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.

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
Depth of Thread
 (mm)
:
 mm
Helix Angle (degrees)
Preferred Wire Size
 (mm)
:
 mm
Maximum Wire Size
 (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.

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,

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

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 (\(\theta\)):

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:

$$ k_2 = 3.4829, k_3 = 1.1363 $$

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