Use the calculator below to calculate the inductance of a single layer round solenoid coil (also known as a helical coil). For rectangular coils, go to the Rectangular Coil Calculator. For coils of other types, see the Downloads Page for calculators in spreadsheet form.
See bottom of this page for detailed information and instructions.
Principal dimensions (Coil Length ℓ, Coil Diameter dc) are measured from centre to centre of the wire. Pitch p is centre to centre spacing between windings (measured parallel to the coil axis). The units for all dimensions, except conductor diameter, are according to the pop up menu at the top of the calculator. The conductor diameter is either mm or AWG according to the units pop op adjacent to the conductor size input field.
For multi-turn coils, you may enter either the Coil Length ℓ or the Winding Pitch p. Select the either Pitch or Coil Length from the pop up menu, and then enter the corresponding p or ℓ value into the input field. For single turn coils, you can leave this field blank.
A field is provided for you to enter the overall wire diameter which includes the insulation thickness. This field is optional, but makes it convenient to specify close wound coils. To do this, leave the Winding Pitch/Coil Length field blank or set to zero, and enter the overall wire diameter into the di field. (You still need to enter the conductor diameter.) When you click the Calculate button, the pitch and coil length will be adjusted to appropriate values for a close wound coil. In addition, if you enter a conductor size dw or overall wire diameter di that is too large for the specified pitch or coil length, the pitch and coil length will be increased automatically to the minimum close wound dimension. If you are using standard enamelled magnet wire, you can check the Auto Calculate box, and the overall diameter for this type of wire will be calculated automatically, based on the conductor size. Calculation of enamel thickness is based on typical magnet wire used by hobbyists, and may vary slightly from the actual value due to different insulation temperature ratings which affects insulation thickness.
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.
This calculator uses the Lorenz solenoid current sheet formula for coils having more than one turn. For single turn loops, Maxwell's elliptic integral formula is used.
Base Inductance is the Lorenz Current Sheet value which contains no corrections, or the Maxwell formula value, depending on the number of turns. Corrected Inductance is Base Inductance value with round wire corrections and frequency correction included. The single turn formula does not require round wire corrections.
KL is Nagaoka's field non-uniformity coefficient, calculated using Lorenz's elliptic integral formula.
KS is Rosa's round wire self inductance correction.
KM is Rosa's round wire mutual inductance correction.
LI is frequency correction due to skin effect only. Copper wire is assumed. No correction for proximity effect has been applied in this calculation.
KM and LI are calculated using David Knight's fitted formulae.
Conductor diameter dW shown in the output data is the same as the Conductor Size input converted to the chosen units.
Calculated Wire Length accounts for wire pitch.
In order to get accurate calculation results, it's important to provide accurate input data. The following coil cross-sectional diagram shows the proper measurements.
Coil diameter and length are to be measured from conductor centre to centre. The number of turns may be counted conveniently on the side away from the leads. For the coil in this diagram, the number of turns, N, is 3. Since it may be inconvenient to measure from wire centre to centre, the dimensions shown on following diagram may be used to measure and calculate the effective dimensions:
Measure the overall diameter of the winding D2 (from outside to outside of wire), and the diameter of the coil form D1. Then, the effective coil diameter, D, is the average of the two, given by:
D = (D1+D2)/2
The wire outside diameter, od, (including insulation) is given by:
od = (D2−D1)/2
To find the effective coil length, ℓ, measure the distance ℓ2, from outside to outside, and then the effective length is given by:
ℓ = ℓ2−od
Pitch p is given by:
p = ℓ/n
For coils which do not have an integral number of turns, the effective length may be determined using the method described above, but measuring from the first turn to the last full turn, then subtracting od, and multiplying the value thus obtained, by the actual number of turns divided by the number of complete turns. For example, for a coil with 5.3 turns, measure the outside to outside length ℓ2, and subtract od to get the centre to centre length of 5 full turns. Then multiply the result by 5.3/5 to get the length of 5.3 turns.