Magnetic energy storage
What is inductance?
Inductance describes the ability of a conductor or coil to oppose changes in current by producing an induced voltage.
It depends on magnetic flux linkage, coil geometry, number of turns, and magnetic permeability.
Flux-linkage model
Inductance from magnetic flux
Flux-linkage inductanceL = NΦ ÷ I
- L is inductance in henries.
- N is the number of coil turns.
- Φ is magnetic flux through one turn in webers.
- I is current in amperes.
Air-core solenoid
Solenoid inductance formula
Air-core solenoidL = μ₀N²A ÷ ℓ
- μ₀ is vacuum permeability.
- N is the number of turns.
- A is cross-sectional area in square metres.
- ℓ is coil length in metres.
Worked example
Calculate inductance from flux linkage
Suppose a coil has 200 turns, magnetic flux of 0.0005 Wb per turn, and current of 2 A.
- Use L = NΦ ÷ I.
- Substitute N = 200, Φ = 0.0005, and I = 2.
- L = 200 × 0.0005 ÷ 2.
- The inductance is 0.05 H.
Coil design
How turns affect inductance
In an ideal air-core solenoid, inductance is proportional to N². Doubling the number of turns increases inductance by approximately four times when area and length remain unchanged.
SI unit guidance
Inductance units
- Inductance: henries (H).
- Magnetic flux: webers (Wb).
- Current: amperes (A).
- Area: square metres (m²).
- Length: metres (m).
- 1 millihenry = 1 × 10⁻³ H.
- 1 microhenry = 1 × 10⁻⁶ H.
Model limitations
Assumptions and limitations
- The solenoid model assumes an ideal air core.
- Fringing magnetic fields are ignored.
- Winding resistance and parasitic capacitance are not included.
- Core saturation and hysteresis are not modelled.
- All values are treated as positive magnitudes.
Common questions
Inductance calculator FAQ
What formulas does the inductance calculator use?
It uses L = NΦ/I for flux linkage and L = μ₀N²A/ℓ for an ideal air-core solenoid.
What is the SI unit of inductance?
The SI unit of inductance is the henry, written H.
How do I calculate inductance from magnetic flux?
Multiply the number of turns by magnetic flux and divide by current using L = NΦ/I.
How do coil turns affect solenoid inductance?
In the air-core solenoid equation, inductance is proportional to the square of the number of turns.
Does this calculator work for iron-core inductors?
The solenoid mode assumes an ideal air core. Magnetic cores require their relative permeability and additional non-ideal effects.