How do I calculate gear ratio?

Gear ratio = Number of teeth on the driven gear ÷ Number of teeth on the driver gear. For example, driver = 20 teeth, driven = 60 teeth: GR = 60 / 20 = 3:1 (3.0:1 speed reduction).

How does a gear ratio affect speed and torque?

A gear ratio greater than 1 (e.g., 3:1) reduces output speed and multiplies torque. A ratio less than 1 (e.g., 0.346:1 overdrive) increases output speed while reducing torque.

What is a compound gear ratio?

A compound gear ratio is the overall ratio of a multi-stage gear train. It equals the product of all individual stage ratios. For two 3:1 stages, the compound ratio is 3 × 3 = 9:1.

What is gear mesh efficiency?

Gear mesh efficiency is the percentage of input power transferred to the output shaft. Spur gears are typically 95–99% efficient, while worm gears range from 30–90% (with single-start high-ratio worms commonly 30–60%) due to sliding contact friction.

Gear Ratio Speed Calculator

Q: What is a gear ratio?

A gear ratio describes the relationship between the number of teeth on the input (driver) gear and the output (driven) gear (GR = Driven ÷ Driver). It determines how speed and torque are transformed.

Q: How do I calculate vehicle speed from engine RPM and gear ratio?

Theoretical vehicle speed (MPH) = (Engine RPM × π × Tire Diameter in inches) / (Transmission Ratio × Final Drive Ratio × 63,360) × 60. Real road speed may vary slightly due to tire tread wear and wheel slip.

Calculate gear ratios, output shaft RPM, torque multiplication, and theoretical vehicle road speed for mechanical gear trains and automotive drivetrains.

System Configuration

Configure your drivetrain mode, gear mesh type, and calculation target.

Target Parameter ("Solve For")

Gear Mesh Type (Automatically updates efficiency)

Quick Gear Presets

How to Use the Gear Ratio Speed Calculator

Calculate gear ratios, output shaft RPM, torque multiplication, and theoretical vehicle speed for mechanical gear trains, bicycles, automotive drivetrains, and industrial machines. Enter gear teeth counts and input RPM, or switch to vehicle mode.

Choose Gear & Shaft Speed for mechanical gear trains, or Automotive Vehicle Speed for drivetrains.

Select what to solve for: Output RPM, Gear Ratio, Required Input RPM, or Required Driven Teeth.

Enter driver and driven gear teeth counts for each stage of your gear train.

Input your shaft or engine RPM to compute the output speed and ratio.

Optionally expand Advanced Options to include torque and per-stage efficiency analysis.

Why Calculate Gear Ratios?

Gear ratios control the tradeoff between speed and torque in any mechanical system. Understanding how gear teeth counts affect output RPM and torque multiplication is essential for designing motors, gearboxes, bicycles, and automotive drivetrains.

Multi-Stage Support: Compound gear trains up to 4 stages with per-stage efficiency.
Vehicle Mode: Convert engine RPM to theoretical road speed using transmission and final drive ratios.

Gear Ratio Formula

Gear ratio is the foundation of all mechanical speed and torque transformations. Per the speed ratio of gears defined by KHK, GR = Driven Teeth ÷ Driver Teeth, and Output RPM = Input RPM ÷ GR. For multi-stage gear trains, the overall ratio is the product of each individual stage ratio.

Step 1: Calculate Gear Ratio

GR = Driven Teeth ÷ Driver TeethOutput RPM = Input RPM ÷ GR

Step 2: Theoretical Vehicle Speed

Overall Ratio = Trans × Final DriveMPH = (RPM × π × Tire Ø) ÷ (Ratio × 63,360) × 60

Identify Gear Teeth

Count or look up the number of teeth on the driver (input) and driven (output) gears for each stage.

Calculate Stage Ratios

Divide each driven tooth count by its driver tooth count. A ratio greater than 1 reduces speed and multiplies torque.

Compound Multi-Stage

Multiply individual stage ratios together to get the overall multi-stage gear ratio for compound gear trains.

Apply to Speed or Torque

Divide input RPM by overall ratio to get output RPM. Use the gear output torque and speed formulas to find torque multiplication, efficiency losses, and power transmission.

Bicycle Overdrive Example

A road bike with a 52T chainring (driver) driving an 18T sprocket (driven) at 90 RPM pedal cadence. Driver: 52, Driven: 18, Input: 90 RPM.

Gear Ratio0.346 : 1 (Overdrive)

FormulaOutput = 90 ÷ 0.346

Rear Wheel Speed260 RPM

*Note: Bicycle chain sprockets are connected by a roller chain, so both driver and driven sprockets rotate in the SAME direction.

Typical Gear Efficiency by Type

Per-mesh efficiency ranges. Worm gears use sliding contact instead of rolling contact, which lowers efficiency (commonly 30–60% for single-start high-reduction ratios).

Gear Type	Efficiency Range
Spur Gear	95–99%
Helical Gear	96–99%
Bevel Gear	93–98%
Worm Drive	30–90%

Units & Rotation Notes

Gear ratios are dimensionless ratios of teeth (Driven ÷ Driver). Vehicle speed is a theoretical calculation assuming zero wheel slip and nominal tire height. Because tire revolutions per mile vary with load, inflation, and tread wear, calculated road speed may differ slightly from actual speed.

Pro Tip — Rotation Direction

"External meshing gears rotate in OPPOSITE directions. Chain sprockets and internal ring gears rotate in the SAME direction."

Calculation Notes

Worm drive "driver" field uses worm starts (threads), not teeth. Ratio = Wheel Teeth ÷ Worm Starts. Efficiency depends strongly on lead angle, sliding speed, and lubrication.

GR > 1 = speed reduction, torque increase

GR < 1 = overdrive (speed increase, torque decrease)

External gear mesh = opposite rotation

Chain drive / sprockets = same direction rotation

Gear Ratio Speed FAQ

Essential answers for gear ratios, mechanical speed reduction, torque multiplication, and drivetrain mechanics.

What is a gear ratio and how is it calculated?

A gear ratio (GR) is the ratio of the number of teeth on the driven gear to the number of teeth on the driver gear (GR = Driven Teeth ÷ Driver Teeth). For example, a 60-tooth driven gear powered by a 20-tooth driver gear has a gear ratio of 3:1.

How does gear ratio affect speed and torque?

Gear ratio inversely affects speed and directly affects torque. A gear reduction (ratio > 1) reduces output shaft RPM while increasing output torque by the same factor (minus mechanical friction losses). An overdrive ratio (< 1) increases speed but decreases torque.

How do you calculate compound gear ratios?

In a multi-stage compound gear train, the overall gear ratio is calculated by multiplying the individual gear ratios of each stage together: GR_total = GR1 × GR2 × GR3.

Why is worm gear efficiency lower than spur or helical gears?

Worm gears transfer motion through sliding contact rather than rolling contact. This sliding friction generates heat and results in lower efficiency (typically 30% to 90%, with single-start high-ratio worms commonly 30–60%), compared to spur or helical gears which achieve 95% to 99% efficiency.

How do you calculate vehicle speed from engine RPM and gear ratio?

Theoretical vehicle speed depends on engine RPM, transmission gear ratio, final drive axle ratio, and tire diameter: Vehicle Speed (MPH) = (Engine RPM × Tire Diameter × π × 60) ÷ (Transmission Ratio × Final Drive Ratio × 63,360). Actual road speed may vary slightly due to wheel slip and tire tread wear.

What is the difference between driver and driven gears?

The driver gear is attached to the input power source (motor, engine, or crank). The driven gear is rotated by the driver gear and delivers power to the output shaft or wheel.