Gear Ratio Calculator
Find gear ratio, output speed and output torque from teeth counts. Handles single gear pairs and compound two-stage gear trains with full working shown.
⚙️ What is a Gear Ratio?
A gear ratio is the ratio of the number of teeth on the driven (output) gear to the number of teeth on the driving (input) gear. Written as GR = driven teeth ÷ driver teeth, it describes how a pair of meshing gears transforms rotational speed and torque between two shafts. A gear ratio of 3, usually written 3:1, means the output shaft turns once for every three turns of the input, while delivering roughly three times the torque.
Gear ratios are everywhere in mechanical systems. Car transmissions use a series of gear ratios so the engine can stay in its efficient RPM band across a wide range of road speeds. Bicycle drivetrains change the ratio between the pedals and the rear wheel so the rider can climb hills or sprint on the flat. Electric drills, winches, clock mechanisms, robot joints, and wind turbine gearboxes all rely on carefully chosen gear ratios to match a motor to its load.
A common misconception is that gears create energy or free power. They do not. A gear ratio trades speed for torque, or torque for speed, but the mechanical power passing through (torque multiplied by rotational speed) stays essentially constant apart from small friction losses. When a ratio multiplies torque by three, it also divides speed by three, so the product is unchanged.
This calculator works out the gear ratio directly from teeth counts, then applies it to any input speed and torque you enter so you can read off the output speed and output torque instantly. It also handles compound two-stage gear trains, where the overall ratio is the product of the two individual stage ratios.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Speed Reduction
12-tooth driver into a 36-tooth driven gear at 1,500 RPM and 20 N·m
Example 2 — Overdrive
40-tooth driver into a 20-tooth driven gear at 2,000 RPM and 100 N·m
Example 3 — Compound Gear Train
Two stages, 15→45 and 20→60 teeth, at 1,800 RPM and 10 N·m
❓ Frequently Asked Questions
🔗 Related Calculators
What is a gear ratio?
A gear ratio is the ratio of the number of teeth on the driven (output) gear to the number of teeth on the driving (input) gear: GR = driven teeth / driver teeth. It tells you how the input speed and torque are transformed. A gear ratio of 3 (written 3:1) means the output shaft turns one third as fast as the input but delivers three times the torque, ignoring friction.
How do you calculate gear ratio?
Divide the number of teeth on the driven gear by the number of teeth on the driver gear. For example, a 12-tooth driver meshing with a 36-tooth driven gear gives 36 / 12 = 3, or a 3:1 ratio. You can also use pitch diameters or the input and output RPM, since the ratio of speeds equals the inverse ratio of teeth.
What is the difference between a driver and a driven gear?
The driver (or drive) gear is connected to the power source and provides the input rotation. The driven gear receives motion from the driver and delivers the output. In gear ratio GR = driven / driver, the driven gear teeth are on top. Swapping which gear is the driver inverts the ratio and turns a reduction into an overdrive.
How does gear ratio affect torque and speed?
Gear ratio multiplies torque and divides speed by the same factor. Output torque = input torque × gear ratio, and output speed = input speed / gear ratio. A 4:1 reduction gives four times the torque at one quarter of the speed. Since power = torque × angular speed, mechanical power stays the same apart from friction losses, so you cannot gain both torque and speed.
What is a compound gear train?
A compound gear train has two or more meshing stages in series, often on shared shafts. The overall gear ratio is the product of the individual stage ratios: GR_total = GR1 × GR2 × ... This lets you achieve large ratios in a compact package. Two 3:1 stages produce a 9:1 overall ratio.
Does an idler gear change the gear ratio?
No. An idler gear placed between the driver and the driven gear changes the direction of rotation but not the overall gear ratio, because its teeth cancel out of the calculation. Idlers are used to reverse rotation direction or to bridge a gap between two shafts that must turn the same way.
What does a gear ratio of 1:1 mean?
A 1:1 gear ratio (direct drive) means the driver and driven gears have the same number of teeth, so the output turns at the same speed and torque as the input. There is no speed reduction or torque multiplication. Top gear in many transmissions is close to 1:1 for efficient cruising.
What is an overdrive gear ratio?
An overdrive ratio is less than 1 (for example 0.5, written 1:2), where the driven gear has fewer teeth than the driver. The output shaft spins faster than the input but delivers less torque. Overdrive gears are used in the highest transmission gears to reduce engine RPM at cruising speed and improve fuel economy.
How do you find output RPM from gear ratio?
Output RPM equals input RPM divided by the gear ratio. For a 1500 RPM input through a 3:1 reduction, output speed = 1500 / 3 = 500 RPM. For an overdrive of 1:2 (ratio 0.5) at 2000 RPM, output = 2000 / 0.5 = 4000 RPM. Speed and torque always move in opposite directions.
What is mechanical advantage in a gear system?
Mechanical advantage is the factor by which a gear set multiplies input torque, and for an ideal gear pair it equals the gear ratio. A 3:1 reduction has a mechanical advantage of 3, tripling the torque. Real systems lose a few percent to friction, so the actual mechanical advantage is slightly lower than the ideal gear ratio.