Standard Spur Gear Size Calculator

Calculate key dimensions of standard spur gears from module, tooth counts, and pressure angle

Inputs

m

Module

\alpha

Pressure angle

Z_1

Pinion teeth

Z_2

Gear teeth

Formula Interpretation

Pitch diameter

D = Zm

Pitch diameter is proportional to tooth count and module.

Addendum diameter

D_a = (Z+2)m

For standard full-depth teeth, addendum diameter is (Z+2)m.

Base diameter

D_b = Zm\cos\alpha

Base diameter is converted from pitch diameter by cos(α).

Center distance

C = \dfrac{1}{2}(Z_1+Z_2)m

Center distance depends on both gears' tooth counts and module.

Circular pitch

t = \pi m

Circular pitch is the arc distance between corresponding points of adjacent teeth on the pitch circle.

Base pitch

t_b = t\cos\alpha

Base pitch is used in involute meshing geometry.

Ratio

i = \dfrac{D_2}{D_1} = \dfrac{Z_2}{Z_1}

For standard external gearing, ratio equals tooth-count ratio.

Empirical face-width range

b = (8\sim15)m

A common design guideline is b = (8~15)m.

Minimum whole depth

h \ge 2.25m

Standard whole depth is typically not less than 2.25m.

Key Knowledge

Application

Standard spur gears are commonly used to transmit power/motion between parallel shafts.

Pressure angle

A 20° pressure angle is widely used for balanced strength and meshing behavior.

Meaning of module

Module is the basic geometric scale parameter of a gear set.

Dimensional dependency

Most standard spur gear dimensions can be derived directly from module and tooth count.

Worked Example

Given a standard spur gear pair: m = 6, Z₁ = 30, Z₂ = 80, α = 20°. Find key dimensions.

Step 1: Compute pitch diameters

D_1 = Z_1 m = 30 \times 6 = 180\,\text{mm},\quad D_2 = Z_2 m = 80 \times 6 = 480\,\text{mm}

Step 2: Compute addendum diameters

D_{a1}=(Z_1+2)m=(30+2)\times6=192\,\text{mm},\quad D_{a2}=(Z_2+2)m=(80+2)\times6=492\,\text{mm}

Step 3: Compute base diameters

D_{b1}=Z_1m\cos\alpha=30\times6\cos20^\circ\approx169\,\text{mm},\quad D_{b2}\approx451\,\text{mm}

Step 4: Compute whole depth and face-width range

h_{\min}=2.25m=2.25\times6=13.5\,\text{mm},\quad b=(8\sim15)m=48\sim90\,\text{mm}

The key dimensions of this gear pair can be derived directly from m, Z, and α, which is efficient for preliminary sizing and checking.

Extended Knowledge

•In reducer concept design, these formulas quickly estimate center distance and package size.
•Pitch and base parameters are useful for tool selection and profile inspection.
•Base pitch and pressure angle are important for contact ratio and smoothness analysis.
•Within the face-width range, load capacity and life can be optimized with material/heat-treatment constraints.

Standard Spur Gear Size Calculator

Calculate key dimensions of standard spur gears from module, tooth counts, and pressure angle

Inputs

m

Module

\alpha

Pressure angle

Z_1

Pinion teeth

Z_2

Gear teeth

Formula Interpretation

Pitch diameter

D = Zm

Pitch diameter is proportional to tooth count and module.

Addendum diameter

D_a = (Z+2)m

For standard full-depth teeth, addendum diameter is (Z+2)m.

Base diameter

D_b = Zm\cos\alpha

Base diameter is converted from pitch diameter by cos(α).

Center distance

C = \dfrac{1}{2}(Z_1+Z_2)m

Center distance depends on both gears' tooth counts and module.

Circular pitch

t = \pi m

Circular pitch is the arc distance between corresponding points of adjacent teeth on the pitch circle.

Base pitch

t_b = t\cos\alpha

Base pitch is used in involute meshing geometry.

Ratio

i = \dfrac{D_2}{D_1} = \dfrac{Z_2}{Z_1}

For standard external gearing, ratio equals tooth-count ratio.

Empirical face-width range

b = (8\sim15)m

A common design guideline is b = (8~15)m.

Minimum whole depth

h \ge 2.25m

Standard whole depth is typically not less than 2.25m.

Key Knowledge

Application

Standard spur gears are commonly used to transmit power/motion between parallel shafts.

Pressure angle

A 20° pressure angle is widely used for balanced strength and meshing behavior.

Meaning of module

Module is the basic geometric scale parameter of a gear set.

Dimensional dependency

Most standard spur gear dimensions can be derived directly from module and tooth count.

Worked Example

Given a standard spur gear pair: m = 6, Z₁ = 30, Z₂ = 80, α = 20°. Find key dimensions.

Step 1: Compute pitch diameters

D_1 = Z_1 m = 30 \times 6 = 180\,\text{mm},\quad D_2 = Z_2 m = 80 \times 6 = 480\,\text{mm}

Step 2: Compute addendum diameters

D_{a1}=(Z_1+2)m=(30+2)\times6=192\,\text{mm},\quad D_{a2}=(Z_2+2)m=(80+2)\times6=492\,\text{mm}

Step 3: Compute base diameters

D_{b1}=Z_1m\cos\alpha=30\times6\cos20^\circ\approx169\,\text{mm},\quad D_{b2}\approx451\,\text{mm}

Step 4: Compute whole depth and face-width range

h_{\min}=2.25m=2.25\times6=13.5\,\text{mm},\quad b=(8\sim15)m=48\sim90\,\text{mm}

The key dimensions of this gear pair can be derived directly from m, Z, and α, which is efficient for preliminary sizing and checking.

Extended Knowledge

•In reducer concept design, these formulas quickly estimate center distance and package size.
•Pitch and base parameters are useful for tool selection and profile inspection.
•Base pitch and pressure angle are important for contact ratio and smoothness analysis.
•Within the face-width range, load capacity and life can be optimized with material/heat-treatment constraints.