Multi-Layer Coil Inductance Calculator

Use this calculator to find the inductance of a multi-layer coil.

For single layer coils, you may also use the following simpler calculators:
Solenoid Inductance Calculator
Rectangular Coil Calculator

Refer to the bottom of the page for explanation of input variables and other notes.

Note: This calculator is also suitable for flat spiral (pancake) coils, by setting the number of turns per layer, NT to 1 and setting the number of layers NL to the number of turns in the spiral.

Refer to the diagram below for terminology.

All length, diameter and pitch measurements are from centre to centre of the conductors as shown.

Definition of Parameters:
A - Coil Length
xR - Radial dimension of winding (winding depth)
pA - Winding pitch along axis
Do - Outside Diameter of Coil
Di - Inside Diameter of Coil
d - Diameter of conductor (excluding insulation)
di - Outside diameter of conductor including insulation
N
T - Number of turns per layer (NT=6 in the diagram)
NL - Number of winding layers (NL=5 in the diagram)
NS - Number sides of polygon (for polygonal coils)
(Note that uppercase D parameters refer to overall coil diameters while lowercase d parameters refer to conductor diameters.)

General Notes

1. 1.Calculation Method:
This calculator uses Maxwell’s formula for the mutual inductance between two circular filaments, applied to every combination of wire pairs in the coil, and then summed to determine the total inductance. For polygonal coils, an equivalent circular coil is determined according to a method by F. W. Grover, and the inductance is calculated from the equivalent coil. More information about these calculations is given in
Calculation Methods Part 1c.

2. 2.Wire size:
You may enter conductor size either as diameter in mm or AWG gauge number in the
Conductor Size field. Select either ‘AWG’ or ‘mm’ from the popup menu as  appropriate. When entering conductor size as AWG, sizes larger than 0 may be entered as 00, 000, etc., or 2/0, 3/0, etc. Although AWG sizes larger than 4/0 do not officially exist, the calculator will accept them and handle them according to the AWG standard ratio between successive sizes of 1.1229322.
Insulation diameter
di is required to be entered only in the case of a close wound coil (see next item). For enamelled magnet wire, you can leave the Auto Calculate box checked, and the calculator will automatically determine the insulation diameter. For other insulation types, uncheck the Auto Calculate box, and enter the actual insulation diameter in the Wire diameter including insulation field.

3. 3.Close Wound Coils:
For close wound coils, set the axial and radial dimension fields to zero or leave them blank. In
Wire diameter including insulation field, enter the value for the insulation diameter, or check the Auto Calculate box as explained above. The calculator will automatically set the correct winding pitch.

Inductance is essentially independent of the order in which the turns are placed on the coil. As long as it is possible to count the turns per layer and number of layers accurately, then the calculator will determine the correct inductance. In the case of these space wound type coils, it may not be easy to determine the effective number of turns per layer beforehand, making it difficult to predict the final dimensions, and hence, the inductance value. However, coil length
A is easily determined beforehand, and if a test winding is made, total turns, and number of layers can be easily counted. From this test winding data, the turns per layer can be found by dividing total number of turns by number of layers. This information can then be used to design the final coil.

5. 5.Frequency Correction:
Optionally, enter the intended operating frequency, and the calculator will calculate a frequency correction due to skin effect. This correction is very small and can be neglected in most cases.
Note that no correction is done for proximity effect.

6. 6.Self-Capacitance Effect:
The effect of self-capacitance causes coil inductance to read lower than its true value, when measured on inexpensive inductance meters. Because multi-layer coils tend to have much higher self-capacitance than single layer coils, the difference between measured and true inductance can be expected to be greater. Therefore, one should be cautious when interpreting the measurements from inductance meters if they appear lower than expected.

7. 7.Coil Form Shape:
The coil form may be either circular or polygonal. For polygonal coils, select
Polygonal from the Coil form popup menu, and then in the Number of Polygon Sides input field, enter the number of sides. For circular coils, leave the popup menu set to Circular, and leave the Number of Polygon Sides input field blank.

8. 8.Polygon Measurements (see diagrams below):
Inner diameter
Di is the same as the diameter of the circumscribed circle of the inner polygon. It is measured, in the case of a polygon with an even number of sides, from one inner vertex across to the opposite inner vertex. For a polygon with an odd number of sides, the measurement is taken from the centre axis to an inner vertex, and that value is then doubled. Alternatively, measure the length, s, of a side, and then the diameter is given by:
Di = s/sin(π/NS)         (Angle in radians)

or
Di = s/sin(180/NS)     (Angle in degrees)
Note that the true radial pitch
pR is less than the radial distance between vertices pR', by a factor of cos(π/NS). Likewise, the radial depth of winding, xR, is smaller than xR', the distance between the innermost and outermost vertex by the same factor. However, since it is generally easier to measure along the vertices, the calculator is designed to accept the pR' and xR' values as measured along the vertices. Therefore, Do not use the pR and xR values for polygonal coils.

Polygonal Coil - Viewed along axis:

Dimension detail:

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