Gear Ratio Calculator: Ring and Pinion Final Drive
How do I calculate a gear ratio from teeth? Enter the ring gear and pinion tooth counts to get the axle (final drive) ratio, such as 4.10:1. Add a transmission gear ratio to get the overall ratio, and the tire and engine rpm to see the wheel rpm it produces. This page is about the ratio itself; for speed tables use the speed from RPM calculator.
Updated
Report a problem
Formula
final drive = ring teeth / pinion teethoverall ratio = transmission gear ratio x final drivewheel rpm = engine rpm / overall ratiospeed (mph) = wheel rpm x pi x tire diameter (in) x 60 / 63360km/h = mph x 1.609344
The tire is assumed to roll without slip at its stated diameter. Real tires change size slightly with load and speed.
Worked example
Ring gear 41 teeth, pinion 10 teeth: final drive = 41 / 10 = 4.10. In direct drive (ratio 1.0) the overall ratio is 4.10. At 3000 rpm the wheels turn 3000 / 4.10 = 731.7 rpm. A 26 inch tire has a circumference of pi x 26 = 81.68 in, so the speed is 56.6 mph (91.1 km/h).
Second example: 43 / 11 gives a 3.91 axle ratio; with a 1.0 gear the wheels turn 767.4 rpm at 3000 rpm, or 59.4 mph on a 26 inch tire.
Use this when
You are choosing or swapping a differential, reading an axle code, or checking what an overdrive gear does to the overall ratio. Typical axle ratios are about 3.0 to 4.5 for road cars; higher numbers accelerate harder and rev higher at speed.
Use another calculator instead when
- You want a speed for every gear: use the speed from RPM calculator.
- You know the road speed and want engine rpm: use the RPM at speed calculator.
- You want to compare tire sizes: use the tire size calculator.
Common mistakes
- Dividing pinion by ring teeth, which gives the inverse (0.24 instead of 4.10).
- Forgetting that the overall ratio includes the transmission gear.
- Using tire width instead of overall diameter in inches.
- Assuming rounding in the tooth count does not matter: 41/10 and 43/11 differ by almost 5 percent.
Frequently asked questions
How do I calculate the final drive ratio from ring and pinion teeth?
Divide the number of ring gear teeth by the number of pinion teeth. A ring gear with 41 teeth and a pinion with 10 teeth gives 41 / 10 = 4.10, usually written 4.10:1.
What is the overall gear ratio?
It is the transmission gear ratio multiplied by the final drive ratio. With a 2.66 gear and a 3.73 axle the engine turns 2.66 x 3.73 = 9.92 times for each turn of the wheels.
How do I find speed from engine rpm and gear ratio?
Divide engine rpm by the overall ratio to get wheel rpm, then multiply by the tire circumference. At 3000 rpm with a 4.10 overall ratio and a 26 inch tire, the wheels turn 731.7 rpm and the car does about 56.6 mph.
Does a higher axle ratio make a car faster?
A higher number (such as 4.10) gives stronger acceleration but a lower top speed at a given rpm and higher revs on the highway. A lower number (such as 3.08) does the opposite. The result ignores tire growth and slip, so treat it as an estimate.
What is the gear ratio formula?
Gear ratio is driven teeth divided by driving teeth. For a differential that is ring teeth divided by pinion teeth, so 43 ring teeth and 11 pinion teeth give 43 / 11 = 3.91:1. Multiply by the transmission gear ratio to get the overall ratio.
What is a good rear axle gear ratio?
There is no single best value. Ratios near 3.08 to 3.55 are typical for relaxed highway cruising, while 3.73 to 4.56 are typical for towing and quick acceleration. Higher numbers raise engine rpm at a given speed.
How do I calculate the gear ratio and speed for a 3.70 axle?
A 37-tooth ring and 10-tooth pinion give 3.70. In a 0.75 overdrive the overall ratio is 2.78, so 2500 rpm gives 900.9 wheel rpm. On a 28 inch tire that is 75.0 mph (120.8 km/h).