Helical Coil Calculator

A helical coil is formed when a wire, tube, or other material is wound in a spiral along a cylindrical axis, tracing a helix shape. Helical coils are used in a wide variety of applications including inductors in electronics, springs in mechanical systems, and heat exchanger tubes in thermal engineering. The defining geometric parameters are the coil diameter, wire diameter, number of turns, and turn spacing.

The inductance of an air-core helical coil is calculated using Wheeler's formula: L = (Dc × N)² / (18 × Dc + 40 × Lw), where Dc is the coil diameter in inches, N is the number of turns, and Lw is the winding length in inches. This formula gives the inductance in microhenries (µH) and is accurate to within 1% for coils where the diameter is comparable to the length.

The main parameters of a helical coil include: coil diameter (Dc) — the mean diameter from wire center to wire center; wire diameter (Dw) — the thickness of the wire or tube; number of turns (N) — how many full loops are wound; turn spacing (S) — the gap between adjacent turns; coil height (H) — the total axial length of the wound section; wire length (Lw) — the total length of wire used; inductance (L); and self-capacitance (C).

The height of a helical coil is calculated as H = N × (S + Dw), where N is the number of turns, S is the turn spacing (gap between turns), and Dw is the wire diameter. This formula gives the total axial length occupied by the wound coil. When turns are closely wound (S = 0), the height simply equals the number of turns multiplied by the wire diameter.

The total wire length required to wind a helical coil is calculated using the formula Lw = π × Dc × N, where Dc is the coil (mean) diameter and N is the number of turns. This gives the approximate arc length traced by the wire as it wraps around the coil form. In practice, a small additional amount should be added for lead-out lengths at each end.

To make a helical coil, wrap a wire or tube tightly around a cylindrical mandrel of the desired coil diameter. Control the number of turns and the spacing between turns to achieve your target coil height and inductance. After winding, the coil can be slipped off the mandrel. For air-core inductors, the form may be removed; for spring applications, a harder material is used and the coil retains its shape.

Self-capacitance (also called distributed capacitance) is the parasitic capacitance that exists between adjacent turns of a coil. It arises because each turn acts like one plate of a small capacitor, with the space between turns acting as the dielectric. At high frequencies, self-capacitance can resonate with the coil's inductance, creating a self-resonant frequency above which the coil behaves as a capacitor rather than an inductor.

Coil diameter (Dc) refers to the mean diameter of the entire coil — measured from the center of the wire on one side to the center of the wire on the opposite side. Wire diameter (Dw) is the thickness of the individual wire or tube used to wind the coil. The outer diameter of the finished coil equals the coil diameter plus one wire diameter (Do = Dc + Dw), and the inner bore equals the coil diameter minus one wire diameter.