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.

Please note: the results produced by this calculator are nominal figures and may need a tolerance applied to them in order to fit. The following two websites are useful references (thanks to Gareth Jones for providing this information):

Thread Class:
Selected Thread:
Thread Nominal Diameter (mm):	mm
Thread Pitch (mm):	mm
Thread Angle (degrees)
Thread Pitch Diameter (mm):	mm (changed)
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.

$\qquad H$ is the height of the fundamental (sharp) thread triangle (defined below).

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

Thread Depth

$$ \delta = k_1 \cdot P $$

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

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

where,

$$ C_p = D_p \cdot \pi $$ $$ D_p = D - k_p \cdot P $$

where $k_p$ depends on the thread form: 0.649519 for 60° threads (metric and unified), 0.640327 for 55° threads (Whitworth and BSF) and 0.6 for 47.5° threads (BA). These come from the basic thread profiles: for 60° threads $D_p = D - 0.75 H$; for Whitworth and BA, the pitch diameter is the major diameter minus the depth of thread.

Preferred Wire Size

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

Minimum / Maximum Wire Size

The minimum wire size is the smallest wire that still stands proud of the crests of the thread (so that the micrometer touches the wires rather than the thread). The maximum wire size is the largest wire that still touches the straight part of the flanks (rather than sitting on the crests). If $h_c$ is the height of the crest and $h_f$ the height of the top of the straight part of the flank, both measured from the apex of the fundamental triangle at the root, then:

$$ H = \frac{P}{2 \tan\left(\frac{\theta}{2}\right)} $$ $$ W_{min} = \frac{2 h_c}{1 + \frac{1}{\sin\left(\frac{\theta}{2}\right)}} \qquad W_{max} = \frac{2 h_f \sin\left(\frac{\theta}{2}\right)}{\cos^2\left(\frac{\theta}{2}\right)} $$

For 60° threads, the crest is flat at $h_c = h_f = 7H/8$, giving $W_{min} = 0.5052 P$ and $W_{max} = 1.0104 P$. For Whitworth threads, the crest is rounded (radius $0.137329 P$) and truncated by $H/6$, giving $W_{min} = 0.5057 P$ and $W_{max} = 0.8527 P$. For BA threads, the crest is rounded (radius $2P/11$) and the thread depth is $0.6 P$, giving $W_{min} = 0.4985 P$ and $W_{max} = 0.7303 P$.

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 ($\theta$):

$$ k_2 = 1 + \frac{1}{\sin\left(\frac{\theta}{2}\right)} \qquad k_3 = \frac{1}{2 \tan\left(\frac{\theta}{2}\right)} $$

which gives:

60° thread angles:

$$ k_2 = 3.0, k_3 = \cos(30) $$

55° thread angles:

$$ k_2 = 3.1657, k_3 = 0.9605 $$

47.5° thread angles:

$$ k_2 = 3.4829, k_3 = 1.1363 $$

Buy me a pizza

This website is free and ad-free, but costs me money to run. If you'd like to support this site, please consider making a small donation or sending me a message to let me know what you liked or found useful.