What is mechanical advantage?

Mechanical advantage is the factor by which a gear system multiplies input torque. A gear ratio of 3:1 provides a mechanical advantage of 3, tripling the input torque while reducing speed by one-third.

Why do cars have multiple gears?

Engines produce optimal power in a narrow RPM range. Multiple gear ratios allow the engine to stay in this range at various vehicle speeds. Low gears provide torque for starting, while high gears provide speed for cruising.

What is a compound gear train?

A compound gear train uses multiple pairs of gears on shared shafts to achieve very high or very low ratios. The total ratio is the product of individual stage ratios. A three-stage train with 3:1 each gives 27:1 overall.

Do gear ratios affect power?

No, gears trade speed for torque (or vice versa) but cannot create power. In a frictionless system, input power equals output power (P = torque × angular velocity). In practice, some power is lost to friction and heat.

What is a planetary gear system?

A planetary (epicyclic) gear system has a central sun gear, surrounding planet gears, and an outer ring gear. It is compact, efficient, and can produce multiple ratios from a single unit, which is why it is used in automatic transmissions and power tools.

Gear Ratio Calculator

Calculate gear ratios and output speed

Gear Ratio

Enter teeth counts

Driving Gear Teeth

Driven Gear Teeth

Input RPM

Formula

Ratio = Driven/Drive, Output RPM = Input RPM x (Drive/Driven)

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 as power is transmitted through a gear pair. A gear ratio greater than 1 (reduction) slows the output while multiplying torque; a ratio less than 1 (overdrive) speeds up the output while reducing torque.

Gear ratios are fundamental in mechanical engineering, automotive design, robotics, and industrial machinery. They allow engineers to match motor characteristics to load requirements — trading speed for torque or vice versa. In a car transmission, different gear ratios let the engine operate efficiently across a wide range of vehicle speeds.

How to Use This Calculator

Enter the number of teeth on the driving gear (input gear).
Enter the number of teeth on the driven gear (output gear).
Optionally, enter the input speed (RPM) to calculate output speed.
Click Calculate to see the gear ratio, output RPM, and torque multiplication factor.

Formula & Explanation

Gear Ratio = Teeth (driven) / Teeth (driving)
Output RPM = Input RPM / Gear Ratio
Output Torque = Input Torque × Gear Ratio × efficiency

For a gear ratio > 1: speed decreases, torque increases (torque multiplier = gear ratio). For ratio < 1: speed increases, torque decreases. In a gear train with multiple stages, multiply all individual ratios together for the total ratio.

Worked Examples

Example 1 — Basic Reduction

Driving gear: 20 teeth, Driven gear: 60 teeth. Ratio = 60/20 = 3:1. If input is 1,500 RPM, output = 1,500 / 3 = 500 RPM. Torque × 3.

Example 2 — Overdrive (Speed Increase)

Driving gear: 60 teeth, Driven gear: 20 teeth. Ratio = 20/60 = 0.333:1. Input 1,000 RPM → output 3,000 RPM. Torque ÷ 3.

Example 3 — Compound Gear Train

Stage 1: 20:60 = 3:1. Stage 2: 15:45 = 3:1. Total ratio = 3 × 3 = 9:1. Input 2,700 RPM → output 300 RPM. Torque × 9 (less losses).

Frequently Asked Questions

What does a 4:1 gear ratio mean?▾

A 4:1 ratio means the driving gear makes 4 full rotations for every 1 rotation of the driven gear. The output shaft rotates at 1/4 the input speed, but with 4 times the input torque (minus friction losses). This is a speed reduction and torque multiplication.

How do gear ratios affect vehicle performance?▾

Lower gear ratios (e.g., 1st gear, 3.5:1) provide high torque for acceleration and hill climbing. Higher gear ratios (e.g., 5th gear, 0.75:1 overdrive) allow high speeds at low engine RPM for fuel efficiency. The final drive ratio (differential) multiplies all transmission ratios.

Can gear ratio be a decimal?▾

Yes. A ratio of 0.5:1 means the output spins twice as fast as the input — this is called overdrive and is used in highway gear ratios to reduce engine speed. Most bicycle cassettes offer ratios ranging from about 0.5:1 to 4:1.

What is the difference between gear ratio and mechanical advantage?▾

They are closely related. In a gear pair, mechanical advantage = output torque / input torque ≈ gear ratio (accounting for efficiency). For simple machines, mechanical advantage = effort distance / load distance.

How do I calculate the gear ratio for a belt or chain drive?▾

The same formula applies: ratio = driven pulley/sprocket diameter ÷ driving diameter. For chains, count sprocket teeth instead of diameter. Belt and chain drives follow the same speed-torque tradeoff as gear pairs.