How to Calculate Speed from Gear Ratio: Step-by-Step Guide

Calculating speed from a gear ratio runs in two steps: find the gear ratio from the teeth counts, then divide the input RPM by that ratio to get the output RPM. The direction that often catches readers out is which gear is the driver and which is the driven. The driver is the input gear, powered by the motor or engine. The driven gear is the output gear, connected to the load. Getting them backwards inverts the ratio and gives the wrong result.

How Do You Find the Gear Ratio from Tooth Counts?

The gear ratio is the number of output (driven) teeth divided by the number of input (driver) teeth. This ratio describes how many times the input gear must rotate to complete one full rotation of the output gear.

Gear ratio formula: GR = T_driven ÷ T_driver

Variables:

• GR: gear ratio (dimensionless)
• T_driven: number of teeth on the driven (output) gear
• T_driver: number of teeth on the driver (input) gear

A gear ratio above 1 means the output spins slower than the input (a reduction). A gear ratio below 1 means the output spins faster than the input (an overdrive). A ratio of exactly 1 means both gears spin at the same speed.

Ratio orientation check: Always ask which shaft receives power from the motor (that is the driver) and which shaft drives the load (that is the driven). A common error is swapping the two, which inverts the ratio. If the driven gear is larger, the ratio is above 1 and speed reduces. If the driven gear is smaller, the ratio is below 1 and speed increases.

How Do You Calculate Output Speed from the Gear Ratio?

Once the gear ratio is known, divide the input RPM by it to find the output RPM:

Output speed formula: Output RPM = Input RPM ÷ GR

Equivalently: Output RPM = Input RPM × (T_driver ÷ T_driven)

Both expressions are the same formula. The first uses the pre-calculated gear ratio; the second uses the tooth counts directly.

To calculate output speed:

1. Identify the driver (input) gear teeth and driven (output) gear teeth.
2. Calculate the gear ratio by dividing driven teeth by driver teeth.
3. Divide input RPM by the gear ratio to find output RPM.

Gear Ratio Speed Examples: Reduction and Overdrive

Example 1: Gear Reduction (Driven Gear Larger)

Inputs: Driver gear = 20 teeth, Driven gear = 60 teeth, Input RPM = 1,500

Step 1: Calculate gear ratio GR = T_driven ÷ T_driver = 60 ÷ 20 = 3

Step 2: Calculate output RPM Output RPM = 1,500 ÷ 3 = 500 RPM (exact)

Result: The output shaft turns at 500 RPM. The driven gear is 3 times larger than the driver, so the output runs at one-third the input speed. Output torque increases by the same factor (3×), minus mechanical losses.

Example 2: Overdrive (Driven Gear Smaller)

Inputs: Driver gear = 60 teeth, Driven gear = 20 teeth, Input RPM = 500

Step 1: Calculate gear ratio GR = T_driven ÷ T_driver = 20 ÷ 60 = 0.333 (rounded to three decimal places)

Step 2: Calculate output RPM Output RPM = 500 ÷ 0.333 = 1,500 RPM (rounded to the nearest whole number)

Result: The output shaft turns at 1,500 RPM, three times the input speed. This is an overdrive configuration. Note the gear arrangement is the mirror of Example 1: the same tooth counts, but the smaller gear is now the driven output. Output torque decreases by the same factor.

Use the Gear Ratio Speed Calculator to test different tooth counts and input speeds.

What Is the Relationship Between Gear Ratio, Speed, and Torque?

Gear ratio, speed, and torque follow the same inverse relationship: as output speed decreases, output torque increases proportionally, and vice versa. A gear ratio of 3 reduces output speed to one-third of input speed but triples the output torque (before friction losses). This exchange is governed by the conservation of power: in an ideal (frictionless) gear pair, input power equals output power. Real gear systems lose a small fraction to friction and heat (typically 1 to 5 percent per gear mesh for well-lubricated spur gears), so the actual output torque is slightly less than the theoretical prediction.

This relationship is why gear reductions are used in high-torque, low-speed applications such as conveyor drives, hoists, and industrial mixers. Overdrive ratios are used where high output speed is needed with relatively lower torque, such as in bicycle top gears or some automotive overdrive transmission stages.

Sources

• Cotta Transmission: Gear Ratio Fundamentals, gear ratio calculation from tooth counts and application to speed and torque.
• Firgelli Automations: Gear Ratio Explained, step-by-step ratio and speed calculation with driver/driven terminology.

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