Calculate the self-inductance (L) of a solenoid based on its physical dimensions and the core material.
Last updated: March 2026 | By ForgeCalc Engineering
Inductance (L) is the property of a conductor by which a change in current flowing through it induces an electromotive force (EMF) in both the conductor itself and in any nearby conductors. A solenoid is a coil of wire that concentrates this magnetic field.
The inductance of a solenoid depends on its physical geometry (number of turns, length, and cross-sectional area) and the magnetic permeability of the core material. Adding a magnetic core (like iron) can increase the inductance by thousands of times.
Where:
• L is the inductance (H)
• μ₀ is the permeability of free space (4π × 10⁻⁷ H/m)
• μ_r is the relative permeability of the core
• N is the total number of turns
• A is the cross-sectional area (πr²)
• l is the length of the solenoid (m)
Inductance is proportional to the square of the number of turns because adding a turn increases both the magnetic field strength and the number of loops that field passes through, doubling the effect.
The formula L = (μN²A)/l assumes the solenoid is much longer than its radius (l >> r). For short solenoids, 'Wheeler's formula' or other correction factors are needed.
You can increase inductance by adding more turns, increasing the radius, using a shorter coil, or inserting a high-permeability core (like ferrite or iron).
One Henry (H) is the inductance of a closed circuit in which an electromotive force of one volt is produced when the electric current in the circuit varies at the rate of one ampere per second.
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