Diametral Pitch Calculator

Q: How do I calculate diametral pitch to module conversion?

To calculate the gear’s module from its diametral pitch, take the reciprocal of the diametral pitch . Exercise caution with unit conversions, as it’s common to express module sizes in millimeters and diametral pitch in inches.

Q: What is the diametral pitch of a gear whose module is 5 mm?

The diametral pitch of a 5 mm module gear is 0.2 mm⁻¹ or 5.08 in⁻¹ . To arrive at this answer, follow these steps: Take the reciprocal of the gear module: p d = 1/5 mm = 0.2 mm⁻¹ Multiply this with 25.4 mm/in to convert the result from mm⁻¹ to in⁻¹: 0.2 mm⁻¹ × 25.4 mm/in = 5.08 in⁻¹ You can verify this result using our diametral pitch calculator.

Creators

Krishna Nelaturu

Krishna Sai is a mechanical engineer with a passion for math and physics. He creates calculators with the aim of helping students understand the mathematical concepts behind the calculation. With an interest in coding, Krishna has recently started learning programming and web development. He enjoys long walks, riding his motorcycle, and loves a good story. Someday, he aspires to write his own fantasy book. See full profile

Check our editorial policy

Reviewers

Steven Wooding

Steven Wooding is a physicist by training with a degree from the University of Surrey specializing in nuclear physics. He loves data analysis and computer programming. He has worked on exciting projects such as environmentally aware radar, using genetic algorithms to tune radar, and building the UK vaccine queue calculator. Steve is now the Editorial Quality Assurance Coordinator here at Omni Calculator, making sure every calculator meets the standards our users expect. In his spare time, he enjoys cycling, photography, wildlife watching, and long walks. See full profile

Check our editorial policy

Add as preferred on Google

Our gear diametral pitch calculator will help you quickly find the diametral pitch of a spur gear. You can also convert diametral pitch to gear module or vice versa! The diametral pitch and module can represent the size of the gear teeth and are crucial parameters in gear design.

If you wish to learn how to calculate the diametral pitch of a spur gear, you’ve come to the right place! In this article, we shall discuss the fundamentals of gear diametral pitch and how to calculate it. You can also learn how to perform diametral pitch-to-module conversion.

Diametral pitch

A pair of spur gears can connect two shafts whose axes are parallel. A spur gear has teeth projecting radially outward, such that the tooth face is parallel to the shaft axis.

two spur gears with pitch circle indicated

🙋 Gears help transmit torque and power between two shafts. If you need help calculating the suitable shaft sizes for your application, our shaft size calculator has your back!

The pitch circle of a spur gear is an imaginary circle that would give the same rotating motion as the actual gear. It passes between the addendum circle and dedendum circle. The pitch circle diameter is the diameter of this pitch circle and is vital for many gear calculations.

The diametral pitch of a gear is the ratio of the number of teeth on the gear to its pitch circle diameter. The formula for diametral pitch is given by:

p_d = \frac{T}{D}

where:

$p_d$ — Diametral pitch of the gear;
$T$ — Number of teeth on the gear; and
$D$ — Pitch circle diameter.

If the pitch circle diameter is in millimeters, the diametral pitch would be per millimeter of pitch circle diameter. In the US, using inches to measure pitch circle diameter is common. In this case, the diametral pitch would be per inch of pitch circle diameter.

How do you calculate diametral pitch of spur gear?

To calculate the diametral pitch of a spur gear, follow these steps:

Measure the pitch circle diameter of the gear.
Count the number of teeth on the gear.
Divide the number of teeth by the pitch circle diameter to obtain the diametral pitch.

Use our diametral pitch calculator to verify your answer.

Say you have a gear with 49 teeth whose pitch circle diameter is 98 mm. Its diametral pitch would be:

\begin{align*} p_d &= \frac{T}{D} = \frac{49}{98 \text{ mm}} = 0.5 \text{ mm}^{-1} \end{align*}

Diametral pitch to module conversion

The gear module is helpful in “sizing” a gear. It is the inverse of the diametral pitch — the ratio of the pitch circle diameter to the number of gear teeth.

m = \frac{D}{T} = \frac{1}{p_d}

where $m$ is the gear module. It has the same unit as the pitch circle diameter.

For two gears to mesh properly, their gear modules (and thus their diametral pitch) must be the same! If you’re interested in calculating the gear ratio of meshed gears, use our gear ratio calculator.

For example, the module of a gear whose diametral pitch is 32 in^-1 is:

\begin{align*} m &= \frac{1}{p_d} = \frac{1}{32}\\[1.2em] & = 0.03125 \text{ in}\\[.6em] &\approx 0.7937 \text{ mm} \end{align*}

Using this gear diametral pitch calculator

Our gear diametral pitch calculator is simple to use:

Enter the number of teeth on the gear.
Input the pitch circle diameter of the gear. To enter the value in a different unit, you must select a different unit before entering the value.
The tool will calculate the diametral pitch in a snap! Even better, it will also calculate the gear module (distance along the pitch circle between teeth) from the diametral pitch.

Gears are not the only way to transmit power between two shafts. Learn how you can achieve this using belts and pulleys with our belt length calculator.

FAQs

How do I calculate diametral pitch to module conversion?

To calculate the gear’s module from its diametral pitch, take the reciprocal of the diametral pitch. Exercise caution with unit conversions, as it’s common to express module sizes in millimeters and diametral pitch in inches.

Why is diametral pitch important in gear design?

The diametral pitch and gear module are vital for calculating the necessary dimensions of a gear, such as its pitch circle diameter and addendum circle diameter. These parameters are also important when calculating gear stresses.

What is the diametral pitch of a gear whose module is 5 mm?

The diametral pitch of a 5 mm module gear is 0.2 mm⁻¹ or 5.08 in⁻¹. To arrive at this answer, follow these steps:

Take the reciprocal of the gear module:

p_d = 1/5 mm = 0.2 mm⁻¹
Multiply this with 25.4 mm/in to convert the result from mm⁻¹ to in⁻¹:

0.2 mm⁻¹ × 25.4 mm/in = 5.08 in⁻¹

You can verify this result using our diametral pitch calculator.