An interactive online tool to calculate the coil inductance value of series of single layer loops formed into a coil.
Coil Inductance Calculator
This single-layer coil inductance calculator is an interactive online tool specifically designed to calculate the inductance value of a single coil of thin round-wire based on the coils loop inductance value. Electric inductance is usually represented by the letter L, and is expressed in Henrys (H).
However, because the Henry is a relatively large unit of measurement, it is more convenient to use smaller sub-units for measuring inductance. In which the milli-henry (mH) is equal to 1/1000 henry, and the micro-henry (uH) is equal to 1/1,000,000 henry. Either way, the Henry is basically a unit of measurement for the back-emf generated in a coil in opposing the change of current through it.
A coil is basically the sum of “N” individual turns of thin insulated wire wrapped around a bobbin (or hollow tube) to produce a tightly packed cylindrical coil of multiple layers. This hollow cored arrangement is known commonly as a solenoid. Then we can think of a solenoid as being an infinite number of single loops of wire connected in series as shown.
Loop Representation of a Coil
The self-inductance of a wound coil, solenoid, choke, or inductor is entirely dependent upon its physical construction, and as such inductance does not depend on the electrical properties of any circuit in which the coil is being used. In other words, a wound coil will always have the same inductance value, as long as you don’t change any of its physical characteristics.
For the basic coil inductance calculation, the physical configuration is that of a single-layer solenoid having more than one turn with zero spacing and no electrical connection between each coil turn. The inductance of a single turn coil is best obtained using a loop inductance formula with a solenoids total inductance simply being a matter of repeated application of the single loop inductance equation for “N” number of turns.
Coil Inductance Calculator
COIL INDUCTANCE CALCULATOR
INPUTS
| Number of Turns | N | ||
| Loop Diameter | D | mil cm mm um inch | |
| Wire Diameter | d | mil cm mm um inch | |
| Relative Permeability | μR |
OUTPUT
Inductance: 2.99e-8 H
How to Use this Coil Inductance Calculator
The calculator calculates the inductance of a wire loop realized in the form of a single circular loop and multiplies it by the number of turns (N). The major parameters used in this tool are the diameter of the conductor, d, the diameter of the wire loop D. The number of loop turns, and the relative permeability, (μr).
Since solenoid coils usually have air as their internal core, a relative permeability, (μr) of 1 can be used in the calculations. Clearly, for solenoid which have ferromagnetic materials like iron, nickel, or cobalt as their core material will have a different relative permeability value.
The calculator also allows you to select the units of measurement for both the loop and the wire diameter as shown.
Coil Inductance Equation
Calculating the inductance of a coil is found using the following equation:
Where:
- L is the total inductance, in Henrys (H)
- r = (D/2) is the radius of the coil loop (m)
- d is the diameter of the wire used (m)
- μ0 = 4πx10-7 (H/m) is the permeability of frees space (essentially, air)
- μr is the relative permeability of the core material
- N is the number of coil turns
Note that the coil inductance is related not only to the individual loop inductance’s, but by the square of the number of turns, N2. Thus, if one coil has twice as many turns as another, it will have four times as much inductance.
Example No1
A 30mm diameter solenoid having 150 turns is wound with 1.25mm diameter insulated copper wire onto a hollow tube. Calculate the coils total inductance.
Data given:
- D = 30mm, therefore radius r = D/2 = 30/2 = 15mm or 0.015m
- d = 1.25mm = 0.00125m
- N = 150 coil turns
- Permeability of free space μ0 = 4π x10-7
- Relative permeability μr of the core = 1 (hollow tube)
Thus, the total inductance of the solenoid coil is calculated as being: 0.00138 Henrys, or 1.38 milli-henrys (1.38 mH). This value can also be confirmed using the coil inductance calculator above.
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