Thread Calculator: Calculate Thread Depth & Diameter

Thread Calculator for Screw and Bolt Measurements

A thread calculator finds the depth, minor diameter, and pitch diameter of a screw or bolt thread. It works from the major diameter and the pitch, or from the threads per inch (TPI). Machinists, engineers, and hobbyists use it to check whether a screw will fit a matching nut or a tapped hole.

Key thread terms

• Major diameter: the widest point of a thread, measured crest to crest.
• Minor diameter: the narrowest point of a thread, measured root to root.
• Pitch diameter: an imaginary diameter halfway between the major and minor diameters, where the thread ridge and the gap beside it are equal in width.
• Pitch: the distance between two neighboring thread crests, measured in millimeters on metric threads.
• Threads per inch (TPI): the number of thread crests in one inch of an imperial thread. Pitch and TPI measure the same thing in different units: pitch (mm) = 25.4 / TPI.
• Thread depth: the radial distance between the major and minor diameters, or how deep the thread groove cuts.

Metric and imperial thread systems

Metric threads follow the ISO standard. A size like M10×1.5 means a 10 mm major diameter with a 1.5 mm pitch. The thread angle is 60°.

Imperial threads follow the Unified Thread Standard (UTS), the system most common in the United States. A size like 3/8"-16 means a 3/8 inch major diameter with 16 threads per inch. Modern imperial threads also use a 60° angle. The older British Whitworth standard used 55°.

How to calculate thread depth

Thread depth measures how deep the thread groove is cut, as a radius rather than a diameter.

For metric threads:

h = 0.6134 × P

For imperial threads, first convert TPI to a pitch in millimeters (P = 25.4 / TPI), then use the same formula:

h = 0.6134 × (25.4 / TPI)

Here h is the thread depth in mm, P is the pitch in mm, and TPI is threads per inch.

Minor diameter formula

The minor diameter equals the major diameter minus twice the thread depth:

d₁ = d − 2h = d − 1.226868 × P

d is the major diameter and d₁ is the minor diameter, both in the same unit as P.

Pitch diameter formula

d₂ = d − 0.6495 × P

d₂, the pitch diameter, sits close to halfway between the major and minor diameters. It is the dimension thread gauges check most closely, because it determines how tightly two threaded parts mesh.

Example: metric thread (M10×1.5)

An M10×1.5 bolt has a major diameter of 10 mm and a pitch of 1.5 mm.

• Thread depth: 0.6134 × 1.5 = 0.920 mm
• Minor diameter: 10 − 1.226868 × 1.5 = 8.160 mm
• Pitch diameter: 10 − 0.6495 × 1.5 = 9.026 mm

Example: imperial thread (3/8"-16)

A 3/8"-16 bolt has a major diameter of 0.375 in (9.525 mm) and 16 threads per inch.

First convert TPI to pitch: 25.4 / 16 = 1.5875 mm.

• Thread depth: 0.6134 × 1.5875 = 0.974 mm
• Minor diameter: 9.525 − 1.226868 × 1.5875 = 7.577 mm
• Pitch diameter: 9.525 − 0.6495 × 1.5875 = 8.494 mm

The calculator on this page shows imperial results in inches, with the millimeter equivalent alongside, matching how imperial thread gauges are normally read.

Where thread calculations are used

Engineers use thread dimensions to choose fasteners that fit a given hole or nut. Machinists use them to set up lathes and mills for cutting threads. Quality inspectors use them to check that finished parts match a printed specification. Mechanics use them to find a matching replacement bolt when the original is lost or stripped. Plumbers use them to match pipe fittings.

Other thread forms fall outside the standard V-thread covered by these formulas. Acme and square threads, used in lead screws and jacks, have different angles and different depth calculations. Pipe threads taper along their length instead of holding a constant diameter. Each of these needs its own set of formulas.

Brief history

Before the 19th century, screws were cut by hand and rarely matched each other. Henry Maudslay built a practical screw-cutting lathe in 1797, making consistent threads possible for the first time. In 1841, Joseph Whitworth proposed the first widely used thread standard, in Britain, with a 55° angle. In the United States, William Sellers proposed a 60° angle system in 1864, which became the American standard.

In 1948, the United States, Britain, and Canada agreed on the Unified Thread Standard, still used today. The International Organization for Standardization set the metric thread standard in the 1960s. Metric threads are now the most common system worldwide, though imperial threads remain standard for many fasteners in the United States.

Frequently asked questions

What is the difference between pitch and TPI?

Pitch is the distance between two thread crests, given in millimeters. TPI counts how many crests fit in one inch. Both describe the same measurement in different units: pitch (mm) = 25.4 / TPI.

How can I tell if a thread is metric or imperial?

Metric threads are labeled with an M and two numbers in millimeters, such as M10×1.5. Imperial threads are labeled with a diameter in inches, often as a fraction, followed by a TPI count, such as 3/8"-16.

What is thread engagement?

Thread engagement is the length of contact between two mated threaded parts, measured along the axis of the screw. A common rule for steel fasteners is engagement of at least one major diameter. Softer materials such as aluminum often need 1.5 times the major diameter to hold securely.

What is the difference between coarse and fine threads?

Coarse threads have a larger pitch and fewer threads per inch. They resist cross-threading and work well in soft materials. Fine threads have a smaller pitch and more threads per inch. They hold tighter under vibration and allow finer adjustment.

How do I measure an unknown thread's pitch or TPI?

A thread pitch gauge, a thin comb with tooth profiles cut to standard pitches, is pressed against the thread until one tooth matches exactly. A caliper can also measure the distance across several threads and divide by the number of threads counted.

What does the thread angle mean?

The thread angle is the angle between the two sloped sides of a single thread ridge. Nearly all metric and modern imperial threads use 60°. Older British Whitworth threads used 55°.

References

1. ISO 68-1:1998, General purpose screw threads — Basic profile — Metric screw threads.
2. ASME B1.1-2003, Unified Inch Screw Threads (UN and UNR Thread Form).
3. Oberg, E., Jones, F. D., Horton, H. L., & Ryffel, H. H. Machinery's Handbook, 31st Edition. Industrial Press, 2020.