Pitch Diameter Calculator

Background.

Ask what size an M10×1.5 bolt is and the honest answer is three diameters, not one. The major diameter (10 mm) is what callipers read across the crests; the minor diameter is the waist at the thread roots; and between them lies the one that decides whether the bolt actually fits its nut — the pitch diameter, the diameter of the imaginary cylinder where the thread's ridges and grooves are exactly equal in width.

Pitch diameter is the fit dimension. Two mating threads bear on their flanks, and the flanks engage correctly only when the pitch diameters agree within tolerance — a bolt can have perfect crests and still jam or wobble if d₂ is off. That is why thread ring and plug gauges, three-wire measurements over a screw thread, and every thread-tolerance class (6g, 6H and kin) are all defined at the pitch diameter, not the major.

For the ISO 60° metric profile the basic geometry is fixed by the pitch alone: d₂ = d − 0.6495P — the constant being 3√3/8, a pure consequence of the 60° triangle — so an M10×1.5 has a basic pitch diameter of 9.026 mm, and this page computes it, along with the basic external minor diameter, from the two numbers on the thread's designation.

‘Basic’ is the operative word: these are the nominal dimensions tolerance zones are built around. A real 6g bolt is deliberately made a few hundredths under basic so it assembles with a 6H nut; gauging against the correct class limits is the manufacturing step this reference arithmetic supports, as the scope note beside the result records.

What is pitch diameter calculator?

The pitch diameter (d₂) of a screw thread is the diameter of the coaxial cylinder that cuts the thread profile where ridge width equals groove width — the mid-flank surface on which mating threads actually bear. For the ISO 60° metric profile it follows from the major diameter d and pitch P as d₂ = d − (3√3/8)P ≈ d − 0.6495P. It is the dimension thread fit is specified and gauged at: tolerance classes, GO/NO-GO gauges, and three-wire measurement all reference d₂. This page returns the basic (nominal) external pitch diameter and the corresponding basic external minor diameter.

How to use this calculator.

1. 01Read the thread designation: M10×1.5 means major diameter 10 mm, pitch 1.5 mm — enter both; for a coarse-series thread without a stated pitch (plain ‘M10’), look up the standard coarse pitch (1.5 for M10).
2. 02Read the basic pitch diameter d₂ — the reference for gauging — and the basic external minor diameter.
3. 03Comparing a measurement: a three-wire reading over the thread converts to pitch diameter; it should land below this basic value by the tolerance-class allowance (a 6g bolt runs a few hundredths of a millimetre under basic, never over).
4. 04Identifying an unknown bolt: measure the major with callipers and the pitch with a gauge or thread-per-25.4 mm count, then confirm the pair against this page's outputs — metric/imperial lookalikes (M10×1.5 vs 3/8-16) separate cleanly at the pitch diameter.
5. 05Remember the sign of fit: external threads tolerance downward from basic d₂, internal threads upward — basic is the boundary the two zones share, not a size either part should measure exactly.

The formula.

The ISO profile is built from an equilateral 60° triangle of height H = (√3/2)P laid along the thread axis. The standard truncates that sharp triangle: the crest is cut back H/8 from the theoretical point and the root filled H/4, and the pitch cylinder passes through the flanks exactly halfway up the fundamental triangle's working depth — 3H/8 below the major diameter on each side. Hence d₂ = d − 2·(3H/8) = d − 0.75H = d − (3√3/8)P; the decimal 0.6495190528 is that surd. The external minor diameter reported alongside descends further, to the rounded root the standard prescribes for bolts — d − (17/12)H ≈ d − 1.2269P — which is why it is smaller than the tap-drill-style internal minor (d − 1.0825P): bolt roots are relieved deeper, with a radius, for fatigue strength. Everything scales with P alone — a fine-pitch M10×1.25 keeps more metal at both d₂ (9.188) and the root than the coarse M10×1.5 — one reason fine threads are stronger in tension and preferred where vibration loosening matters. The engine multiplies the exact surd coefficients by P and subtracts in Decimal arithmetic, rounding once to twelve significant digits.

A worked example.

Frequently asked questions.

References& sources.

1. [1]International Organization for Standardization. ISO 68-1:1998. Basic profile dimensions (PAYWALL). Retrieved 2026-08-06. independence: primary; access: gated.