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Gear Ratio Formula

GoGear Ratio given Number of Teeth on Wheel and Pinion Formula

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The Gear Ratio is the ratio of output gear speed to the input gear speed or the ratio of number of teeth on gear to that on the pinion. Check FAQs

G = \frac{R wheel}{r}

G - Gear Ratio?R_wheel - Radius of Pitch Circle of Wheel?r - Radius of Pitch Circle of Pinion?

Gear Ratio Example

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With units

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Here is how the Gear Ratio equation looks like with Values.

Here is how the Gear Ratio equation looks like with Units.

Here is how the Gear Ratio equation looks like.

1.2157 = \frac{12.4}{10.2}

1.2157 = \frac{12.4mm}{10.2mm}

1.2157 = \frac{12.4}{10.2}

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Gear Ratio Solution

Follow our step by step solution on how to calculate Gear Ratio?

FIRST Step Consider the formula

G = \frac{R wheel}{r}

Next Step Substitute values of Variables

∴

G = \frac{12.4mm}{10.2mm}

Next Step Convert Units

∴

G = \frac{0.0124m}{0.0102m}

Next Step Prepare to Evaluate

∴

G = \frac{0.0124}{0.0102}

Next Step Evaluate

∴

G = 1.2156862745098

LAST Step Rounding Answer

∴

G = 1.2157

Gear Ratio Formula Elements

Variables

Gear Ratio

The Gear Ratio is the ratio of output gear speed to the input gear speed or the ratio of number of teeth on gear to that on the pinion.

Symbol: G

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Gear Ratio

Radius of Pitch Circle of Wheel

Radius of pitch circle of wheel is radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.

Symbol: R_wheel

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Pitch Circle of Wheel

Radius of Pitch Circle of Pinion

The Radius of Pitch Circle of Pinion is the radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Pitch Circle of Pinion

Other Formulas to find Gear Ratio

Go Gear Ratio given Number of Teeth on Wheel and Pinion

G = \frac{T}{Z p}

Other formulas in Toothed Gear Terminologies category

Go Torque Exerted on Gear Shaft

τ = P t \cdot \frac{d pitch circle}{2}

Go Work Output on Driven

w = R \cdot \cos (α 2 + Φ) \cdot π \cdot d 2 \cdot N 2

Go Work Output on Driver

w = R \cdot \cos (α 1 - Φ) \cdot π \cdot d 1 \cdot N 1

Go Addendum of Pinion

A p = \frac{Z p}{2} \cdot (\sqrt{1 + \frac{T}{Z p} \cdot (\frac{T}{Z p} + 2) \cdot {(\sin (Φ gear))}^{2}} - 1)

How to Evaluate Gear Ratio?

Gear Ratio evaluator uses Gear Ratio = Radius of Pitch Circle of Wheel/Radius of Pitch Circle of Pinion to evaluate the Gear Ratio, Gear Ratio formula is defined as a measure of the ratio of the rotational speed of the wheel gear to that of the pinion gear in a toothed gear system, providing a fundamental characteristic of the gear train's overall performance and efficiency. Gear Ratio is denoted by G symbol.

How to evaluate Gear Ratio using this online evaluator? To use this online evaluator for Gear Ratio, enter Radius of Pitch Circle of Wheel (R_wheel) & Radius of Pitch Circle of Pinion (r) and hit the calculate button.

FAQs on Gear Ratio

What is the formula to find Gear Ratio?

The formula of Gear Ratio is expressed as Gear Ratio = Radius of Pitch Circle of Wheel/Radius of Pitch Circle of Pinion. Here is an example- 1.215686 = 0.0124/0.0102.

How to calculate Gear Ratio?

With Radius of Pitch Circle of Wheel (R_wheel) & Radius of Pitch Circle of Pinion (r) we can find Gear Ratio using the formula - Gear Ratio = Radius of Pitch Circle of Wheel/Radius of Pitch Circle of Pinion.

What are the other ways to Calculate Gear Ratio?

Here are the different ways to Calculate Gear Ratio-

Gear Ratio=Number of Teeth on Wheel/Number of Teeth on Pinion

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Gear Ratio Formula

​GoGear Ratio given Number of Teeth on Wheel and Pinion Formula

Gear Ratio Example

Gear Ratio Solution

Gear Ratio Formula Elements

Other Formulas to find Gear Ratio

Other formulas in Toothed Gear Terminologies category

How to Evaluate Gear Ratio?

FAQs on Gear Ratio

Variable Name

GoGear Ratio given Number of Teeth on Wheel and Pinion Formula