Inductance Calculator
Find the inductance of a solenoid coil.
1 for air; higher for cores
Results update as you type.
How it works
Inductance describes how strongly a coil opposes changes in current by storing energy in a magnetic field, and this calculator finds the inductance of a solenoid from its geometry. You enter the number of turns, the cross-sectional area of the coil, its length, and the relative permeability of the core, and it returns the inductance in henries and microhenries. The formula for a long, straight solenoid multiplies the permeability of free space by the core's relative permeability, the turns squared, and the area, then divides by the length. The most striking feature is the squared dependence on turns: doubling the number of turns quadruples the inductance, making turn count the most powerful lever in coil design. The core material matters enormously too, since an iron or ferrite core with a relative permeability in the hundreds or thousands multiplies the inductance far above an air core. Inductance is central to transformers, motors, chokes, filters, and tuned circuits, and this estimate helps engineers and hobbyists design coils for a target value. The formula assumes an ideal long solenoid where the length is much greater than the diameter; short or unusual coils need correction factors. Enter the turns, area, length, and permeability to compute the inductance.
L = μ₀·μr·N²·A / length
The inductance of a solenoid equals the permeability of free space times the relative permeability of the core, times the number of turns squared, times the cross-sectional area, divided by the coil length. Inductance rises sharply with the number of turns because of the square term, and a magnetic core with high permeability multiplies it further.
Source:Electromagnetism
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter number of turns, coil cross-section area and coil length.
- 2
Adjust the options
Adjust relative permeability if they apply — sensible defaults are already set.
- 3
Read your result
Inductance updates instantly as you type — no button to press.
Frequently asked questions
What is inductance?
Inductance is a coil's ability to store energy in a magnetic field and to oppose changes in the current flowing through it. Measured in henries, it depends on the coil's geometry and core material. Higher inductance means the coil resists current changes more strongly, which is key to transformers, filters, and tuned circuits.
How is solenoid inductance calculated?
Multiply the permeability of free space by the core's relative permeability, the number of turns squared, and the cross-sectional area, then divide by the coil length. The calculator does this from your inputs. Because turns are squared, they have the largest effect on the resulting inductance.
Why does the number of turns matter so much?
Inductance depends on the square of the number of turns, so doubling the turns quadruples the inductance. This makes turn count the most powerful factor in coil design. Adding turns is often the easiest way to increase inductance, though it also increases resistance and physical size, which must be balanced.
What is relative permeability?
Relative permeability describes how much more magnetic flux a core material carries compared with a vacuum or air, which has a value of one. Iron and ferrite cores have relative permeabilities in the hundreds or thousands, dramatically boosting inductance. Choosing a high-permeability core lets a smaller coil achieve a large inductance.
Does this formula work for any coil?
It is accurate for a long, straight solenoid where the length is much greater than the diameter. Short coils, toroids, and multilayer windings deviate from this ideal and need correction factors or different formulas. For a typical single-layer solenoid, though, this calculation gives a good estimate of the inductance.