ThreeWire Screw Measurement
This tool can be used to calculate the correct measurement for a given thread using the threewire 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 webbased 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:  
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 righthand 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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