Inductance Calculator - Solenoid Inductance
Calculate the inductance of an air-core solenoid from the number of turns, coil length, and coil radius.
Inductance
39.478 µH
0.039478 mH | 3.9478e-5 HHow to Calculate Solenoid Inductance
For a simple air-core solenoid (a straight cylindrical coil), inductance depends on the number of turns, the coil's length, and its cross-sectional area. Enter the turn count, coil length, and coil radius to get the inductance using the standard solenoid formula.
Example
A coil with 100 turns, a length of 10 cm, and a radius of 1 cm has a cross-sectional area of about 3.1416 cm². Converting to meters and applying the formula gives an inductance of roughly 39.5 microhenries (µH).
Common Use Cases
- Designing a hobby electronics inductor or RF coil.
- Estimating how changing turn count or coil length affects inductance.
- Physics or electrical engineering coursework on solenoids and magnetic fields.
FAQs
What is μ₀ (mu-naught)?
μ₀ is the permeability of free space, a physical constant equal to about 4π × 10⁻⁷ henries per meter (H/m). It describes how easily a magnetic field can form in a vacuum (or air, which is very close to vacuum for this purpose) and appears in this formula because the coil here has an air core.
Does this work for coils with a magnetic core?
No — this assumes an air-core coil. Adding a ferromagnetic core (like iron or ferrite) multiplies the inductance by that material's relative permeability (μr), which can be dozens or hundreds of times higher than air, so a cored inductor's actual inductance will be much higher than this result.
Does wire gauge or turn spacing matter?
Not directly in this formula — it assumes turns are wound evenly along the given coil length, regardless of the wire's thickness. Wire gauge determines how many turns physically fit in that length, but once you know the turn count and length, the inductance formula itself doesn't need the gauge.