# Spur Gear Dimensions Calculator

> Source: https://netray.co/tools/spur-gear-dimensions-calculator-module-and-center-distance
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Compute standard full-depth spur gear geometry for a gear and pinion pair: diameters, tooth depth, circular pitch, center distance and ratio.

## Category

engineering-plm

## Industry

Industrial Machinery

## Audience

- Design engineer
- CNC programmer
- Estimator

## Tool

**Kind:** calculator

**Inputs:**

#### Module

**Key:** module

**Type:** number

**Default:** 3

**Min:** 0.2

**Step:** 0.25

**Unit:** mm

**Help:** Pitch diameter divided by tooth count. Choose a standard value, see the module reference table.

#### Gear teeth

**Key:** z_gear

**Type:** number

**Default:** 48

**Min:** 8

**Step:** 1

**Unit:** teeth

#### Pinion teeth

**Key:** z_pinion

**Type:** number

**Default:** 16

**Min:** 8

**Step:** 1

**Unit:** teeth

#### Pressure angle

**Key:** cos_pa

**Type:** select

**Default:** 0.93969

**Options:**

##### 14.5 degrees (legacy)

**Value:** 0.96815

##### 20 degrees (standard)

**Value:** 0.93969

##### 25 degrees

**Value:** 0.90631

**Help:** The selection stores the cosine of the angle, which is what the base circle formula needs.

#### Face width

**Key:** face

**Type:** number

**Default:** 30

**Min:** 1

**Step:** 1

**Unit:** mm

#### Pinion speed

**Key:** pinion_rpm

**Type:** number

**Default:** 1450

**Min:** 1

**Step:** 10

**Unit:** rpm

**Outputs:**

#### Gear pitch diameter (mm)

**Key:** d_gear

**Expr:** module * z_gear

**Format:** decimal

**Description:** d = m x z.

#### Pinion pitch diameter (mm)

**Key:** d_pinion

**Expr:** module * z_pinion

**Format:** decimal

#### Gear outside diameter (mm)

**Key:** da_gear

**Expr:** module * (z_gear + 2)

**Format:** decimal

**Description:** Blank diameter for a standard full-depth tooth: da = m x (z + 2).

#### Pinion outside diameter (mm)

**Key:** da_pinion

**Expr:** module * (z_pinion + 2)

**Format:** decimal

#### Pinion root diameter (mm)

**Key:** df_pinion

**Expr:** module * (z_pinion - 2.5)

**Format:** decimal

**Description:** df = m x (z - 2.5) with a dedendum of 1.25 m.

#### Pinion base circle diameter (mm)

**Key:** db_pinion

**Expr:** d_pinion * cos_pa

**Format:** decimal

#### Center distance (mm)

**Key:** center_dist

**Expr:** module * (z_gear + z_pinion) / 2

**Format:** decimal

**Primary:** true

#### Whole tooth depth (mm)

**Key:** whole_depth

**Expr:** 2.25 * module

**Format:** decimal

#### Circular pitch (mm)

**Key:** circ_pitch

**Expr:** pi * module

**Format:** decimal

#### Gear ratio

**Key:** ratio

**Expr:** z_gear / z_pinion

**Format:** decimal

**Primary:** true

#### Pitch line velocity (m/s)

**Key:** pitch_line_vel

**Expr:** pi * d_pinion * pinion_rpm / 60000

**Format:** decimal

**Description:** Drives lubrication method and the quality grade you need.

**Chart:**

#### Center distance and gear outside diameter vs module

**Type:** line

**X:** module

**From:** 1

**To:** 10

**Steps:** 19

**Series:**

- center_dist
- da_gear

**Disclaimer:** Geometry for standard full-depth, zero-shift involute spur gears (addendum 1 m, dedendum 1.25 m). Profile shift, undercut limits and tooth strength are not checked.

## Content

**Intro:** Enter the module, tooth counts and pressure angle and this calculator returns the pitch, outside, root and base diameters, whole depth, circular pitch and center distance for a standard spur gear pair. It is what a machinist, programmer or estimator needs to size the blank and set the shaft spacing.

**Sections:**

#### How to use it

**Body:** Pick a standard module (see the related module table), then enter the number of teeth on the gear and pinion. Choose the pressure angle: 20 degrees is the modern default and 14.5 degrees appears on older equipment. Add face width and pinion speed to get pitch line velocity. The outside diameter is the blank size to turn before cutting, and the center distance is the bore spacing for the housing. The chart shows how both grow linearly with module.

#### Formulas and conventions

**Body:** For a standard full-depth gear: pitch diameter d = m x z, outside diameter da = m x (z + 2), root diameter df = m x (z - 2.5), whole depth h = 2.25 m, circular pitch p = pi x m, and base diameter db = d x cos(pressure angle). Center distance a = m x (z1 + z2) / 2. These follow ISO 54 and ISO 53 proportions and match the usual metric handbook formulas. Diametral pitch in inch units is 25.4 divided by module.

**Bullets:**

- Addendum equals one module
- Dedendum equals 1.25 modules
- Tooth thickness at the pitch circle is pi x m / 2 with no backlash

#### Reading the result

**Body:** With module 3, a 48-tooth gear and a 16-tooth pinion, the pitch diameters are 144 mm and 48 mm, the center distance is 96 mm and the ratio is 3:1. A pinion with 16 teeth at 20 degrees is just under the 17-tooth limit where undercut starts, so consider 17 or more teeth, or profile shift. Pitch line velocity above roughly 5 m/s usually calls for ground or at least shaved teeth and oil lubrication rather than grease.

#### Common mistakes

**Body:** Mixing module and diametral pitch is the classic error: a 3 module gear is not a 3 DP gear. Another is ordering a blank at pitch diameter instead of outside diameter. Gear pairs must share module and pressure angle, and real drives need backlash allowance, so cut center distance tolerance and tooth thickness reduction must be specified on the drawing and on the purchase order.

**Cta:** If gear dimensions live in drawings and spreadsheets while your ERP routings and item masters are retyped by hand, Netray can help connect the two.

**Faq:**

#### How do I calculate the outside diameter of a spur gear?

**Answer:** Multiply the module by the number of teeth plus two. For module 3 and 48 teeth the outside diameter is 3 x 50 = 150 mm. In diametral pitch units the formula is (N + 2) divided by DP, in inches.

#### How do I calculate center distance between two spur gears?

**Answer:** Add the two pitch diameters and halve the result, which equals module times the sum of both tooth counts divided by two. Add a small tolerance or backlash allowance from your tolerancing practice before finalizing bore positions.

#### What is the difference between module and diametral pitch?

**Answer:** Module is pitch diameter in millimeters per tooth, while diametral pitch is teeth per inch of pitch diameter. They are reciprocal systems: module equals 25.4 divided by DP. Gears can only mesh if they share the same module and pressure angle.

#### Why does the calculator ask for pressure angle?

**Answer:** Pressure angle sets the base circle diameter, which defines the involute profile, and affects tooth strength and bearing load direction. Meshing gears must have the same pressure angle. Twenty degrees is the common standard for new designs.

## Search terms

spur gear calculator, spur gear dimensions, gear pitch diameter calculator, module gear calculator, gear center distance calculator, outside diameter of gear formula, gear base circle diameter, gear tooth depth formula

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