Transmission (Gear Ratio) Calculator

Calculate the overall gear ratio, output speed, output torque, and mechanical advantage of a gear transmission system from input/output gear teeth or RPM values.

GEAR RATIO
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Output Speed
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Output Torque
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Input Power
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Output Power
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What Is a Gear Ratio?

A gear ratio is the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear. It determines how speed and torque are transformed through a gear system. A gear ratio greater than 1 indicates speed reduction with torque multiplication, while a ratio less than 1 means speed increase with torque reduction.

Gear transmissions are fundamental to mechanical engineering and appear in automobiles, bicycles, industrial machinery, clocks, and power tools. They allow engineers to match the speed and torque characteristics of a motor to the requirements of the load.

Transmission Formulas

Gear Ratio = Driven Teeth / Driving Teeth
Output Speed = Input Speed / Gear Ratio
Output Torque = Input Torque × Gear Ratio × Efficiency
Power = Torque × 2π × RPM / 60

Common Gear Types

TypeEfficiencyTypical Use
Spur Gears94-98%Parallel shafts, simple reduction
Helical Gears94-98%Quieter than spur, automotive
Bevel Gears93-97%Right-angle drives
Worm Gears50-90%High reduction ratio, self-locking
Planetary95-97%Compact high-ratio, automatic transmissions

Frequently Asked Questions

What is mechanical advantage?

Mechanical advantage is the factor by which a mechanism multiplies force or torque. For gears, the mechanical advantage equals the gear ratio. A 3:1 ratio triples the torque while reducing speed by 1/3 (minus friction losses).

How does efficiency affect output?

Gear mesh losses from friction, windage, and oil churning reduce the output power. Each gear stage typically loses 2-5% efficiency. For multi-stage systems, efficiencies multiply: three stages at 95% each give 0.95^3 = 85.7% overall efficiency.

Can gears increase both speed and torque simultaneously?

No. Conservation of energy dictates that power in equals power out (minus losses). Gears trade speed for torque or vice versa. Increasing torque necessarily decreases speed, and increasing speed decreases torque proportionally.