Three-Wire Thread
Compute thread pitch diameter d₂ from a three-wire measurement M, wire diameter, pitch and thread angle (incl. 60° metric form).
Inputs
Formula
d₂ = M − dw(1 + 1/sin(α/2)) + P/(2 tan(α/2))
Fundamentals
The three-wire method measures an external thread's pitch diameter with three wires — a precise thread check.
From measured over-wires distance $M$, pitch diameter $d_2=M-3d_w+0.866p$, $d_w$ wire dia, $p$ pitch. Best-size wires touch at the pitch line to minimise flank-angle error.
History
The three-wire method was introduced by Pratt & Whitney around 1900 for precise pitch-diameter measurement.
Engineering applications
Used in metrology labs for thread gauges, leadscrews and precision screws.
Glossary
| Pitch dia $d_2$ | Diameter where thread thickness equals space. |
| Wire dia $d_w$ | Standard wire diameter used. |
| Pitch $p$ | Axial distance between adjacent threads. |
How to use
- Fill in Reading M, Pitch P, Thread angle α, Wire dia. dw in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Pitch dia. d₂ in the results area.
Formula notesThree-wire method: M = d₂ + 3·d_w − 0.866·p (d_w wire dia, p pitch, d₂ pitch dia); invert d₂ = M − 3d_w + 0.866p.
Formula · Worked Example · Knowledge
Formula
Three-wire pitch dia $d_2=M-d_w(1+1/\sin(\alpha/2))+P/(2\tan(\alpha/2))$; metric 60° simplifies to $d_2=M-3d_w+0.866P$.
Worked Example
M=20.2, dw=1.433, P=2.5, α=60° → d₂≈18.376 mm.
Key Points
- Pick wire dia near pitch line (optimal dw≈0.577P).
- Three-wire is high-precision, used for gauge calibration.
- Thread-angle error biases the result.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Reading M (mm) | M | mm | 20.2 |
| Pitch P (mm) | P | mm | 2.5 |
| Thread angle α (°) | alpha | ° | 60 |
| Wire dia. dw (mm) | dw | mm | 1.433 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Pitch dia. d₂ | d2 | mm |
Applications
- Cutting parameters and speed
- Gear measurement (3-wire/base tangent)
- Blanking and deep-drawing process
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: d₂ = M − dw(1 + 1/sin(α/2)) + P/(2 tan(α/2))
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Cutting parameters and speed