# Helical Coil Calculator

Created by Rahul Dhari
Reviewed by Steven Wooding
Last updated: Nov 11, 2022

The helical coil calculator helps you determine various parameters of a coil. A helical coil is a crucial part of a machine, from aviation to automobiles and in electricity to heat exchangers. It is used in different applications for different qualities. For instance, a coil is used as a spring for its energy storing and shock absorption capabilities but also in heat exchangers for its large surface area.

Regardless of applications, the basic coil design formulae remain the same. Read on to understand how to estimate parameters like the height and length of a helical coil using the pipe coil length calculator.

You can also read more about specific applications of coils in Solenoid Inductance Calculator and LMTD calculator.

## What is a helical coil?

A helical coil is formed when the material is wound or twisted along a helix. For instance, If you wrap a wire or tube around a circular object, say a pencil, you get a helical coil. A helical coil can be obtained in various combinations of design parameters, such as coil diameter, wire diameter, pitch or spacing, coil height, etc. The advantage is this versatile part can be customized using these parameters for various applications such as a helical coil spring and heat exchanger.

## Formulae for coil design

Let's have a look at different coil parameters used in the helical coil calculator.

• Coil diameter ($D_\mathrm{c}$): The coil diameter is measured from the center of the coil to the neutral circle (as shown in the figure).

• Wire diameter ($D_\mathrm{w}$): This dimension refers to the diameter of the wire used for the coil. The coil and wire diameters are related using the equation:

$\qquad D_\mathrm{w}= 2 (D_\mathrm{o} - D_\mathrm{i})$

where $D_\mathrm{o}$ is the outer diameter of the helical coil.

• Turns ($N$): The number of times the wire is wound on the helix axis.

• Spacing ($S$): The distance between the consecutive coils is known as pitch or spacing.

• Height of coil (H): It is defined as the distance between the top and the bottom most points in the coil. The height of the coil can be found out using the equation:

$\qquad H = N (S + D_\mathrm{w})$
• Length of a helical coil ($L_\mathrm{w}$): It is the total measure of length of wire used to make the coil. In other words, the circumference of the coil taken N times. Mathematically, the length of helical coil formula can be written as:
$\qquad L_\mathrm{w} = N \sqrt { (\pi D_\mathrm{c})^2 + S^2}$
• Inductance (L): Inductance is the property of a material to change the electric current flowing through it. It is measured in Henries. The inductance L is a function of coil parameters, such as:
$\qquad L = \frac{D_\mathrm{c} N^2 }{18 D_\mathrm{c} + 40 L_\mathrm{w}}$
• Volume of wire used in the coil (V): It is the volume swept by the cross-section along the helix.
$\qquad V = \frac{\pi D_\mathrm{w}^2L_\mathrm{w}}{4}$
• Resonant frequency ($R_\mathrm{f}$): It is the frequency at which an inductor's capacitance resonates with the ideal inductance that results in high impedance. It can be found out using the equation:
$\qquad R_\mathrm{f} = \frac{1}{2 \pi \sqrt{LC}}$

where $C$ is the capacitance of the coil. You can read more about the topic in our resonant frequency calculator and capacitance calculator.

## How to calculate coil design parameters?

This tool primarily focuses on the estimation of coil inductance and volume based on the coil parameters. You can also use it in a reverse manner to determine coil parameters using the given inductance. To determine coil inductance:

1. Enter coil diameter $D_\mathrm{c}$ or coil radius $R_\mathrm{c}$ (in Advanced mode).
2. Fill in the wire diameter $D_\mathrm{w}$.
3. Insert the number of turns in the coil, N.
4. Enter the coil spacing or pitch, S.
5. The coil spring calculator will then return the height, H and wire length, $L_\mathrm{w}$.
6. The helical coil calculator also estimates the inductance, L in microHenries, and total volume of the coil, V.
7. Enter the capacitance, C in picofarads.
8. The calculator will return the resonant frequency for the coil.

## Example of using the helical coil calculator

Determine the inductance of the helical coil spring having coil diameter, 10 mm and wire diameter, 0.5 mm. Take coil spacing as 0.3 mm and number of turns as 15. Find the resonant frequency in kHz, given the capacitance is 0.46 pF.

To find the inductance of spring coil:

1. Enter coil diameter, $D_\mathrm{c} = 10~\mathrm{mm}$.
2. Fill in the wire diameter, $D_\mathrm{w} = 0.5~\mathrm{mm}$.
3. Insert the number of turns in the coil, N = 15.
4. Enter the coil spacing or pitch, S = 0.3 mm.
5. Using the length of helical coil formula:
\qquad \scriptsize \begin{align*} L_\mathrm{w} &=N \sqrt { (\pi D_\mathrm{c})^2 + S^2} \\ &= \sqrt { (\pi 10)^2 + 0.3^2} = 471.3~\mathrm{mm} \end{align*}
1. Height of coil spring, $H = N \times (S + D_\mathrm{w}) = 15 \times (0.3 + 0.5) = 12~\mathrm{ mm}$.
2. Volume of coil, $V = \pi \times 0.5^2 \times 471.3 / 4 = 92.53~\mathrm{mm^3}$
3. The inductance, L of the helical coil is calculated as:
\qquad \scriptsize \begin{align*} L &= \frac{(10 \times 15)^2 }{ (18 \times 10 + 40 \times 471.3)} \\ &= 1.342~\mathrm{\mu H} \end{align*}
1. The resonant frequency of the coil is:
\qquad \scriptsize \begin{align*} R_\mathrm{f} &= \frac{1}{(2 \times π \times √\frac{1.342}{10^5} \frac{0.46}{10^{11}} 1000} \\ &= 202,553~\mathrm{kHz} \end{align*}

## FAQ

### How to make a helical coil?

To make a helical coil:

1. Take a pencil or a straight object to use as a helix axis.
2. Wind the wire along the pencil (axis) closely or, based on your desired pitch, tightly.
3. Pull out the straight object to obtain the helical coil.

### How to calculate height of coil spring?

To determine the height of coil:

1. Count the number of turns on the coil.
2. Add the pitch of the coil and the diameter of the wire.
3. Multiply the resultant sum and number of turns.

Mathematically, that's: H = N × (S + Dw).

### What are the helical coil parameters?

Various helical coil parameters are as follows:

• Coil diameter;
• Wire diameter;
• Number of turns;
• Spacing or pitch;
• Height of coil; and
• Length of coil.

### How to calculate inductance of coil spring?

To determine the inductance of a helical coil:

1. Multiply the number of turns and diameter of the coil.
2. Square the resultant to obtain the numerator.
3. Add the products of the coil diameter and 18 with wire length and 40 to get the denominator.
4. Divide the numerator with the denominator to obtain the inductance of the helical coil.

L = (Dc × N)² / (18 × Dc + 40 × Lw).

Rahul Dhari
Coil parameters
Coil diameter (Dc)
in
Wire diameter (Dw)
in
Number of turns (N)
Coil spacing (S)
in
Coil height (H)
in
Wire length (Lw)
in
Coil properties
Volume of wire used (V)
cu in
Inductance (L)
μH
Capacitance (C)
pF
Resonant frequency (Rf)
kHz
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