Gear Modulus Calculator

The Gear Modulus Calculator helps you determine the modulus of a gear, which is a key dimension in metric gear systems. This modulus represents the size of the gear teeth and is essential for designing gears that work together smoothly. It plays a major role in defining gear compatibility, performance, and reliability.

In simple terms, modulus tells you how big each tooth of the gear is. When two gears are to be meshed together, they must have the same modulus to ensure proper engagement. This calculator saves time and eliminates guesswork by providing accurate values based on the gear's pitch diameter and the number of teeth.

This tool is widely used by mechanical engineers, product designers, and anyone working with gear trains in machines or robotics. It falls under the category of mechanical engineering design calculators.

formula

Gear Modulus Formula:

Modulus (m) = Pitch Diameter ÷ Number of Teeth

Variables Explanation:

Modulus (m) is the ratio of the pitch diameter to the number of teeth, expressed in millimeters per tooth (mm/tooth)

Pitch Diameter is the diameter of the pitch circle of the gear (in millimeters)

Number of Teeth is the total number of teeth on the gear

Rearranged Formulas (if needed):

Pitch Diameter = Modulus × Number of Teeth
Number of Teeth = Pitch Diameter ÷ Modulus

Gear Modulus Reference Table

Below is a helpful reference table showing standard gear modulus values, their corresponding pitch diameters, and example tooth counts. These values are often used in metric gear designs and are useful for rough estimations and quick selections.

Standard Modulus (mm/tooth)	Example Number of Teeth	Pitch Diameter (mm)
1	20	20
1.5	30	45
2	25	50
2.5	40	100
3	35	105
4	50	200
5	60	300

This table gives users a quick idea of the expected pitch diameter when choosing a certain modulus and number of teeth. Designers often use these standard moduli in gear selection processes.

Example

Let’s say you have a gear with a pitch diameter of 60 mm and 20 teeth.

Use the formula:

Modulus (m) = Pitch Diameter ÷ Number of Teeth
Modulus (m) = 60 ÷ 20
Modulus (m) = 3 mm/tooth

So, the modulus of the gear is 3 mm per tooth. This means the gear teeth are relatively large and the gear may be suitable for higher load applications.

Now, suppose you know the modulus and want to find the pitch diameter. For a gear with 30 teeth and a modulus of 2 mm:

Pitch Diameter = Modulus × Number of Teeth
Pitch Diameter = 2 × 30
Pitch Diameter = 60 mm

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