gear ratio calculator

Interactive Gear Ratio Calculator

Enter the teeth count for your driving and driven gears. Optionally add RPM and wheel diameter to estimate output speed and vehicle speed.

Used only for speed and gear-inches estimates.

What is a gear ratio?

A gear ratio tells you how many times one gear turns relative to another. It is one of the most useful numbers in mechanical design because it directly affects speed, torque, and feel. Whether you're tuning a bicycle drivetrain, selecting transmission gearing for a vehicle, or designing a robot arm, gear ratio choices determine how your system performs.

In this calculator, we define:

  • Driving gear = the input gear (connected to the motor, crank, or engine)
  • Driven gear = the output gear (receives power from the driving gear)

Gear ratio formula used by this calculator

For a two-gear pair, the key relationships are:

Gear Ratio = Driven Teeth / Driving Teeth
Output RPM = Input RPM × (Driving Teeth / Driven Teeth)
Ideal Torque Multiplier = Driven Teeth / Driving Teeth

If the ratio is greater than 1, you get a reduction: output turns slower but with more torque. If the ratio is less than 1, you get overdrive: output turns faster but with less torque.

How to use this gear ratio calculator

Step 1: Enter tooth counts

Put the tooth count of your input gear in Driving Gear Teeth and your output gear in Driven Gear Teeth. Tooth count should always be a positive number.

Step 2: Optionally enter input RPM

If you know motor or crank speed, enter it to compute output RPM. This helps when you're trying to match target speed in a machine, wheel, or spindle.

Step 3: Optionally add wheel diameter

If your driven gear is connected to a wheel, add wheel diameter to estimate:

  • Gear inches (commonly used in cycling)
  • Linear speed in mph and km/h

Worked example

Suppose your driving gear has 20 teeth and your driven gear has 40 teeth:

  • Gear Ratio = 40 ÷ 20 = 2.00:1
  • Output RPM multiplier = 20 ÷ 40 = 0.50×
  • If input RPM is 1200, output RPM = 1200 × 0.50 = 600 RPM

This is a classic speed reduction setup: lower speed, higher torque.

Interpreting results correctly

High numerical ratio (e.g., 4:1)

  • Much slower output speed
  • Higher output torque
  • Great for climbing, starting loads, and precision motion

Low numerical ratio (e.g., 0.7:1)

  • Faster output speed
  • Lower output torque
  • Good for cruising speed and low-load, high-speed operation

Where gear ratio calculations are used

  • Bicycles: choosing chainring and cassette combinations for cadence and terrain
  • Automotive: transmission and differential tuning for acceleration versus highway efficiency
  • Robotics: matching motor characteristics to actuator force and control precision
  • Industrial equipment: conveyors, mixers, and machine tools requiring specific RPM and torque ranges

Common mistakes to avoid

  • Swapping driving and driven gears (this flips the interpretation)
  • Ignoring unit consistency when using wheel diameter
  • Assuming real systems are ideal (friction and losses reduce actual output)
  • Forgetting that multi-stage gear trains multiply overall ratios stage by stage

Final note

This calculator gives fast, practical estimates for design and planning. For precision engineering, always validate with real efficiency, bearing losses, chain/belt slip, and load-dependent behavior. Still, for quick drivetrain setup, this tool is an excellent starting point.

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