Gear Ratio Calculator
Calculate gear ratio, output RPM, and torque for single and multi-stage gear trains. Supports up to 4 stages with configurable efficiency.
Introduction
Every gear stage trades speed for torque, and the Gear Ratio Calculator quantifies that trade: enter driving and driven tooth counts plus input RPM and torque, and it returns the ratio, output speed, and output torque — including the efficiency loss that ideal-gear arithmetic ignores. It handles single stages and stacked multi-stage trains, which is where mental math fails first, since ratios multiply and so do the per-stage losses. Use it to size motor-gearbox pairings, predict spindle torque, or work out what a transmission swap does to wheel speed.
How it Works
The ratio is driven teeth ÷ driving teeth. Output speed = input RPM ÷ ratio, and output torque = input torque × ratio × efficiency, with a default efficiency of 0.98 per stage representing a well-lubricated spur mesh's roughly 2% loss. For multi-stage trains the overall ratio is the product of stage ratios and the efficiency compounds — three stages at 0.98 deliver about 94% of ideal torque. A 12T pinion driving a 60T gear (ratio 5) at 1800 RPM and 10 N·m thus outputs 360 RPM and 10 × 5 × 0.98 = 49 N·m.
Usage Scenarios
- Sizing a gearmotor: confirming that a 30:1 two-stage train turns a 3000 RPM motor into 100 RPM at the output with usable torque after compounded losses.
- Predicting realistic output torque for a robot joint, where the 0.98-per-stage factor across four stages knocks 8% off the catalog ideal.
- Choosing tooth counts for a 3:1 camera-slider drive and checking that the resulting output speed matches the target traverse rate.
- Reverse-engineering a salvaged gearbox by counting teeth on each mesh and multiplying stage ratios to identify its overall reduction.
- Comparing a single 9:1 stage against a 3:1 + 3:1 two-stage layout, weighing the extra mesh loss against packaging size.
FAQ
Why does output torque include an efficiency factor?
Real meshes lose energy to sliding friction at the tooth flanks. The default 0.98 reflects a typical lubricated spur stage; worms and hypoids run far lower and need their own figures.
How do multi-stage ratios combine?
Multiply them — a 4:1 stage into a 5:1 stage gives 20:1 overall. Efficiency also multiplies, so each added stage costs roughly 2% of the remaining torque at the default value.
Does a higher ratio always mean more torque?
More output torque, less output speed — power is conserved minus losses. The ratio cannot create power; it only re-proportions speed and torque to suit the load.
Do these formulas apply to belts and chains too?
Yes — substitute pulley pitch diameters or sprocket teeth for gear teeth. Only the efficiency differs: chains run about 0.97–0.98, V-belts typically 0.94–0.96 due to slip.