Inductance of a Coil Calculator

Measure inductance using coil dimensions and permeability. Compare air core and magnetic core behavior quickly. Export clean reports for classes, testing, and practical design.

Calculated Result

Inductance	6.316547e-4 H
Inductance	0.631655 mH
Inductance	631.654682 µH
Cross-sectional area	0.001257 m²
Magnetic field	0.002513 T
Magnetic flux	3.158273e-6 Wb
Flux linkage	6.316547e-4 Wb-turn
Stored energy	3.158273e-4 J
Inductive reactance	3.968803 Ω
Impedance magnitude	6.383682 Ω
Time constant	1.263309e-4 s
AL value	1.579137e-8 H/turn²
Induced voltage	0.006317 V
Q factor	0.793761
Energy density	2.513274 J/m³

Calculator Inputs

Turns (N)

Coil length

Coil radius

Core type

Relative permeability (μr)

Current

Frequency

Resistance (Ω)

Current change rate (A/s)

Reset

Example Data Table

Turns	Length	Radius	μr	Approx. Inductance
120	0.08 m	0.015 m	1	0.160 mH
250	0.10 m	0.012 m	200	71.061 mH
400	0.18 m	0.020 m	1	1.404 mH
600	0.05 m	0.010 m	100	284.245 mH

Formula Used

The calculator uses the long solenoid approximation for coil inductance:

L = μ × N² × A / l

Here, μ = μ₀ × μr, where μ₀ is free-space permeability and μr is relative permeability. N is the number of turns, A is the cross-sectional area, and l is the magnetic path length of the coil.

The tool also derives B = μNI/l, Φ = BA, E = ½LI², X_L = 2πfL, |Z| = √(R² + X_L²), τ = L/R, and V = L(di/dt).

This approximation is most reliable when the coil length is reasonably larger than its diameter. For short coils, practical measurements may differ from theoretical values.

How to Use This Calculator

Enter the number of turns in the coil.
Provide coil length and radius using the most convenient units.
Select a core type, or choose custom and enter your own μr value.
Enter current, operating frequency, resistance, and current change rate.
Press Calculate to show the result block above the form.
Review inductance, field strength, flux, reactance, impedance, energy, and derived values.
Use the CSV or PDF buttons to export the current calculation.
Check the Plotly graph to see how inductance changes with turns.

Frequently Asked Questions

1) What does this calculator estimate?

It estimates coil inductance using the solenoid approximation. It also reports magnetic field, flux, stored energy, inductive reactance, impedance magnitude, AL value, and induced voltage.

2) Does core material affect inductance strongly?

Yes. Inductance scales directly with relative permeability. An air-core coil usually has much lower inductance than a ferrite or steel-core coil of identical geometry.

3) Why do turns matter so much?

Inductance is proportional to the square of turns. Doubling turns ideally increases inductance by about four times, assuming geometry and permeability stay unchanged.

4) Why is coil length included?

A longer coil spreads the magnetic field over a greater path. That reduces inductance when other variables remain the same.

5) What is AL value?

AL value is inductance per turn squared. Designers use it to compare cores and to estimate turns needed for a target inductance.

6) What does the reactance result mean?

Inductive reactance shows how much the coil resists alternating current at a chosen frequency. Higher frequency or higher inductance increases reactance.

7) Can I use this for air-core and ferrite coils?

Yes. Choose a listed core type or enter a custom permeability. The same page can compare air-core, ferrite, iron powder, or laminated steel cases.

8) Why might measured inductance differ from this result?

Real coils have leakage flux, spacing effects, fringing, winding thickness, and core nonlinearity. Those factors can shift measured values away from an ideal estimate.