Spur Gear Cutting Calculation Formula

What Is Spur Gear Cutting?

Spur gears are among the most widely used gears in mechanical power transmission systems. Their straight teeth are cut parallel to the gear axis, making them simple to manufacture and highly efficient. Before machining a spur gear on a milling machine, important dimensions such as pitch diameter, outside diameter, addendum, dedendum, whole depth, and tooth thickness must be calculated accurately.

This page explains the standard formulas used for spur gear cutting calculations and provides a practical example that can be used in workshop and manufacturing applications.

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Standard Spur Gear Formulas

Gear Parameter	Formula
Pitch Diameter (D)	D = Module × Number of Teeth
Outside Diameter (OD)	OD = Module × (Number of Teeth + 2)
Addendum (a)	a = Module
Dedendum (b)	b = 1.25 × Module
Whole Depth (h)	h = 2.25 × Module
Working Depth	2 × Module
Tooth Thickness	1.5708 × Module

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Step-by-Step Spur Gear Calculation Example

Assume the following gear data:

• Module = 4 mm
• Number of Teeth = 30

Step 1: Calculate Pitch Diameter

Pitch Diameter = Module × Teeth
= 4 × 30
= 120 mm

Step 2: Calculate Outside Diameter

Outside Diameter = Module × (Teeth + 2)
= 4 × (30 + 2)
= 128 mm

Step 3: Calculate Addendum

Addendum = Module
= 4 mm

Step 4: Calculate Dedendum

Dedendum = 1.25 × Module
= 1.25 × 4
= 5 mm

Step 5: Calculate Whole Depth

Whole Depth = 2.25 × Module
= 2.25 × 4
= 9 mm

Step 6: Calculate Tooth Thickness

Tooth Thickness = 1.5708 × Module
= 1.5708 × 4
= 6.283 mm

These dimensions are then used to select the correct involute gear cutter and machine settings.

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Important Spur Gear Terms

Term	Description
Module	Metric gear size parameter used to determine tooth size.
Pitch Circle	Imaginary circle where mating gears theoretically roll together.
Addendum	Height of tooth above pitch circle.
Dedendum	Depth of tooth below pitch circle.
Whole Depth	Total tooth depth from top to root.
Tooth Thickness	Width of tooth measured on pitch circle.

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Applications of Spur Gears

• Industrial gearboxes
• Machine tools
• Conveyors
• Automotive systems
• Agricultural machinery
• Printing machines
• Packaging equipment
• Power transmission systems

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Advantages of Spur Gears

• Simple manufacturing process
• High efficiency
• Cost-effective design
• Easy maintenance
• Suitable for moderate and high speeds
• Excellent power transmission capability

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Frequently Asked Questions (FAQ)

What is the formula for pitch diameter?

Pitch Diameter = Module × Number of Teeth.

How do I calculate outside diameter of a spur gear?

Outside Diameter = Module × (Number of Teeth + 2).

What is module in gear design?

Module is the ratio of pitch diameter to the number of teeth and defines the size of gear teeth.

Why is spur gear calculation important?

Accurate calculations ensure proper gear meshing, smooth operation, reduced wear, and longer service life.

Can these formulas be used for milling machine gear cutting?

Yes. These formulas are standard values used before cutting spur gears on milling machines with dividing heads.

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Related Engineering Calculations

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• Differential Indexing Calculation
• Simple Indexing Calculation
• Worm Gear Cutting Calculation
• Gear Train Calculation