Gear Ratio Calculator
Find the gear ratio from the number of teeth on two gears, with output speed and torque, or work out vehicle speed from engine RPM, gear ratios and tire size.
Results
| Item | Value |
|---|
Quick Answer
Gear ratio = driven teeth ÷ driving teeth. A 12-tooth gear driving a 36-tooth gear has a 3:1 ratio, so the output turns 3 times slower with about 3 times the torque. For a car, mph = RPM ÷ (gear × axle ratio) × tire diameter × π × 60 ÷ 63,360; at 2,500 RPM, 0.75 top gear, 3.73 axle and 30-inch tires that is about 79.8 mph.
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Table of Contents
- Gear Ratio Calculator
- Quick Answer
- Related Calculators
- How This Gear Ratio Calculator Works
- How to Use the Gear Ratio Calculator
- Core Formulas
- Key Terms
- Worked Example
- Real-Life Examples
- Gear Ratio vs Gear Reduction
- RPM at 60 mph by Axle Ratio
- Tips
- Common Mistakes to Avoid
- Frequently Asked Questions
- References & Sources
How This Gear Ratio Calculator Works
In gear mode, enter the teeth on the driving gear (the one connected to the motor) and on the driven gear. The calculator gives the gear ratio in simplest form, tells you whether it is a reduction or an overdrive, and shows the output speed and torque if you enter them. In vehicle mode, enter engine RPM, the transmission and axle ratios and the tire diameter to find road speed, or the RPM at 60 mph.
Quick explanation: a bigger driven gear trades speed for torque.
- Ratio above 1: slower and stronger (reduction).
- Ratio below 1: faster and weaker (overdrive).
- Overall ratio: multiply the ratios of each stage.
How to Use the Gear Ratio Calculator
- Choose gear ratio or vehicle speed.
- For gears, enter the teeth on both gears and, optionally, input speed and torque.
- For a vehicle, enter engine RPM, transmission and axle ratios and tire size.
- Press Calculate.
- Read the ratio, output speed, torque or road speed.
Core Formulas
- Gear ratio: driven teeth ÷ driving teeth
- Output speed: input speed ÷ gear ratio
- Output torque: input torque × gear ratio (before losses)
- Overall ratio: transmission ratio × axle ratio
- Speed (mph): RPM ÷ overall ratio × tire diameter (in) × π × 60 ÷ 63,360
Key Terms
- Driving gear: the gear connected to the power source.
- Driven gear: the gear that receives the motion.
- Gear reduction: a ratio above 1 that trades speed for torque.
- Final drive: the last gear set, usually in the axle, before the wheels.
- RPM: revolutions per minute.
Worked Example
A motor spins at 1,800 RPM with 10 N·m of torque, driving a 12-tooth gear that turns a 36-tooth gear.
- Ratio = 36 ÷ 12 = 3:1
- Output speed = 1,800 ÷ 3 = 600 RPM
- Output torque = 10 × 3 = 30 N·m, before friction losses
Real-Life Examples
- Robotics: slow a fast motor down for more torque at the wheels.
- Bikes: a 50-tooth chainring and 25-tooth cog give a 0.5 ratio, so the wheel turns twice per pedal turn.
- Axle swaps: changing from 3.73 to 4.10 gears raises RPM at 60 mph from 1,881 to 2,067.
- Bigger tires: 33-inch tires at the same RPM go about 87.7 mph instead of 79.8.
Gear Ratio vs Gear Reduction
- Gear ratio: the number that compares the two gears.
- Gear reduction: a ratio above 1, which lowers speed and raises torque.
- Overdrive: a ratio below 1, which raises speed and lowers torque.
RPM at 60 mph by Axle Ratio
For a transmission gear of 1:1. Multiply by your gear ratio for other gears.
| Axle ratio | 28-inch tire | 30-inch tire | 33-inch tire | 35-inch tire |
|---|---|---|---|---|
| 3.08 | 2,218 | 2,071 | 1,882 | 1,775 |
| 3.42 | 2,463 | 2,299 | 2,090 | 1,971 |
| 3.55 | 2,557 | 2,387 | 2,170 | 2,046 |
| 3.73 | 2,687 | 2,508 | 2,280 | 2,149 |
| 4.1 | 2,953 | 2,756 | 2,506 | 2,363 |
| 4.56 | 3,285 | 3,066 | 2,787 | 2,628 |
Tips
- Gear trains: idler gears in between do not change the overall ratio.
- Chains and belts: use sprocket teeth or pulley diameters the same way.
- Bigger tires: lower the effective ratio and raise speed at the same RPM.
- Efficiency: real gears lose some power to friction.
Common Mistakes to Avoid
- Swapping driving and driven. The ratio is driven ÷ driving.
- Counting idler gears. They change direction, not the ratio.
- Forgetting the final drive. Vehicle speed needs both transmission and axle ratios.
- Using wheel size instead of tire size. Use the overall tire diameter.
- Ignoring losses. Real torque output is a little lower.
Frequently Asked Questions
Divide the teeth on the driven gear by the teeth on the driving gear.
The input turns 3 times for each output turn, giving about 3 times the torque.
No. A higher numeric ratio gives more torque and less speed.
It depends on use. Higher numbers like 4.10 help towing and acceleration, while lower ones like 3.08 favor highway cruising.
mph = RPM ÷ (transmission × axle ratio) × tire diameter × π × 60 ÷ 63,360.
They change the effective ratio, lowering RPM at a given speed.
A gear between two others that changes direction but not the ratio.
Multiply the ratio of each stage together.
Yes, by the ratio, minus friction losses.
Yes. Use the pulley diameters instead of teeth.
A ratio below 1:1, where the output spins faster than the input.
Often on a tag on the axle, in the owner’s manual or on the vehicle build sheet.
References & Sources
| Source | Used For | Link |
|---|---|---|
| Wikipedia, Gear train | Gear ratios, idler gears and torque. | https://en.wikipedia.org/wiki/Gear_train |
| Wikipedia, Gear ratio | Gear ratios, mechanical advantage and vehicle gearing. | https://en.wikipedia.org/wiki/Gear_ratio |