Thread Pitch Diameter Calculator (ISO metric and Unified, 3-wire measurement)

Understanding the thread pitch diameter calculator — concept and principle

This calculator gives the basic pitch diameter, minor diameter and fundamental triangle height of ISO metric and Unified screw threads, and the measurement over three wires used to check the pitch diameter. Machinists, inspectors and mechanical designers use it.

Three wires sit in the grooves; a micrometer over them reads 10.3248 mm when the thread is right.

How it is calculated

H = (√3/2) P = 0.866025 P

Pitch diameter d₂ = d − 0.649519 P (= d − 3H/4)

Basic minor diameter of the nut D₁ = d − 1.082532 P (= d − 5H/4)

Best wire W = P ÷ √3; measurement over wires M = d₂ + 3W − 0.866025 P

For Unified threads P = 25.4 ÷ TPI (in mm). Results also in inches.

The principle

ISO metric and Unified threads share a 60° profile built on an equilateral "fundamental triangle" of height H. The pitch diameter is the imaginary cylinder where the thread ridge and groove are equally wide; it is what controls the fit between bolt and nut. Because it cannot be measured directly with a caliper, three precise wires are laid in the grooves and the distance over them is measured; the best wire size touches the flanks exactly at the pitch line.

Worked example

Default inputs: ISO metric, d = 10 mm, P = 1.5 mm, best wire.

H = 0.866025 × 1.5 = 1.299 mm.
d₂ = 10 − 0.649519 × 1.5 = 9.0257 mm = 0.3553 in.
D₁ = 10 − 1.082532 × 1.5 = 8.3762 mm.
W = 1.5 ÷ √3 = 0.866 mm.
M = 9.0257 + 3 × 0.866 − 1.299 = 10.3248 mm = 0.4065 in.

Each point is the calculator re-run with only “Nominal (major) diameter — mm for metric, inches for Unified” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Nominal (major) diameter — mm for metric, inches for Unified	Basic pitch diameter d₂ (mm)
2.5	1.5257
5	4.0257
7.5	6.5257
10	9.0257
12.5	11.5257
15	14.0257
20	19.0257

How to read the result

These are basic sizes with zero tolerance. Real bolts are made slightly smaller and nuts slightly larger according to their tolerance class, so measured pitch diameters fall a little below the basic value for external threads. Compare the three-wire measurement with the limits for your class.

Common mistakes

Using threads per inch directly as pitch for Unified threads.
Using wires of the wrong size without entering their diameter.
Comparing a measured value with the basic size instead of the tolerance limits.

Keep in mind: Thread acceptance must follow the applicable standard and calibrated gauges.

Frequently asked questions

What is pitch diameter?

The diameter at which ridge and groove widths are equal.

Why use three wires?

They let a micrometer measure the pitch diameter indirectly.

What is the best wire size?

P ÷ √3, which touches the flanks at the pitch line.

What is M10 × 1.5?

A metric thread with 10 mm nominal diameter and 1.5 mm pitch, the standard coarse pitch for M10.

Sources: 60° basic thread profile shared by ISO metric and Unified threads (ISO 68-1 basic profile) and the standard three-wire measurement formula

Checked 9 Nov 2026. 60° basic thread profile shared by ISO metric and Unified threads (H = 0.866025P, d₂ = d − 0.649519P, D₁ = d − 1.082532P) and the three-wire measurement formula M = d₂ + 3W − 0.866025P: standard formula.

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