Gear Module Calculator

Compute module (m), pitch diameter (d), addendum, dedendum, base circle, center distance, and contact ratio. Customizable addendum coefficient (ha*), clearance coefficient (c*), and profile shift (x). Interactive visualization of involute spur gear proportions.

Typical: 1.0 (standard), 0.8 (short teeth), 1.2 (high teeth)
ISO standard: 0.25; stub teeth: 0.3–0.35
Positive for stronger teeth
Usually x₂ = -x₁ for equal strength
⚙️ Standard: z=24, m=2.5, ha*=1.0, c*=0.25
? High torque: z=18, m=3, ha*=1.0, c*=0.25
? Stub teeth: z=20, m=2, ha*=0.8, c*=0.3
? Fine module: m=1, z=60, ha*=1.0
? Automotive: m=3.5, z=22, ha*=1.0, c*=0.25
➕ Profile shift: z=16, m=2.5, x1=0.3, x2=-0.3
All calculations are local. No data leaves your browser.

Understanding Gear Module

The gear module (m) is the fundamental size unit in metric spur gears, defined as m = d / z. The addendum coefficient (ha*) and clearance coefficient (c*) determine tooth height proportions: ha = ha*·m and hf = (ha*+c*)·m. ISO 54 and DIN 780 standardize ha* = 1.0, c* = 0.25, but engineers often modify these for short teeth (higher strength) or high addendum (increased contact ratio). Profile shift (x) moves the tool inward or outward, allowing undercut avoidance, center distance adjustment, and balanced tooth strength. This calculator empowers you to explore non‑standard geometries with full accuracy.

Core formulas (with profile shift): d = m·z ; ha = (ha*+x)·m ; hf = (ha*+c*-x)·m ; da = d + 2·ha ; df = d - 2·hf ; db = d·cosα ; a = m·(z₁+z₂)·cosα / (2·cosα_w) ; ε ≈ √(ra₁²−rb₁²) + √(ra₂²−rb₂²) − a·sinα_w) / (π·m·cosα) where α_w solves inv(α_w) = inv(α) + 2(x₁+x₂)tanα/(z₁+z₂)

Practical Applications & Customization

Adjusting ha*, c*, and x allows designers to optimize gear sets for specific constraints:

  • Standard (ha*=1.0, c*=0.25, x=0): Balanced strength, noise, and manufacturability – default for most industrial gears.
  • Stub teeth (ha*=0.8, c*=0.3–0.35): Shorter teeth provide higher bending strength at the root, suitable for heavy loads and limited center distance.
  • High addendum (ha*=1.2): Increases contact ratio and smoothness, often used in precision instruments.
  • Profile shift (x ≠ 0): Prevents undercutting for small tooth counts, adjusts center distance, and can equalize bending stresses.

Our calculator automatically computes all derived dimensions, center distance, and contact ratio (ε) when a mating gear is specified – essential for verifying transmission quality.

Case Study: Stub Teeth with Profile Shift for Heavy‑Duty Gearbox

A mining conveyor gearbox requires increased tooth root strength. Using ha* = 0.8, c* = 0.3, m=5, z₁=18, z₂=54, x₁=+0.2, x₂=-0.2 yields pitch diameters 90 mm and 270 mm. The dedendum hf = (0.8+0.3-0.2)·5 = 4.5 mm (pinion), improving bending strength by ~25% compared to standard teeth. The center distance becomes 180 mm (unchanged due to equal and opposite shift), and contact ratio (ε ≈ 1.42) remains excellent.

Why Use This Advanced Gear Module Tool?

  • ✓ Full coefficient control: Modify ha*, c*, and x to match any standard or custom tooth profile.
  • ✓ Pair gear support: Input z₂ and profile shifts to instantly get center distance and contact ratio – crucial for gearbox design.
  • ✓ Visual feedback: Real‑time scaled circles and radial teeth show proportions.
  • ✓ Educational depth: Learn how coefficients affect addendum, dedendum, and root clearance.

Deep Dive: Involute Gear Geometry & Engineering Significance

The involute profile ensures constant angular velocity ratio. Our tool computes the base circle diameter (db = m·z·cosα), which is the circle from which the involute curve originates. The contact ratio (ε) indicates smoothness of power transmission; values above 1.2 are recommended. We calculate an approximate contact ratio based on standard formulas (ε ≈ √( (da1/2)² - (db1/2)² ) + ... ), giving you a reliability indicator.

Engineers rely on these parameters for stress analysis (Lewis equation), material selection, and backlash control. For high-torque applications, larger modules and 25° pressure angles enhance tooth strength. For precision instruments, fine modules (m ≤ 1) with 20° pressure angle deliver smoother motion.

Step-by-Step Calculation Procedure

  1. Enter number of teeth (z₁) and module (m).
  2. Specify pressure angle (α) – standard 20°.
  3. Optionally set addendum coefficient (ha*), clearance coefficient (c*), and profile shifts (x₁, x₂) to match your design intent.
  4. If designing a gear pair, enter mating gear teeth (z₂) for center distance and contact ratio.
  5. Click Calculate – all dimensions update instantly, and the gear sketch reflects the proportions.
  6. Use preset examples to explore standard and non‑standard configurations.

Standard Module Series (ISO 54)

Preferred Module (mm) Typical Application Tooth Range
0.5 – 1.0 Precision instruments, watches, small robotics 20–120
1.25 – 3.0 Automotive, industrial machinery, pumps 12–80
3.5 – 6.0 Heavy trucks, wind turbines, construction 10–50
8 – 12 Mining equipment, marine propulsion 8–35

Common Mistakes & Misconceptions

  • Ignoring clearance coefficient: c* affects root diameter and tip clearance; using wrong c* may cause interference.
  • ha* > 1.0 without profile shift: May cause pointed teeth; our tool warns if tip thickness becomes too small.
  • Minimum teeth for undercut: For 20° pressure angle, z < 17 risks undercut; profile shift can compensate.
  • Mating gear required for contact ratio: Without z₂, contact ratio cannot be computed – always specify it for complete analysis.

Engineering Authority: Based on DIN 3960, ISO 6336, AGMA 2001, and classic gear theory. Validated against industry software. Updated March 2025 by GetZenQuery Tech team. All calculations are performed locally with double precision.

Frequently Asked Questions

Addendum coefficient (ha*) determines tooth height above pitch circle; clearance coefficient (c*) adds extra root clearance to prevent tip‑root contact. They are key to tooth strength and meshing.

Yes. The calculator accepts any positive values, but ensure that resulting dedendum and tip clearance are compatible with the mating gear. Custom coefficients are common in specialized gear designs.

Using standard involute geometry: ε = (√(ra₁²−rb₁²) + √(ra₂²−rb₂²) − a·sinα_w) / (π·m·cosα) for external spur gears. Values above 1.2 are recommended for smooth operation.

For gears with few teeth and high pressure angle, db may exceed df. This is normal; the involute starts at the base circle; below it the profile is non‑involute.

The canvas shows circles to scale and radial lines for tooth orientation. For exact involute shape, use CAD; but the visual quickly verifies proportions.
References: ISO 54:1996, AGMA 910-C90, "Gear Geometry and Applied Theory" by Faydor L. Litvin. KHK Gear Technical Reference.