Pitch Diameter Calculator - Gear & Thread Design Tool

What is a pitch diameter calculator?

A pitch diameter calculator finds the pitch diameter of a gear or a screw thread. For a gear, it multiplies the number of teeth by the module. For a thread, it subtracts a fixed constant times the thread pitch from the major diameter. The result is a length in millimeters that engineers, machinists, and students use to check whether parts will mesh or fit together correctly.

Pitch diameter is not the outer edge of a gear or bolt. It is a theoretical diameter that sits partway through the part, at the point where two mating pieces actually make contact.

What is pitch diameter in a gear?

A gear's teeth sit around a circle called the pitch circle. The pitch circle is imaginary; it does not appear as a physical edge on the part. It marks the diameter at which the tooth of one gear meets the tooth of a mating gear. The pitch diameter is the diameter of this circle.

Each tooth extends slightly above the pitch circle (a section called the addendum) and slightly below it (the dedendum). The tooth is neither entirely above nor entirely below the pitch circle; that circle simply marks the reference point engineers use for every other gear calculation.

Gear pitch diameter formula

$D = m \times z$

• D = pitch diameter, in millimeters
• m = module, in millimeters
• z = number of teeth

The module describes the size of each tooth. A gear with a large module has large, widely spaced teeth. A gear with a small module has small, closely spaced teeth. Two gears can only mesh if they share the same module; matching pitch diameters alone is not enough.

Gear example

A gear has 24 teeth and a module of 2 mm.

D = 2 mm × 24 = 48 mm

What is pitch diameter in a thread?

A screw thread also has a pitch diameter, though it works differently from a gear's. It is the diameter of an imaginary cylinder that cuts through the thread at the point where the width of the thread ridge equals the width of the groove next to it. This point is where two mating threads, such as a bolt and a nut, actually bear against each other.

Thread pitch diameter formula

$D_2 = D - 0.6495 \times P$

• D₂ = pitch diameter, in millimeters
• D = major diameter, the largest diameter of the thread, in millimeters
• P = thread pitch, the distance from one thread crest to the next, in millimeters

The constant 0.6495 applies to standard 60-degree thread forms, which include ISO metric threads and Unified (UN/UNC/UNF) threads used in the United States. It does not apply to other thread angles, such as 29-degree Acme threads or British Standard Pipe threads, which use different formulas.

Thread example

A metric thread has a major diameter of 12 mm and a pitch of 1.5 mm.

D₂ = 12 mm − (0.6495 × 1.5 mm) = 12 mm − 0.97425 mm = 11.0258 mm

How to use the pitch diameter calculator

For a gear:

1. Select "Gear."
2. Enter the number of teeth.
3. Enter the module, in millimeters.
4. Read the pitch diameter shown in the results.

For a thread:

1. Select "Thread."
2. Enter the major diameter, in millimeters.
3. Enter the thread pitch, in millimeters.
4. Read the pitch diameter shown in the results.

A diagram updates as the numbers change, showing where the pitch diameter falls on the gear or thread.

Why pitch diameter matters

For gears, pitch diameter sets the center distance between two meshing gears: it equals half the sum of their pitch diameters. A design error here means the gears either fail to reach each other or bind together too tightly. Pitch diameter also determines the gear ratio, since the ratio of two meshing gears equals the ratio of their pitch diameters (or, equivalently, their tooth counts).

For threads, pitch diameter controls how tightly a bolt and nut fit together. A pitch diameter that is too large causes the threads to bind; one that is too small leaves the joint loose. Thread pitch diameter tolerances are set by standards such as ISO 965-1, which define fit classes like 6H and 6g.

Related measurements

A few other dimensions come up alongside pitch diameter:

• Diametral pitch is used in imperial gear systems. It is the number of teeth per inch of pitch diameter and is the inverse of the module: module = 25.4 ÷ diametral pitch.
• Circular pitch is the distance between the same point on two adjacent teeth, measured along the pitch circle.
• Outer diameter of a standard gear equals the pitch diameter plus twice the module (the addendum on each side).
• Root diameter is the diameter at the base of the teeth, typically the pitch diameter minus 2.5 times the module.
• Minor diameter of a thread is its smallest diameter, at the bottom of the thread groove.

Frequently asked questions

How do you calculate gear pitch diameter? Multiply the module by the number of teeth: D = m × z. A gear with 30 teeth and a 2 mm module has a pitch diameter of 60 mm.

How do you calculate thread pitch diameter? Subtract 0.6495 times the thread pitch from the major diameter: D₂ = D − 0.6495 × P. A thread with a 12 mm major diameter and a 1.75 mm pitch has a pitch diameter of 12 − (0.6495 × 1.75) = 10.8634 mm.

Does pitch diameter equal outer diameter? No. The outer diameter of a gear is larger than its pitch diameter. For a standard gear, outer diameter equals pitch diameter plus twice the module.

Can this calculator handle imperial measurements? Convert imperial values to metric first. For gears, module = 25.4 ÷ diametral pitch. For threads, pitch = 25.4 ÷ threads per inch. Enter the converted value and convert the result back if needed.

Does the 0.6495 constant work for every thread type? No. It applies only to 60-degree thread forms, including ISO metric and Unified inch threads. Acme threads, pipe threads, and other thread angles use different constants.

What tools measure pitch diameter in practice? Thread pitch micrometers measure thread pitch diameter directly using shaped anvils. Gear pitch diameter is commonly checked with the "over pins" method, in which precision pins are placed in opposite tooth gaps and the distance across them is measured, then converted to pitch diameter. Coordinate measuring machines (CMMs) can also measure both, per standards such as ASME B89.3.4.

References

1. Oberg, E., Jones, F. D., Horton, H. L., & Ryffel, H. H. (2016). Machinery's Handbook (30th ed.). Industrial Press.
2. ISO 54:1996. Cylindrical gears for general engineering and for heavy engineering — Modules. International Organization for Standardization.
3. ISO 68-1:1998. ISO general purpose screw threads — Basic profile — Metric screw threads. International Organization for Standardization.
4. ISO 965-1. ISO general purpose metric screw threads — Tolerances. International Organization for Standardization.
5. ASME B1.1-2003. Unified Inch Screw Threads (UN and UNR Thread Form). American Society of Mechanical Engineers.
6. Dudley, D. W. (1994). Handbook of Practical Gear Design. CRC Press.