Enter the wire diameter, the total wire length used to form the coil, and the number of turns into the calculator to estimate the coil’s inner diameter (ID). This calculator helps in designing and understanding the dimensions of coiled wire.

Coil Diameter Calculator

Main
OD/ID Converter
Wire Length & Pitch

Enter any 3 values to calculate the missing variable. Assumes each turn’s wire length is approximately the circumference at the wire centerline (pitch contribution ignored).

Results will appear here.

Coil Diameter Formula

The following formula is used to estimate the inner coil diameter (ID) from the total wire length, number of turns, and wire diameter (single-layer coil; pitch contribution ignored). 

CD = \frac{CL}{\pi N} - WD

Variables:

  • CD is the coil diameter (inner ID) (any length unit, e.g., mm)
  • CL is the total wire length used to form the coil (same length unit as CD, e.g., mm)
  • N is the number of turns
  • WD is the wire diameter (same length unit as CD, e.g., mm)

To calculate the inner coil diameter, divide the total wire length by (π × number of turns) to get the mean diameter, then subtract the wire diameter to convert mean diameter to inner diameter.

What is Coil Diameter?

Coil diameter describes the size of a coil formed by winding wire (or another flexible material) around an axis or mandrel. In practice, “coil diameter” can refer to the inner diameter (ID), outer diameter (OD), or mean diameter (measured to the wire centerline). Coil diameter is an important parameter in the design of springs and solenoids because it affects stiffness, stress, fit/clearance, and the amount of space the coil occupies.

How to Calculate Coil Diameter?

The following steps outline how to calculate the Coil Diameter.

  1. First, determine the wire diameter (WD) in a length unit (e.g., millimeters).
  2. Next, determine the total wire length used to form the coil (CL) in the same unit (e.g., millimeters).
  3. Next, determine the number of turns (N).
  4. Next, gather the formula from above = CD = (CL / (πN)) − WD.
  5. Finally, calculate the Coil Diameter (CD) in the chosen unit.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

wire diameter (WD) = 1 mm

wire length (CL) = 100 mm

number of turns (N) = 10

CD = (100 / (π × 10)) − 1 = 2.1831 mm (inner diameter). The mean diameter is CD + WD = 3.1831 mm, and the outer diameter is CD + 2WD = 4.1831 mm.