Helical Coil Calculator — Inductance, Wire Length, Height & Resonant Frequency

What is a helical coil?

A helical coil is formed when a 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 (spacing), coil height, and number of turns.

This versatile part can be customized through these parameters for many applications. A coil is used as a spring for its energy-storing and shock-absorption capabilities, and in heat exchangers for its large surface area. Helical coils appear everywhere — from aviation and automobiles to electricity and heat transfer. Regardless of the application, the basic coil design formulae remain the same.

Formulae for coil design

The helical coil calculator uses the following parameters and equations:

• Coil diameter (D_c) — measured from the centre of the coil to the neutral circle.
• Wire diameter (D_w) — the diameter of the wire used for the coil.
• Turns (N) — the number of times the wire is wound around the helix axis.
• Spacing / pitch (S) — the distance between consecutive coils.

Height of the coil (H) — the distance between the top-most and bottom-most points of the coil:

Length of the helical coil (L_w) — the total length of wire used to make the coil (the circumference taken N times):

Inductance (L) — the property of the coil to oppose a change in the electric current flowing through it, measured in Henries. This calculator uses Wheeler's formula for a single-layer air-core coil, which returns the inductance in microhenries (µH) when the diameter and height are expressed in inches:

Volume of wire used in the coil (V) — the volume swept by the cross-section along the helix:

Resonant frequency (R_f) — the frequency at which the coil's inductance resonates with a capacitance C, resulting in high impedance:

How to calculate coil design parameters?

This tool primarily estimates the coil inductance and volume based on the coil parameters. To determine the coil inductance:

1. Select your unit system — Metric (mm) or American (inches).
2. Enter the coil diameter (D_c).
3. Fill in the wire diameter (D_w).
4. Insert the number of turns (N) in the coil.
5. Enter the coil spacing or pitch (S).
6. The calculator returns the height (H) and wire length (L_w), the inductance (L) in microhenries, and the total volume (V) of the coil.
7. Optionally, enter the capacitance (C) in picofarads to get the resonant frequency of the coil.

Example of using the helical coil calculator

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

• Wire length: L_w = 15 × √((π × 10)² + 0.3²) ≈ 471.3 mm
• Coil height: H = 15 × (0.3 + 0.5) = 12 mm
• Volume: V = π × 0.5² × 471.3 / 4 ≈ 92.53 mm³
• Inductance (with D_c = 0.3937 in and H = 0.4724 in): L = (0.3937² × 15²) / (18 × 0.3937 + 40 × 0.4724) ≈ 1.342 µH
• Resonant frequency: R_f = 1 / (2π × √(1.342×10⁻⁶ × 0.46×10⁻¹²)) ≈ 202.6 MHz

FAQs

How to make a helical coil?

To make a helical coil: (1) take a pencil or straight object to use as a helix axis; (2) wind the wire along the axis closely, or to your desired pitch; (3) pull out the straight object to obtain the helical coil.

How to calculate the height of a coil spring?

To determine the height of the coil: count the number of turns (N), add the pitch of the coil (S) and the diameter of the wire (D_w), then multiply the sum by the number of turns. Mathematically: H = N × (S + D_w).

What is the inductance of a helical coil?

Inductance is the property of the coil to oppose a change in the current flowing through it, measured in Henries. It depends on the coil diameter, number of turns, and coil height. This calculator uses Wheeler's single-layer solenoid approximation, returning the result in microhenries (µH).

What is the resonant frequency of a coil?

The resonant frequency is the frequency at which the coil's inductance resonates with a given capacitance, producing high impedance. It is given by R_f = 1 / (2π√(LC)), where L is the inductance and C is the capacitance.

Does the unit system change the result?

The geometric results (height, wire length, volume) are reported in your chosen unit system as well as its counterpart. The inductance is always computed using Wheeler's formula in inches and reported in microhenries, so it is independent of the unit system you enter.