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## Helical Spring Mandrel Design Calculator

Hand made springs/coils are typically wound around a mandrel, that is inserted into a chuck on a milling machine, or lathe. When the spring is released from the jig it will spring back and will have a greater diameter than the diameter of the mandrel. It is therefore useful to know what mandrel diameter is needed, to render a given spring diameter.

This calculator takes as input the diameter of the wire, the desired spring diameter, and the wire material types, and outputs the diameter of the mandrel.

Units can be inches or mm, just be consitent.

Coil Diameter Music Wire Stainless Steel Wire Phosphor Bronze Wire

This calculator is based on the following article:

"Helical Springs" by Kozo Hiraoka, in Home Shop Machinist, May/June and July/August issues, 1987

### Equations:

Dm= kD - d

where:
Dm is the diameter of the mandrel,
k is the diameter coefficient,
D is the final diameter of the spring, measured from the center of the wire (not the outer or the inner spring diameter).
d is the diameter of the wire.

Wire Diameter Coefficients
Music Wire and Stainless Steel:
k = -0.01245x + 0.98425

Phosphor Bronze Wire:
k = -0.011x + 0.987

where:
k is the diameter coefficient,
x is the spring index: D/d.