# Calculating Pitch Diameter of Symmetrical Threads

The general formula for determining the pitch diameter of anyÂ thread whose sides are symmetrical with respect to a line drawnÂ through the vertex and perpendicular to the axis of the thread, inÂ which the slight effect of lead angle is taken into account, is:

**Formula 1**

IN WHICH | |

Pitch Diameter | |

Measurement Over Wires | |

Half Angle of Thread | |

n |
Number of Threads per Inch = |

Mean Diameter of Wires | |

Angle Between Axis or Wire and Plane Perpendicular to Axis of Thread |

This formula is a very close approximation, being based onÂ certain assumptions regarding the positions of the points ofÂ contact between the wire and the thread.

Formula 1 can be converted to the following simplified form,Â which is particularly useful when measuring threads of large leadÂ angle:

**Formula 2**

IN WHICH | |

The Angle Whose Tangent = |

When Formula 1 is used, the usual practice is to expand theÂ square root term as a series, retaining only the first and secondÂ terms, which gives the following:

**Formula 3**

For large lead angles it is necessary to measure the wire angle,Â , but for lead angles of 5 degrees or less, if the “best size” wire isÂ used, this angle may be assumed to be equal to the lead angleÂ of the thread at the pitch line, . The value of tan , theÂ tangent of the lead angle, is given by the formula:

IN WHICH | |

Lead | |

Number of Turns per Inch | |

Nominal Pitch Diameter, or an Approximation of the Measured Pitch Diameter |