How this instrument works
An ISO metric screw thread's profile is built from a single equilateral triangle whose height, H, is fixed entirely by the pitch: H = P × √3⁄2. Every other characteristic dimension of the basic thread profile is defined as a fraction of that one triangle height, which is why the whole family of thread proportions collapses into a couple of clean formulas once H is known.
The pitch diameter — the diameter at which the thread ridge and the groove are equal in width, and the dimension that actually determines whether a bolt and nut fit together — sits three-eighths of H in from the major diameter on each side of the thread, giving d₂ = D − 0.649519×P. The minor diameter, the theoretical root of a perfectly sharp thread, sits five-eighths of H in from each side: d₁ = D − 1.082532×P. Both coefficients are exact algebraic simplifications of those fixed 3/8 and 5/8 fractions, not independently measured or rounded figures.
This calculator reports the basic, pre-tolerance dimensions defined by ISO 68-1 — the nominal geometry a thread is designed around, before any manufacturing tolerance class is applied. It deliberately does not attempt the full ISO 965 tolerance-grade and fundamental-deviation system, which layers a chosen fit class (like 6g or 6H) on top of these basic dimensions to produce the actual allowable manufacturing range. The minor diameter reported here is also the theoretical sharp-V minor diameter, not the smaller, root-rounded minimum minor diameter used in real external-thread tolerance tables — a genuine scope limit, not an oversight.
- Enter the thread's nominal major diameter, D, in millimeters — the number before the × in a designation like M10×1.5.
- Enter the thread pitch, P, in millimeters — the number after the ×.
- Read the Fundamental triangle height, H, the base geometric figure every other dimension derives from.
- Read the Basic pitch diameter and Basic minor diameter — the nominal, pre-tolerance dimensions of the thread profile.
Worked example — an M10×1.5 thread
An M10×1.5 bolt has a 10 mm nominal major diameter and a 1.5 mm pitch. Fundamental triangle height: H = 1.5 × 0.866025 = 1.299038 mm. Basic pitch diameter: d₂ = 10 − 0.649519 × 1.5 = 10 − 0.974279 = 9.025721 mm. Basic minor diameter: d₁ = 10 − 1.082532 × 1.5 = 10 − 1.623798 = 8.376202 mm.
The formula checks out against well-known reference values for other common coarse threads: an M6×1.0 thread gives d₂ = 6 − 0.649519 = 5.350481 mm, matching the widely published 5.350 mm pitch diameter for M6 coarse thread; an M8×1.25 thread gives d₂ = 8 − 0.811899 = 7.188101 mm, matching the published 7.188 mm figure for M8 coarse thread — two independent confirmations that these coefficients reproduce the standard, not just a formula that looks plausible.
Questions
How do you calculate the pitch diameter of a metric thread?
d₂ = D − 0.649519 × P, where D is the nominal major diameter and P is the thread pitch, both in the same unit. The coefficient 0.649519 is an exact simplification of "three-eighths of the fundamental triangle height," the standard ISO 68-1 relationship that defines a metric thread's basic profile.
What is the fundamental triangle height in a metric thread?
H = P × √3⁄2 ≈ 0.866025 × P — the height of the equilateral triangle formed by a 60° thread's flank angles at a given pitch. Every other basic dimension of the ISO metric thread profile (crest height, root depth, pitch diameter, minor diameter) is defined as a fixed fraction of this one value, which is why H is calculated first.
Is the minor diameter from this calculator the same as a real bolt's minimum diameter?
No — this calculator reports the theoretical, sharp-V basic minor diameter defined directly by ISO 68-1's idealized triangle geometry. Real external threads have a rounded root rather than a perfectly sharp one, and the actual minimum minor diameter used in manufacturing tolerance tables (ISO 965) is smaller than this theoretical figure. Use this result for understanding basic thread proportions, not as a manufacturing tolerance spec.
What's the difference between major, pitch, and minor diameter?
Major diameter is the largest diameter of the thread, measured at the crest of an external thread — the nominal size in a designation like M10. Pitch diameter is the diameter where thread and groove widths are equal, and it's what actually governs whether two mating threads fit. Minor diameter is the smallest diameter, at the root of an external thread (or crest of an internal one). All three shrink from the major diameter by fixed fractions of the fundamental triangle height H.
Does this calculator apply a tolerance class like 6g or 6H?
No — it calculates only the basic, nominal thread dimensions defined by ISO 68-1, before any tolerance class is applied. Real manufactured threads are cut to a range around these basic dimensions, defined by an ISO 965 tolerance grade and fundamental deviation (the "6g," "6H," and similar designations) — a separate lookup-table system this calculator does not attempt to reproduce.