Inductor Calculator
An inductor's value comes from its geometry. This calculator uses the ideal long-solenoid formula to find inductance from the number of turns, the coil cross-sectional area, the coil length, and the relative permeability of the core (1 for air). It then gives the inductive reactance at a frequency you choose and the energy stored at a chosen current. The permeability of free space is a defined physical constant, so no empirical figure is needed; the results are exact for an ideal long coil.
Inductor formulas
mu0 = 4 * pi * 1e-7 (permeability of free space, H/m)
Inductance L = mu_r * mu0 * N^2 * area / length
Reactance XL = 2 * pi * frequency * L
Stored energy = 0.5 * L * current^2
The permeability of free space is a defined constant. The solenoid formula is exact for an ideal long coil. Reactance is the opposition to alternating current, and stored energy is the magnetic field energy at the given current.
Inductor context
- Inductance scales with the square of the number of turns.
- The permeability of free space mu0 equals 4 pi times 1e-7 henries per metre.
- A magnetic core multiplies inductance by its relative permeability.
- Reactance increases with frequency, so inductors oppose higher frequencies more.
- The long-solenoid formula ignores end effects, which reduce inductance in short coils.
Inductor: frequently asked questions
How is the inductance of a solenoid calculated?
For a long air-core solenoid, inductance equals the permeability of free space times the number of turns squared times the cross-sectional area, divided by the coil length. The permeability of free space is a defined physical constant, so the formula needs no empirical input.
What is inductive reactance?
Inductive reactance is the opposition an inductor presents to alternating current. It equals two pi times the frequency times the inductance, in ohms. Reactance rises with both frequency and inductance, so an inductor blocks high frequencies more than low ones.
How much energy does an inductor store?
An inductor carrying a current stores energy in its magnetic field equal to one half times the inductance times the current squared. With inductance in henries and current in amperes, the energy is in joules.
Does this formula apply to cored inductors?
The default uses the permeability of free space for an air core. For a magnetic core, multiply by the core's relative permeability. The relative permeability input lets you model a cored inductor; set it to 1 for air.
Is the solenoid formula exact?
It is the standard ideal long-solenoid formula, exact in the limit of a long coil where end effects are negligible. The permeability of free space is a defined constant. For short coils, end effects make the true inductance slightly lower.
Official sources
- NIST: Vacuum magnetic permeability constant.
- NASA Glenn Research Center: Physics fundamentals.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.