# Gear Module Calculator Calculate the gear module m. m = d/z = p/π. Solve the module from the pitch diameter d and tooth count z, or from the circular pitch p. Also returns the pitch diameter, circular pitch and addendum. > Canonical page: https://elysiatools.com/en/tools/gear-module-calculator - **Category:** Math & Numbers - **Keywords:** gear module, module, pitch diameter, circular pitch, gear tooth, m = d/z, gear design, mechanical engineering ## Overview The Gear Module Calculator is a precision engineering tool designed to determine the gear module (m) using either the pitch diameter (d) and tooth count (z) or the circular pitch (p). It instantly computes key gear parameters including the module, pitch diameter, circular pitch, and addendum to streamline mechanical design and manufacturing workflows. ## Inputs - **Calculation Mode** (select) - **Pitch Diameter d (mm)** (number): Used in 'Module from d and z' mode. - **Number of Teeth z** (number): Used in 'Module from d and z' mode. - **Circular Pitch p (mm)** (number): Used in 'Module from pitch p' mode. - **Decimal Places** (number) ## When to use - When designing spur or helical gears and needing to determine the standard module from physical dimensions like pitch diameter and tooth count. - When reverse-engineering an existing gear by measuring its circular pitch to find the matching module. - When verifying gear compatibility and calculating the addendum height for manufacturing specifications. ## How it works - Select the calculation mode: either 'Module from d and z' or 'Module from pitch p'. - Input the required parameters, such as pitch diameter and number of teeth, or the circular pitch. - Set the desired decimal precision for the output values. - Click calculate to generate the gear module, circular pitch, pitch diameter, and addendum height. ## Use cases - Determining the module of a custom gear during the CAD modeling phase of mechanical design. - Identifying replacement gear specifications for worn machinery by measuring the pitch diameter and counting the teeth. - Calculating circular pitch and addendum values to set up CNC milling or gear hobbing machines. ## Frequently asked questions ### What is a gear module? The gear module is the ratio of the pitch diameter to the number of teeth, representing the unit of size indicating how big or small the gear teeth are. ### How is the gear module calculated from the pitch diameter and teeth? It is calculated using the formula m = d / z, where d is the pitch diameter and z is the number of teeth. ### Can I calculate the module if I only know the circular pitch? Yes, select the 'Module from pitch p' mode and enter the circular pitch; the tool calculates it using m = p / π. ### What is the relationship between the module and the addendum? For standard full-depth teeth, the addendum (h_a) is equal to the module (m). ### What units are used for the calculations? The calculator uses millimeters (mm) for pitch diameter, circular pitch, addendum, and the resulting module. ## Related tools - [Absolute Value Calculator](https://elysiatools.com/en/tools/absolute-value-calculator): Calculate the absolute value of positive, negative, or decimal numbers and explain the sign relationship - [Adjusted R-Squared Calculator](https://elysiatools.com/en/tools/adjusted-r-squared-calculator): Calculate adjusted R squared from R squared, sample size, and predictor count - [Air Changes per Hour (ACH, n = Q/V)](https://elysiatools.com/en/tools/air-changes-per-hour): Compute the air change rate (ACH / n) of a room from the outdoor supply airflow Q and the room volume V: n = Q/V (1/h). Three modes: solve ACH (given Q and V), solve airflow (given n and V), or solve volume (given n and Q). Flow in m³/s/m³/h/CFM, volume in m³/ft³/L. 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Treat every result as preliminary, not a certified design.