Inductor Energy Calculator: E = 1/2 LI^2

The energy stored in the magnetic field of an inductor.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • E = \tfrac12\,L\,I^2
  • I = \sqrt{\frac{2E}{L}}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the stored energy: stored energy = 1/2 x inductance x current^2
  2. Put the values in (every value in its SI unit): stored energy = 1/2 x 0.01 x 5^2
  3. The answer: stored energy: 0.125 J
  4. The same answer in other units: 125 mJ; 125000 uJ

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is the formula for the energy in an inductor?

Half times the inductance times the current squared. A 10 mH coil carrying 5 A stores 0.125 J.

Why do relay coils need a diode?

To give the stored energy a safe path when the current is switched off, so it does not make a damaging voltage spike.

How is an inductor like a capacitor?

Both store energy. A capacitor stores it in an electric field, and an inductor in a magnetic field.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any school physics or electrical text (energy in inductors).

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