Helical Coil Calculator

Q: 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 that this versatile part can be customized with these parameters for various applications, such as helical coil springs and heat exchangers.

Q: How do I calculate height of coil spring?

To determine the height of the coil: Count the number of turns on the coil. Add the spacing between wires of the coil and the diameter of the wire. Multiply the resultant sum and number of turns. Mathematically, that's: H = N × (S + Dw)

Q: How do I calculate inductance of coil spring?

To determine the inductance of a helical coil: Multiply the number of turns and the diameter of the coil. Square the resultant to obtain the numerator. Add the products of the coil diameter and 18 with the wire length and 40 to get the denominator. Divide the numerator by the denominator to obtain the inductance of the helical coil. L = (Dc × N)² / (18 × Dc + 40 × Lw)

Creators

Rahul Dhari

Research Gate

Rahul is a researcher and engineering expert dedicated to applying his skills to solve complex world problems. He has contributed to impactful projects in advanced material manufacturing and 3D printing failure analysis frameworks, among others. His research is a testament to his devotion to discovery and innovation within mechanical and aerospace engineering. His expertise ranges from 3D printing and computational modeling through advanced engineering simulation to material characterization and additive manufacturing. Whenever he is not revolutionizing engineering research, he enjoys outdoor adventures with his dog, who is his biggest fan. See full profile

Check our editorial policy

Reviewers

Steven Wooding

Steven Wooding is a physicist by training with a degree from the University of Surrey specializing in nuclear physics. He loves data analysis and computer programming. He has worked on exciting projects such as environmentally aware radar, using genetic algorithms to tune radar, and building the UK vaccine queue calculator. Steve is now the Editorial Quality Assurance Coordinator here at Omni Calculator, making sure every calculator meets the standards our users expect. In his spare time, he enjoys cycling, photography, wildlife watching, and long walks. See full profile

Check our editorial policy

Add as preferred on Google

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 that this versatile part can be customized with these parameters for various applications, such as helical coil springs and heat exchangers.

Formulae for coil design

Let’s have a look at the 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:

\quad 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. The pitch is the spacing plus the wire diameter.
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 using the equation:

\quad 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:

\quad L_\mathrm{w} = N \sqrt { (\pi D_\mathrm{c})^2 + (S+D_{\rm w})^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:

\quad 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.

\quad 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:

\quad 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:

Enter coil diameter $D_\mathrm{c}$ or coil radius $R_\mathrm{c}$ .
Fill in the wire diameter $D_\mathrm{w}$ .
Insert the number of turns in the coil, $N$ .
Enter the coil spacing, $S$ .
The coil spring calculator will then return the height, $H$ and wire length, $L_\mathrm{w}$ .
The helical coil calculator also estimates the inductance, $L$ in microHenries, and total volume of the coil, $V$ .
Enter the capacitance, $C$ in picofarads.
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, $10\ \mathrm{mm}$ and wire diameter, $0.5\ \mathrm{mm}$ . Take coil spacing as $0.3\ \mathrm{mm}$ and number of turns as $15$ . Find the resonant frequency in $\mathrm{kHz}$ , given the capacitance is $0.46\ \mathrm{pF}$ .

To find the inductance of the spring coil:

Enter coil diameter, $D_\mathrm{c} \approx 10\ \mathrm{mm}$ .
Fill in the wire diameter, $D_\mathrm{w} \approx 0.5\ \mathrm{mm}$ .
Insert the number of turns in the coil, $N = 15$ .
Enter the coil spacing, $S = 0.3\ \rm mm$ .
Using the length of helical coil formula:

\quad \begin{align*} L_\mathrm{w} &=N \sqrt { (\pi D_\mathrm{c})^2 + (S+D_{\rm w})^2} \\[1em] &= \sqrt { (\pi 10)^2 + 0.3^2} \approx 471.4\ \mathrm{mm} \end{align*}

💡 Note that the unit of length used in these equations is inches. The calculator converts between millimeters and inches for you.

Height of coil spring is:

\quad \begin{align*} H &= N \times (S + D_\mathrm{w}) \\ &= 15 \times (0.3 + 0.5) \approx12\ \mathrm{ mm} \end{align*}

Volume of coil:

\quad \begin{align*} V &= \pi \times 0.5^2 \times 471.3 / 4 \\&\approx 92.53\ \mathrm{mm^3} \end{align*}

The inductance, $L$ of the helical coil is calculated as:

\quad \begin{align*} L &= \frac{(10 \times 15)^2 }{ (18 \times 10 + 40 \times 471.3)} \\[1em] &\approx 1.342\ \mathrm{\mu H} \end{align*}

The resonant frequency of the coil is:

\quad \begin{align*} R_\mathrm{f} &= \frac{1}{(2 \times π \times \sqrt{\frac{1.342}{10^5}} \frac{0.46}{10^{11}} 1000} \\[1.5em] &\approx202,553\ \mathrm{kHz} \end{align*}

FAQs

How do I make a helical coil?

To make a helical coil:

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

How do I calculate height of coil spring?

To determine the height of the coil:

Count the number of turns on the coil.
Add the spacing between wires of the coil and the diameter of the wire.
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 do I calculate inductance of coil spring?

To determine the inductance of a helical coil:

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

L = (Dc × N)² / (18 × Dc + 40 × Lw)