Gear Modulus Calculator

Rebbeca Jones

Rebbeca Jones

Gear Modulus Calculator

Calculate Metric Module (m), Pitch Diameter, or Tooth Count using ISO standard spur gear geometry.

Use this mode to identify an unknown gear by measuring its total width (OD) and counting teeth.

Measure from tip-to-tip across the center of the gear.

Calculated Module
0
Pitch Diameter (d)
Outside Diameter (da)
Whole Depth (h)
Circular Pitch (p)

What Is Gear Modulus?

Gear modulus is a metric measurement that defines tooth size.
In simple words, it tells you how large or small the gear teeth are.

The formula is:

Modulus (m) = Pitch Diameter (d) ÷ Number of Teeth (z)

  • A small modulus means fine, small teeth
  • A large modulus means thick, strong teeth

Two gears can only mesh properly if they have:

  • The same modulus
  • The same pressure angle

This is why modulus is a core value in gear design.


Why a Gear Modulus Calculator Is Useful

Manual gear calculations are easy to get wrong, especially when converting units or standards. This calculator removes that risk.

With one tool, you can:

  • Calculate modulus from diameter and teeth
  • Convert Diametral Pitch (DP) to metric modulus
  • Convert Circular Pitch (CP) to modulus
  • View full involute gear geometry
  • Switch between millimeters and inches

It is useful for:

  • Mechanical engineers
  • CNC machinists
  • Gear designers
  • Students and educators
  • Anyone working with gear drawings

Calculation Methods Supported by the Calculator

This calculator supports three standard ways to find gear modulus.


1. Pitch Diameter and Number of Teeth (Metric Standard)

This is the most direct and accurate method.

You enter:

  • Pitch Diameter (d)
  • Number of Teeth (z)

The calculator computes:

m = d ÷ z

This method is best when you already have a gear drawing or measured dimensions.


2. Convert from Diametral Pitch (Imperial Standard)

Diametral Pitch (DP) is commonly used in US and imperial systems. It measures how many teeth fit into one inch of diameter.

The conversion formula is:

m = 25.4 ÷ DP

The calculator handles this automatically and also estimates the rest of the gear geometry.

This is ideal when converting:

  • Old drawings
  • Imported gear specs
  • Inch-based designs to metric

3. Convert from Circular Pitch

Circular pitch is the distance between corresponding points on adjacent teeth, measured along the pitch circle.

The formula is:

m = Circular Pitch ÷ π

This option is helpful when circular pitch is given instead of diameter or DP.


Technical Parameters Explained in Plain English

Pressure Angle

The pressure angle affects how force moves between meshing teeth.

Common options:

  • 14.5° – Older standard, smoother but weaker
  • 20° – Modern standard, strong and widely used
  • 25° – High strength, higher load capacity

Most modern gears use 20°, which is why it is selected by default.


Output Units

You can choose:

  • Metric (mm)
  • Imperial (inches)

The calculator keeps internal accuracy and converts only for display.


What the Calculator Shows After Analysis

This is more than a basic modulus tool. It gives you full gear geometry.

Key Results Displayed

  • Gear Modulus (m)
  • Pitch Diameter
  • Diametral Pitch (DP)
  • Addendum
  • Dedendum
  • Circular Pitch
  • Outside Diameter
  • Total Tooth Depth
  • Base Circle Diameter

You also get a visual bar showing the ratio between addendum and dedendum. This makes tooth proportions easy to understand at a glance.


Understanding Addendum and Dedendum

  • Addendum is the height of the tooth above the pitch circle
  • Dedendum is the depth below the pitch circle

In standard metric gears:

  • Addendum = 1 × modulus
  • Dedendum = 1.25 × modulus

The calculator applies these standards automatically.


Engineer’s Insight Feature

One unique part of this calculator is the Engineer’s Insight box.

Based on your modulus value, it explains what the result means in practice.

Examples:

  • Small modulus → precision gears, robotics, instruments
  • Medium modulus → standard industrial gears
  • Large modulus → heavy-duty, high-load applications

It also warns about design risks, such as interference with low tooth counts at certain pressure angles.

This makes the calculator useful not just for numbers, but for design decisions.


Why This Gear Modulus Calculator Stands Out

This tool is designed for real users, not just formulas.

Key strengths:

  • Clear input modes
  • Automatic unit conversion
  • Full involute geometry output
  • Visual feedback
  • Practical engineering guidance
  • Mobile-friendly and fast

You do not need spreadsheets, handbooks, or extra charts.


When You Should Use This Calculator

Use it when:

  • Designing a new gear
  • Checking an existing gear size
  • Converting DP to metric modulus
  • Teaching or learning gear fundamentals
  • Preparing CNC or manufacturing data

If gear teeth must mesh correctly, this calculator helps you get it right the first time.