Screw Thread Calculator

Every dimension of an ISO metric or Unified thread derives from one construction: a 60 degree equilateral triangle of height H repeated along the axis at the pitch p, giving H equal to p times the square root of 3 over 2, or 0.866025p. That sharp theoretical form is then truncated, one eighth of H removed at the crest and one quarter at the root, because sharp corners are fragile, hard to produce and act as stress raisers. The truncation is what produces the working constants: pitch diameter is the major diameter minus 0.6495p and minor diameter is the major diameter minus 1.2269p, so for an M10 x 1.5 thread the pitch diameter is 9.026 mm and the minor diameter 8.160 mm. Pitch diameter is the critical dimension because it is where mating flanks actually bear, and it carries the tightest tolerance. Strength is computed on the tensile stress area, based on the mean of the pitch and minor diameters rather than the nominal size, since the threads remove material. The M10 x 1.5 value of about 58 square millimeters is why a property class 8.8 bolt of that size has a proof load near 32 kN. Fit is specified by tolerance class, 6g external and 6H internal being the general purpose metric pairing, against Unified classes 2A and 2B, with 3A and 3B for precision work. The tap drill for a metric thread is approximately the major diameter minus the pitch, giving about 75 percent engagement, beyond which strength gains are marginal while tapping torque and tap breakage rise sharply. Note that these are basic sizes, not the allowances and tolerance bands of a specific class, and they exclude plating thickness, which consumes clearance on coated fasteners.

Before the mid nineteenth century each workshop cut threads to its own proportions, so a nut from one shop rarely fit a bolt from another. Joseph Whitworth addressed this in 1841 by surveying threads in use across British industry and proposing a uniform system with a 55 degree included angle and rounded crests and roots, together with a fixed pitch for each diameter. British Standard Whitworth became the first widely adopted thread standard and demonstrated that interchangeability was an economic proposition rather than a theoretical nicety. The United States took a different path. William Sellers presented a rival system to the Franklin Institute in 1864 using a 60 degree angle with flat crests and roots, arguing it was easier to cut and gauge because it did not require the rounded form tooling Whitworth threads needed. It was adopted by the Navy and the railroads and became the US Standard, later the American National thread. The two incompatible systems caused serious problems during the Second World War, when British, American and Canadian equipment could not share fasteners. That experience produced the Unified Thread Standard, agreed by the three countries in 1948, which kept the 60 degree Sellers profile and reconciled the tolerance and class systems. In parallel, ISO built the metric standard on the same 60 degree profile, defined in ISO 68 with basic dimensions in ISO 724, diameter and pitch combinations in ISO 261 and 262, and tolerances in ISO 965; ASME B1.1 continues to govern Unified inch threads.