Thread Calculator

Find out the different cross-sectional dimensions of any metric bolt's external thread and nut's internal thread using this thread calculator, given the thread pitch, basic major diameter, and tolerance class details of the threads.

Pitch diameter (d2)9.0257 mmd − 0.649519 × pitch — where the thread is measured

Major diameter (d)10 mmthe nominal size, M10 × 1.5

Minor diameter, external (d3)8.1597 mmthe bolt’s root

Minor diameter, internal (D1)8.3762 mmthe nut’s bore

Tap drill size8.376 mmnominal diameter less the pitch is the usual shop rule: 8.5 mm

Thread height (H)1.299 mm0.866025 × pitch, the full triangle

Working thread depth0.8119 mm5H/8, after the root and crest truncations

Tensile stress area57.9896 mm²0.08988 in²

Threads per inch equivalent16.933for comparison with imperial sizes

Lead angle at the pitch diameter3.0282°

Proof load at class 8.833.63 kN8 lb at 580 MPa

Yield strength at class 8.837.11 kNat 640 MPa

The formula

ISO 60° thread: d2 = d − 0.649519 P, d3 = d − 1.226869 P

Pitch diameter is the working size

A screw thread does not bear on its crest or its root — both are deliberately truncated so they cannot interfere. It bears on the flanks, and the diameter where the flanks are half engaged is the pitch diameter. That is why thread gauges and micrometers measure d2 rather than the outside diameter.

The 0.649519 and 1.226869 constants come from the 60° profile geometry: the fundamental triangle is 0.866 P tall, and the standard truncations remove H/8 at the crest and H/4 at the root.

The shop rule for a tap drill — nominal diameter minus the pitch — lands very close to the basic minor diameter, which is why it works. It gives roughly 75% thread engagement, the usual compromise between strength and tapping torque.