch tire at 65 mph with 3.73 gears in direct drive gives about 2,578 rpm.
What is a 3.73 gear ratio?
An axle ratio: the driveshaft turns 3.73 times for each turn of the wheels, as with a 41-tooth ring gear and an 11-tooth pinion. A numerically higher ratio, such as 4.10, gives more acceleration and a higher engine speed at a given road speed.
Does a bigger tire change the gear ratio?
It changes the effective gearing. A taller tire covers more ground per turn, so the engine turns slower at the same speed. Going from 31.61-inch to 33-inch tires on 3.73 gears drops the engine from 2,578 to 2,470 rpm at 65 mph.