# Three-Wire Screw Measurement

This tool can be used to calculate the correct measurement for a given thread using the three-wire method. It is based in concept on Screwmez by Pete Worden (described in Model Engineer's Workshop issue 246), but has been written from scratch to be a web-based application usable on any operating system. I don't have a Windows PC upon which to run Screwmez, so if you notice any discrepancies, please use the contact page to let me know!

All the fields that expect a number (diameter, pitch etc), will accept fractions (e.g. 1 1/4) and numbers followed by an explicit unit (" or mm), so if you chose to do so you could specify an imperial thread with a diameter of 25 1/2 mm and a pitch of 0.1" (rather than specifying a TPI). More usefully, if you have measuring wires that are specified in imperial units, you can select a metric thread but still enter (e.g.) 0.040" as the actual wire size.

Note that the minimum and maximum wire size fields may be wrong as I haven't yet managed to find consistent equations for all thread angles (in particular 47.5°). If anyone can help with this, then please do get in touch.

 Thread Class: Metric Coarse Metric Fine Custom Metric BA UNC UNF BSW BSF Custom Imperial Selected Thread: Thread Nominal Diameter (mm): mm Thread Pitch (mm): mm Thread Angle (degrees) 47.5° 55° 60° Thread Pitch Diameter (mm): mm Depth of Thread (mm): mm Helix Angle (degrees) Preferred Wire Size (mm): mm ??? mm Maximum Wire Size (mm): mm ??? mm Minimum Wire Size (mm): mm Actual Wire Size (mm): mm Dimension Over Wires (mm): mm

## Background

This calculator uses the following equations - let me know if you think they're wrong! Regardless of thread type, all entered data is converted into millimetres prior to calculating the results; if the thread type is an imperial one, the result is then converted back into inches for display (although both inches and millimetres are displayed in the right-hand column regardless of the thread unit).

### Key

$$\qquad D$$ is the Thread Diameter (e.g. 6 mm for M6).

$$\qquad C_p$$ is the Pitch Circumference (defined below).

$$\qquad D_p$$ is the Pitch Diameter (defined below).

$$\qquad P$$ is the Thread Pitch (for imperial threads, $$P = 1/TPI$$).

$$\qquad \theta$$ is the Thread Angle.

$$\qquad \alpha$$ is the Helix Angle.

$$\qquad \delta$$ is the depth of thread.

$$\qquad M$$ is the dimension over the wires.

$$\qquad W_p$$ is the preferred wire size.

$$\qquad W_a$$ is the actual wire size.

$$\qquad W_{max}$$ is the maximum wire size.

$$\qquad W_{min}$$ is the minimum wire size.

$$\qquad k_1$$, $$k_2$$ and $$k_3$$ are constants, defined below.

$$\delta = k_1 \cdot P$$

where $$k_1$$ depends on thread type as follows:

Metric:

$$k_1 = \frac{5}{8} \cdot \cos(30)$$

UNC:

$$k_1 = 0.625 \cdot \cos(30)$$

Whitworth/BSF:

$$k_1 = 0.640327$$

BA:

$$k_1 = 0.6$$

### Helix Angle

$$\alpha = \frac{\arctan(P)}{C_p}$$

where,

$$C_p = D_p \cdot \pi$$ $$D_p = D - \left( 0.75 \cdot P \cdot \cos \left( \frac{\theta}{2} \right) \right)$$

### Preferred Wire Size

$$W_p = \frac{0.5 \cdot P}{\cos\left(\frac{\theta}{2}\right)}$$

### Minimum / Maximum Wire Size

$$W_{max} = \frac{0.873 \cdot P}{\cos\left(\frac{\theta}{2}\right)}$$ $$W_{min} = \frac{0.485 \cdot P}{\cos\left(\frac{\theta}{2}\right)}$$

### Dimension Over Wires

$$M = D_p + \left( k_2 \cdot W_a \right) - \left( k_3 \cdot P \right)$$

where $$k_2$$ and $$k_3$$ depend on the thread angle ($$\theta$$):

$$k_2 = 3.0, k_3 = \cos(30)$$
$$k_2 = 3.1657, k_3 = 0.9605$$
$$k_2 = 3.4829, k_3 = 1.1363$$