Inductor Energy
E = ½LI²
Quick answer
This calculator solves E = ½LI² for Energy. With Inductance 10 mH, Current 2 A, the result is 20 mJ. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The energy stored in an inductor is held in its magnetic field and is proportional to the inductance and the square of the current. This is analogous to the capacitor energy formula E = ½CV², with inductance replacing capacitance and current replacing voltage. The quadratic current dependence means that doubling the current quadruples the stored energy. This stored magnetic energy is what enables switching power supplies (buck, boost, and buck-boost converters) to efficiently transfer energy between input and output at different voltage levels.
Variables
- E — Energy in joules (J)
- L — Inductance in henries (H)
- I — Current through the inductor (A)
Practical Notes
In switching regulator design, the inductor must be chosen so that its saturation current rating exceeds the peak operating current. When an inductor saturates, its inductance drops dramatically and current spikes, potentially damaging the switching transistor.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| E | Energy | mJ | µJ, mJ, J, kJ, Wh, kWh |
| L | Inductance | mH | nH, µH, mH, H |
| I | Current | A | pA, nA, µA, mA, A, kA |
Step by step
- 1. What you know: Inductance 10 mH, Current 2 A
- 2. The relation: E = ½LI²
- 3. Substitute: L = 10 mH, I = 2 A
- 4. Result: Energy = 20 mJ
Worked examples
Minimum range
Given: Inductance 100 µH, Current 2 mA
Result: Energy = 2 × 10⁻⁴ µJ
Low range
Given: Inductance 1 mH, Current 20 mA
Result: Energy = 0.2 µJ
Typical
Given: Inductance 10 mH, Current 2 A
Result: Energy = 20 mJ
High range
Given: Inductance 100 mH, Current 100 A
Result: Energy = 0.5 kJ
Maximum range
Given: Inductance 1 H, Current 1 kA
Result: Energy = 138.9 Wh
Solving for each variable
Solve for Energy
Inductance 100 µH, Current 2 mA → 2 × 10⁻⁴ µJ
Solve for Inductance
Energy 100 µJ, Current 2 mA → 50 H
Solve for Current
Energy 100 µJ, Inductance 100 µH → 1.414 A
How Energy changes with Inductance
| Inductance (input) | Energy (result) |
|---|---|
| 1 mH | 2 mJ |
| 2.5 mH | 5 mJ |
| 5 mH | 10 mJ |
| 7.5 mH | 15 mJ |
| 10 mH | 20 mJ |
| 15 mH | 30 mJ |
| 20 mH | 40 mJ |
| 40 mH | 80 mJ |
| 70 mH | 140 mJ |
| 100 mH | 0.2 J |
The same result in other units
| Unit | Value |
|---|---|
| µJ | 20000 |
| mJ | 20 |
| J | 0.02 |
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<p><a href="https://vbatpower.com/formulas/inductor-energy/">Inductor Energy</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Inductor Energy?
Use E = ½LI². With Inductance 10 mH, Current 2 A, Energy works out to 20 mJ.
What is the formula for Inductor Energy?
The formula is E = ½LI². The energy stored in an inductor is held in its magnetic field and is proportional to the inductance and the square of the current.
How do you find Inductance when you know the other values?
Rearrange for Inductance: with Energy 100 µJ, Current 2 mA, Inductance is 50 H.
How do you find Current when you know the other values?
Rearrange for Current: with Energy 100 µJ, Inductance 100 µH, Current is 1.414 A.
What units does Inductor Energy use?
Energy is shown in µJ, mJ, J. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Inductors formulas →Need more features?
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