Gear Ratio Calculator
Find gear ratios and their effects on speed and torque.
Calculate
Formulas
Ratio = N_driven / N_driveRatio > 1: speed reduction, torque increase. Ratio < 1: speed increase, torque reduction.
Gear Ratios
A 3:1 ratio triples torque but reduces speed to 1/3. Bicycle gears: 0.6-4.0. Car 1st gear: ~3.5. Car 5th gear: ~0.8. Used in transmissions, clocks, robotics.
How Gear Ratio Works
A gear ratio describes how rotational speed and torque change between two meshed gears. It is the ratio of teeth on the driven gear to teeth on the driving gear:
Ratio = N_driven / N_driveN_driven is the number of teeth on the output gear and N_drive is the number on the input gear.
A ratio greater than 1 reduces speed and multiplies torque (a reduction gear). A ratio less than 1 increases speed and reduces torque (an overdrive). Speed and torque always trade off inversely.
Worked Examples
Driving gear 12 teeth, driven gear 36 teeth:
Ratio = 36 / 12 = 3:1
The output turns one-third as fast but with three times the torque.
If the input runs at 1500 rpm with a 3:1 reduction, output speed = 1500 / 3 = 500 rpm.
Speed and Torque Relationship
| Ratio | Output speed | Output torque | Use |
|---|---|---|---|
| > 1 (e.g. 4:1) | Lower | Higher | Heavy loads |
| 1:1 | Same | Same | Direct drive |
| < 1 (e.g. 1:2) | Higher | Lower | High speed |
Frequently Asked Questions
Does a gear ratio change power?
No. Ignoring friction losses, power in equals power out. Gears trade speed for torque (or vice versa) but cannot create power.
What is a gear train?
Multiple gear pairs in sequence. The overall ratio is the product of the individual ratios, allowing large reductions in a compact space.
Why use a reduction gear?
Motors often spin fast with low torque. A reduction gear converts that into the slower, higher-torque output needed to drive wheels, lifts, or machinery.