Gear Module Calculator
Calculate gear module (m) from common input methods, then get key derived gear dimensions instantly.
Assumes standard full-depth involute proportions for derived values (addendum = 1m, dedendum ≈ 1.25m).
What Is Gear Module?
Gear module is one of the most important parameters in metric gear design. It defines tooth size and the scale of the gear. In simple terms, module tells you how many millimeters of pitch diameter you get per tooth.
The basic definition is:
- m = d / z
- where m is module (mm), d is pitch diameter (mm), and z is number of teeth
Two gears must have the same module (and compatible pressure angle) to mesh correctly.
Formulas Used in This Calculator
Direct module formulas
- From pitch diameter and teeth: m = d / z
- From outside diameter and teeth (standard spur gear): m = da / (z + 2)
- From diametral pitch: m = 25.4 / DP
- From circular pitch: m = p / π
Derived values calculated after module is found
- Pitch diameter: d = m × z
- Outside diameter: da = m × (z + 2)
- Approx. root diameter: df = m × (z − 2.5)
- Circular pitch: p = π × m
- Diametral pitch: DP = 25.4 / m
- Base diameter: db = d × cos(α)
How to Use the Gear Module Calculator
- Select your calculation method.
- Enter the required fields for that method.
- Optionally add tooth count to generate diameters and geometry values.
- Click Calculate to view results.
If you choose a method that needs tooth count and diameter, both values are required. If you calculate from DP or circular pitch, module can still be found without tooth count, but diameters require z.
Example Calculation
Suppose you have a 24-tooth gear and measure pitch diameter as 48 mm.
- Module: m = 48 / 24 = 2.0 mm
- Outside diameter: da = 2.0 × (24 + 2) = 52 mm
- Circular pitch: p = π × 2.0 ≈ 6.283 mm
This confirms a standard module-2 gear.
Module vs Diametral Pitch
Metric systems usually use module. Inch-based systems commonly use diametral pitch. They represent the same concept (tooth size) in different units:
- m = 25.4 / DP
- DP = 25.4 / m
When converting across standards, keep pressure angle and tooth profile standards in mind as well.
Practical Design Notes
1) Match module exactly
Even a small mismatch in module prevents proper meshing and quickly damages teeth.
2) Verify pressure angle
Common values are 20° and 14.5°. Mismatched pressure angle causes poor contact and noise.
3) Check center distance
For two external spur gears, center distance is approximately half the sum of pitch diameters. This is often the first assembly check after selecting module and tooth counts.
4) Confirm manufacturing tolerances
Real gears include profile shift, backlash, and tolerance classes. Use this calculator for fast design estimation, then validate with your manufacturing standard.
FAQ
Can I use this for helical gears?
Yes, for quick checks. But helical gears may use normal module and transverse module relationships based on helix angle, so detailed design should include those conversions.
Why is root diameter marked approximate?
Because dedendum can vary with specific standards and profile modifications. The shown value uses typical full-depth assumptions.
What unit should I use?
Use millimeters for module, pitch diameter, and circular pitch. DP is always in teeth per inch.