Coil Self Inductance Calculator

Analyze coils using geometry, turns, and permeability. Review energy, reactance, voltage, and timing in seconds. Get reliable results, exports, formulas, and guidance for design.

Calculator Inputs

Use the responsive grid below. Large screens show three columns, medium screens show two, and mobile shows one.

Used for stored energy.
Used for inductive reactance.
Used for the RL time constant.
Used for induced voltage, V = L × dI/dt.

Formula Used

The calculator is built around the magnetic circuit estimate for self inductance:

L = μ₀ μᵣ N² A / l

L is self inductance in henries, μ₀ is free space permeability, μᵣ is relative permeability, N is turns, A is cross sectional area, and l is magnetic path length.

Solenoid: A = π(d/2)² and l ≈ coil length. This works best when the coil is long compared with its diameter.

Toroid: A = (rₒ − rᵢ)h and l = 2πrₘ, where rₘ is the mean radius. This suits toroidal cores with rectangular cross sections.

Custom path: enter your own magnetic path length and area when you already know the effective core dimensions.

Derived values use standard relations: XL = 2πfL, E = 0.5LI², τ = L/R, and V = L(dI/dt).

How to Use This Calculator

  1. Choose the coil model that best matches your geometry: solenoid, toroid, or custom magnetic path.
  2. Enter the number of turns and the relative permeability of the core material.
  3. Select the length unit for your geometry. If you use the custom model, choose the area unit too.
  4. Fill in the geometry values for the selected model only.
  5. Add optional operating values such as current, frequency, resistance, and dI/dt to see extra electrical outputs.
  6. Press Calculate. The result appears above the form, directly below the header section.
  7. Use the CSV or PDF buttons after calculation to save a portable record of your inputs and results.

Example Data Table

Case Model Turns μr Geometry Calculated L
Example 1 Solenoid 500 1 Diameter 25 mm, Length 80 mm 1.927657 mH
Example 2 Toroid 120 150 Inner radius 15 mm, Outer radius 25 mm, Height 10 mm 2.16 mH
Example 3 Custom path 800 200 Path length 180 mm, Area 120 mm² 107.233029 mH

Design Notes

This estimator is useful for early design, study, and comparison work. It assumes a mostly linear magnetic path and does not model strong saturation, fringing, proximity effects, temperature drift, or complex winding distribution.

For high accuracy hardware work, compare these results with measured inductance, manufacturer core data, or a field solver. The calculator is strongest as a fast engineering estimate, not as a final verification method.

FAQs

1. What does self inductance measure?

Self inductance measures how strongly a coil resists changes in its own current by storing magnetic energy and producing an opposing induced voltage.

2. Why does permeability matter so much?

Permeability describes how easily magnetic flux forms in a material. Higher relative permeability usually raises inductance sharply when geometry and turn count stay fixed.

3. When should I use the solenoid model?

Use the solenoid model for straight cylindrical coils where the magnetic path is approximated by the winding length and the cross section is circular.

4. When is the toroid model better?

Use the toroid model for ring shaped cores. It usually gives tighter flux containment and often reduces external magnetic field leakage.

5. Why does the calculator ask for current and frequency?

Those values are optional operating conditions. They let the tool estimate stored magnetic energy, inductive reactance, and induced voltage alongside inductance.

6. Is the result exact for real coils?

No. Real coils can differ because of fringing, core saturation, winding spacing, material tolerance, temperature, and frequency dependent losses.

7. What if my resistance is zero?

The RL time constant needs resistance. If resistance is zero, the tool still calculates inductance but does not report a finite time constant.

8. Can I use this for ferrite and iron cores?

Yes, as long as you provide a reasonable relative permeability and remember that strong saturation or nonlinear behavior can reduce accuracy.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.