Helical Coil Calculator

Created by Luciano Mino
Last updated: Sep 05, 2022

The helical coil calculator is the perfect tool to find every parameter of a helical coil.

We can also call this tool a coil length or helix length calculator! It can tell you everything about a helical coil, including but not limited to:

  • The coil's diameter, height, and length;
  • Wire diameter;
  • Number of turns;
  • Coil spacing;
  • Inductance; and
  • Capacitance.

Are you curious about how to calculate the number of turns in a coil? Keep reading, and we'll show you each of the formulas for these parameters, including the coil length formula!

Check our similar calculators about capacitors to find out the capacitors in series formula or capacitor code.

Helical coils

What is a helical coil? Simply put, a helical coil is an object twisted along a helix.

The coil's material depends on its use, and they have a wide range of applications. For example, because of their large surface area, we can use coils as efficient heat exchangers for cooling or heating air or liquids. We can also generate magnetic fields using coils which is the main topic of the solenoid magnetic field calculator.

Let's now look at all the different parameters this helical coil calculator has.

A coil's parameters as used in the helical coil calculator

We have a lot of parameters for describing a coil. Let's look at each of them and their formulas:

  • Coil diameter (Dc) is the diameter measured from the center of the coil to the neutral circle (the circle right between the inner and outer circles).
  • Wire diameter (Dw). We can relate both diameters using the following equation:
    Dw = 2 * (Do - Dc)
    with Do as the outer circle diameter.
  • Turns (N). The number of turns the wire is twisted around the helix axis.
  • Spacing (S). The distance between consecutive coils.
  • Height (H). We can obtain the height of the coil with this expression:
    H = N * (S + Dw)
  • Length (L). The total length of the wire used to create the coil. Below is the coil length formula:
    L = π * Dc * N
  • Inductance. The opposition to current flow produced by an inductor:
    L = (Dc * N)² / (18 * Dc + 40 * Lw)
  • Volume (V). Volume swept by the cross-section along the helix:
    V = π * Dw² * Lw / 4
  • Resonant frequency (Rf). The frequency at which the inductive reactance equals the capacitive reactance:
    Rf = 1 / (2 * π * √(L * C))
    where C is the coil's capacitance.

This is everything you need to start using the helical coil calculator. Feel free to experiment and test with it!

How to calculate the number of turns in a coil

You can also rearrange any expression containing N in the previous section to calculate the number of turns in a coil, for example:
N = L / (π * Dc)
Try it. Input L and Dc in the helical coil calculator, and it will output the number of turns!

Luciano Mino
Helical spring/coil
Coil parameters
Coil diameter (Dc)
Wire diameter (Dw)
Number of turns (N)
Coil spacing (S)
Coil height (H)
Wire length (Lw)
Coil properties
Volume of wire used (V)
cu in
Inductance (L)
Capacitance (C)
Resonant frequency (Rf)
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