Pitch Diameter Calculator (Three-Wire Method) 📏

Understanding the Thread Pitch Diameter ($E$)

The **Pitch Diameter** ($E$) is the most critical dimension for determining the fit and quality of a screw thread. It is the diameter of an imaginary cylinder where the **thread thickness** and **space thickness** are equal. In essence, it defines the effective diameter where the mating threads make contact.

The Three-Wire Measurement Method

The three-wire method is a highly accurate, universally accepted technique for measuring the pitch diameter of **external screw threads**. It involves placing three precision wires (two in one thread groove, one in the opposite groove) and measuring the overall distance ($M$) using a micrometer.

Three-Wire Pitch Diameter Formula

The formula calculates the Pitch Diameter ($E$) by subtracting the total contribution of the wires from the overall measurement ($M$) and adding a constant that accounts for the thread geometry.

$$E = M - W \left( 1 + \csc\left(\frac{A}{2}\right) \right) + P \cdot \cot\left(\frac{A}{2}\right)$$

Key Formula Components:

• **$M$**: **Measurement Over Wires** (The micrometer reading).
• **$W$**: **Wire Diameter** (The actual measured size of the precision wires).
• **$A$**: **Thread Angle** (e.g., $60^\circ$ for Unified/Metric threads).
• **$P$**: **Pitch** (The distance between adjacent thread crests, $P = 1/n$).
• **$\csc(A/2)$**: Cosecant of the half-angle, which is $1/\sin(A/2)$.
• **$\cot(A/2)$**: Cotangent of the half-angle, which is $1/\tan(A/2)$.

Best Size Wire ($W$)

For the highest accuracy, the wire used should be the **"Best Size Wire"**. This is the diameter ($W$) that touches the thread flank exactly at the pitch diameter line, minimizing errors due to thread form variations.

$$W_{\text{best}} = \frac{P}{2} \cdot \sec\left(\frac{A}{2}\right) = \frac{0.5 \cdot P}{\cos\left(\frac{A}{2}\right)}$$