Gear Ratio Calculator — How to Calculate Gear Ratio Instantly

Compute the gear ratio from driving and driven gear teeth. Learn the formula, see step‑by‑step examples, and understand torque & speed trade‑offs.

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Gear Ratio Calculator

Enter the number of teeth on the driving gear and the driven gear. The ratio determines torque multiplication and speed reduction.

Enter teeth counts and click Calculate Gear Ratio to see the result.

Gear Ratio Formula Explained

The gear ratio formula is the relationship between the number of teeth on two meshing gears. It determines how many times the driving gear must rotate to turn the driven gear once.

Gear Ratio = N₂ / N₁

Variable Definitions

  • N₁ – Number of teeth on the driving gear (input)
  • N₂ – Number of teeth on the driven gear (output)
  • Gear Ratio – The torque multiplier and speed divisor

If the ratio is greater than 1, torque increases and speed decreases (reduction). If less than 1, it’s an overdrive – speed increases and torque decreases.

How to Calculate Gear Ratio

Calculating a gear ratio from teeth counts is straightforward. Follow these steps:

  1. Identify the driving gear – the gear that receives the input power (e.g., motor shaft).
  2. Identify the driven gear – the gear that receives motion from the driving gear.
  3. Count the teeth – record the number of teeth on each gear (N₁ and N₂).
  4. Divide driven by driving – Gear Ratio = N₂ / N₁.
  5. Interpret the result – a ratio of 3 means the driving gear rotates 3 times per one rotation of the driven gear, tripling torque and cutting speed to one‑third.

For example, 12‑tooth driving gear and 36‑tooth driven gear: ratio = 36/12 = 3:1.

Gear Ratio Calculation Examples

Example 1: Torque Multiplication

Driving gear 15 teeth, driven gear 45 teeth.

Gear Ratio = 45 / 15 = 3 : 1
Torque is tripled, speed is one‑third.

Example 2: Overdrive (Speed Increase)

Driving gear 40 teeth, driven gear 20 teeth.

Gear Ratio = 20 / 40 = 0.5 : 1
Output speed doubles, torque halves.

Example 3: Exact 1:1 Ratio

Both gears have 24 teeth.

Gear Ratio = 24 / 24 = 1 : 1
No change in speed or torque – only direction may be reversed.

Real‑World Gear Ratio Applications

  • Bicycles: Changing gear ratios alters pedalling effort vs. wheel speed – high ratio for climbing, low ratio for speed.
  • Automotive transmissions: Low gears (high ratio) for acceleration, high gears (low ratio) for fuel‑efficient cruising.
  • Industrial machinery: Conveyor belts, mixers, and lifts use reduction gears to multiply torque for heavy loads.
  • Clock mechanisms: Precision gear ratios translate seconds to minutes to hours.
  • Robotics: Servo motors use gearboxes to match required torque and speed.
  • Wind turbines: Gearboxes step up slow rotor speed to generator‑friendly RPM.

People Also Ask

Gear Ratio = Number of Teeth on Driven Gear / Number of Teeth on Driving Gear (N₂/N₁). It tells how many input revolutions are needed for one output revolution.
Count the teeth on both gears. Divide the driven gear teeth by the driving gear teeth. For example, 10 driving teeth and 30 driven teeth give 30/10 = 3:1.
A 3:1 ratio means the driving gear turns three times to rotate the driven gear once. This triples the torque and reduces the output speed to one‑third.
If the driven gear has fewer teeth, the gear ratio is less than 1 (overdrive). Output speed increases while torque decreases, common in vehicle overdrive gears.
Torque is multiplied by the gear ratio; speed is divided by the ratio (ignoring losses). A high ratio increases torque and reduces speed; a low ratio (overdrive) does the opposite.

Frequently Asked Questions

Gear ratio compares how many times one gear turns relative to another. It’s the number of driven gear teeth divided by driving gear teeth, directly affecting torque and speed.
Yes, if the driven gear has fewer teeth than the driving gear. This is called overdrive – output speed increases and torque decreases.
Multiply the ratios of each pair of meshing gears. For two stages: total ratio = (N₂/N₁) × (N₄/N₃), where N₁ drives N₂, and N₃ (on same shaft as N₂) drives N₄.
For meshing gears, the ratio is determined by teeth count, not diameter. However, teeth count is proportional to diameter for the same module (pitch). So diameter ratio equals teeth ratio.
Yes, the gear ratio can be a decimal (e.g., 0.75 : 1). In practice, ratios are often expressed as a ratio of whole numbers (e.g., 3:4), but decimal form is also used.

Gear Ratio Glossary

Gear Ratio

The relationship between the teeth counts of two meshing gears, determining torque and speed changes.

Driving Gear

The gear that receives input power and transmits motion to another gear.

Driven Gear

The gear that receives motion from the driving gear; its rotation is determined by the ratio.

Teeth Count

The number of projections (teeth) on a gear; directly used in ratio calculation.

Torque

Rotational force. A higher gear ratio multiplies torque at the expense of speed.

RPM

Revolutions per minute. The output RPM = input RPM / gear ratio (ignoring losses).

Overdrive

A gear ratio less than 1:1 where the driven gear rotates faster than the driving gear, reducing torque.

Reduction Gear

A gear pair with a ratio > 1:1 that reduces output speed while increasing torque.

Editorial Review & Methodology

This gear ratio calculator was built and reviewed by the NumbrWiz Editorial Team. The formula is a fundamental principle in mechanical engineering, verified against standard textbooks and gear design handbooks.

  • Formula verification: Cross‑checked with authoritative sources on machine design and kinematics.
  • Edge case testing: Tested with extreme teeth counts, identical gears, and decimal outputs.
  • UX design: Clear input validation and step‑by‑step breakdown ensure understanding.

Transparency note: All calculations run client‑side in your browser. No data is ever collected, stored, or transmitted. Results are for educational purposes; verify critical engineering calculations independently.

Page last reviewed: May 2026 · NumbrWiz Editorial Team