Gear Ratio Calculator

✖Radius of pitch circle of wheel is radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.ⓘ Radius of Pitch Circle of Wheel [R_wheel]			+10% -10%
✖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.ⓘ Radius of Pitch Circle of Pinion [r]			+10% -10%

✖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.ⓘ Gear Ratio [G]

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Formula

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Gear Ratio

Formula

`"G" = "R"_{"wheel"}/"r"`

Example

`"1.215686"="12.4mm"/"10.2mm"`

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Gear Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Gear Ratio = Radius of Pitch Circle of Wheel/Radius of Pitch Circle of Pinion
G = R_wheel/r
This formula uses 3 Variables

Variables Used

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.
Radius of Pitch Circle of Wheel - (Measured in Meter) - Radius of pitch circle of wheel is radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.
Radius of Pitch Circle of Pinion - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Radius of Pitch Circle of Wheel: 12.4 Millimeter --> 0.0124 Meter (Check conversion here)
Radius of Pitch Circle of Pinion: 10.2 Millimeter --> 0.0102 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

G = R_wheel/r --> 0.0124/0.0102

Evaluating ... ...

G = 1.2156862745098

STEP 3: Convert Result to Output's Unit

1.2156862745098 --> No Conversion Required

FINAL ANSWER

1.2156862745098 ≈ 1.215686 <-- Gear Ratio

(Calculation completed in 00.004 seconds)

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 22 Toothed Gear Terminologies Calculators

Efficiency of Spiral Gears using Pitch Circle Diameter

Go Efficiency = (cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)*Pitch Circle Diameter of Gear 2*Speed of Gear 2)/(cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)*Pitch Circle Diameter of Gear 1*Speed of Gear 1)

Efficiency of Spiral Gears

Go Efficiency = (cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)*cos(Spiral Angle of Gear Teeth for Gear 1))/(cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)*cos(Spiral Angle of Gear Teeth for Gear 2))

Addendum of Pinion

Go Addendum of Pinion = Number of Teeth on Pinion/2*(sqrt(1+Number of Teeth on Wheel/Number of Teeth on Pinion*(Number of Teeth on Wheel/Number of Teeth on Pinion+2)*(sin(Pressure Angle of Gear))^2)-1)

Addendum of Wheel

Go Addendum of Wheel = Number of Teeth on Wheel/2*(sqrt(1+Number of Teeth on Pinion/Number of Teeth on Wheel*(Number of Teeth on Pinion/Number of Teeth on Wheel+2)*(sin(Pressure Angle of Gear))^2)-1)

Work Output on Driven

Go Work Output = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)*pi*Pitch Circle Diameter of Gear 2*Speed of Gear 2

Work Output on Driver

Go Work Output = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)*pi*Pitch Circle Diameter of Gear 1*Speed of Gear 1

Maximum Efficiency of Spiral Gears

Go Efficiency = (cos(Shaft Angle+Angle of Friction)+1)/(cos(Shaft Angle-Angle of Friction)+1)

Resisting Force Acting Tangentially on Driven

Go Resisting Force acting Tangentially on Driven = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)

Force Applied Tangentially on Driver

Go Force Applied Tangentially on Driver = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)

Axial Thrust on Driven

Go Axial Thrust on Driven = Resisting Force acting Tangentially on Driven*tan(Spiral Angle of Gear Teeth for Gear 2)

Axial Thrust on Driver

Go Axial Thrust on Driver = Force Applied Tangentially on Driver*tan(Spiral Angle of Gear Teeth for Gear 1)

Radius of Base Circle of Pinion

Go Radius of Base Circle of Pinion = Radius of Pitch Circle of Pinion*cos(Pressure Angle of Gear)

Radius of Base Circle of Wheel

Go Radius of Base Circle of Wheel = Radius of Pitch Circle of Wheel*cos(Pressure Angle of Gear)

Addendum of Rack

Go Addendum of Rack = (Number of Teeth on Pinion*(sin(Pressure Angle of Gear))^2)/2

Tangential Force on Gear Shaft

Go Tangential Force = Maximum Tooth Pressure*cos(Pressure Angle of Gear)

Normal Force on Gear Shaft

Go Normal Force = Maximum Tooth Pressure*sin(Pressure Angle of Gear)

Shaft Angle

Go Shaft Angle = Spiral Angle of Gear Teeth for Gear 1+Spiral Angle of Gear Teeth for Gear 2

Gear Ratio

Go Gear Ratio = Radius of Pitch Circle of Wheel/Radius of Pitch Circle of Pinion

Torque Exerted on Gear Shaft

Go Torque Exerted on Wheel = Tangential Force*Diameter of Pitch Circle/2

Gear Ratio given Number of Teeth on Wheel and Pinion

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

Module

Go Module = Diameter of Pitch Circle/Number of Teeth on Wheel

Contact Ratio

Go Contact Ratio = Path of Contact/Circular Pitch

Gear Ratio Formula

Gear Ratio = Radius of Pitch Circle of Wheel/Radius of Pitch Circle of Pinion
G = R_wheel/r

What is a good gearing ratio?

A gearing ratio higher than 50% is typically considered highly levered or geared. A gearing ratio lower than 25% is typically considered low-risk by both investors and lenders. A gearing ratio between 25% and 50% is typically considered optimal or normal for well-established companies.

How to Calculate Gear Ratio?

Gear Ratio calculator uses Gear Ratio = Radius of Pitch Circle of Wheel/Radius of Pitch Circle of Pinion to calculate the Gear Ratio, Gear ratio is the ratio of the number of teeth in the gear to the number of teeth in the pinion, the pinion being the smaller of the two gears in mesh. Gear Ratio is denoted by G symbol.

How to calculate Gear Ratio using this online calculator? To use this online calculator for Gear Ratio, enter Radius of Pitch Circle of Wheel (R_wheel) & Radius of Pitch Circle of Pinion (r) and hit the calculate button. Here is how the Gear Ratio calculation can be explained with given input values -> 1.215686 = 0.0124/0.0102.

FAQ

What is Gear Ratio?

Gear ratio is the ratio of the number of teeth in the gear to the number of teeth in the pinion, the pinion being the smaller of the two gears in mesh and is represented as G = R_wheel/r or Gear Ratio = Radius of Pitch Circle of Wheel/Radius of Pitch Circle of Pinion. Radius of pitch circle of wheel is radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space & 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.

How to calculate Gear Ratio?

Gear ratio is the ratio of the number of teeth in the gear to the number of teeth in the pinion, the pinion being the smaller of the two gears in mesh is calculated using Gear Ratio = Radius of Pitch Circle of Wheel/Radius of Pitch Circle of Pinion. To calculate Gear Ratio, you need Radius of Pitch Circle of Wheel (R_wheel) & Radius of Pitch Circle of Pinion (r). With our tool, you need to enter the respective value for Radius of Pitch Circle of Wheel & Radius of Pitch Circle of Pinion and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Gear Ratio?

In this formula, Gear Ratio uses Radius of Pitch Circle of Wheel & Radius of Pitch Circle of Pinion. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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