Inductance & Inductor Energy Calculator

Calculate inductor energy using E = ½LI², inductance, or current.

🔌 Circuits📐 E = ½LI²📡 Inductor
Inductance (L) Henries
Current (I) A
⚠️ Enter valid positive numbers.

What Is Inductor Energy?

An inductor stores energy in its magnetic field: E = ½LI², where L is inductance (Henries, H) and I is current (A). This is the magnetic analogue of E = ½CV² for capacitors. Inductance L measures how strongly a coil opposes changes in current — a large L resists rapid current changes.

The inductance of a solenoid: L = μ₀μᵣN²A/l, where N is turns, A is cross-sectional area (m²), l is length (m), and μᵣ is relative permeability (1 for air, 1,000–100,000 for iron cores). Iron cores dramatically increase L, enabling compact inductors for power electronics.

Inductors oppose changing current: V_L = L·dI/dt. When switched off, an inductor drives a voltage spike (kick-back) V = L·ΔI/Δt — potentially thousands of volts for fast switching. Flyback diodes and snubber circuits protect switch components from this spike.

In LC circuits, inductors and capacitors exchange energy at frequency f₀ = 1/(2π√LC). This resonance is fundamental to radio tuning, filter design, and impedance matching. The quality factor Q = ωL/R determines selectivity — how sharply the circuit responds at f₀.

Formula Reference Table

Solve ForFormulaNotes
Stored energyE = ½LI²L in H, I in A
InductanceL = 2E/I²H
Current from energyI = √(2E/L)A
Solenoid LL = μ₀μᵣN²A/lμ₀ = 4π×10⁻⁷ H/m
Induced EMFV = L·dI/dtVolts; opposes current change
Inductive reactanceX_L = 2πfLΩ; impedance to AC

3 Worked Examples

Example 1
Power Supply Inductor

L = 100 μH, I = 5 A. Stored energy.

  • E = ½LI² = ½ × 100×10⁻⁶ × 25 = 1.25×10⁻³ J = 1.25 mJ
  • At 100 kHz switching: energy transferred per cycle = 1.25 mJ × 2 = 2.5 mJ/cycle
  • Power handling = 2.5×10⁻³ × 100,000 = 250 W
✓ E = 1.25 mJ; 250 W power handling at 100 kHz
Example 2
Solenoid Inductance

Air-core solenoid: N = 500, l = 20 cm, d = 2 cm.

  • A = π×(0.01)² = 3.14×10⁻⁴ m²
  • L = μ₀N²A/l = 4π×10⁻⁷ × 250,000 × 3.14×10⁻⁴ / 0.2
  • L = 4.93×10⁻⁴ H = 493 μH
✓ L = 493 μH
Example 3
Kick-Back Voltage

L = 100 mH, I = 2 A switched off in 1 μs.

  • V = L·ΔI/Δt = 0.1 × 2 / 10⁻⁶ = 200,000 V (!)
  • This is why inductive loads need flyback protection
  • Snubber RC or flyback diode limits this to safe levels
✓ V_spike = 200,000 V — must use flyback diode protection

Real-World Applications

📡
RF Circuits
Inductors in LC tanks select radio frequencies. L and C values set f₀ = 1/(2π√LC). Variable inductors (slug-tuned) adjust frequency.
⚡
Switching Power Supplies
Boost/buck converters store energy in inductors during switch-on and release during switch-off. Larger L → smoother current, less ripple.
🔌
Choke Filters
Inductors block high-frequency AC while passing DC. Power line filters use high-L chokes to prevent switching noise from entering the mains.
🚂
Rail Guns
Pulsed power rail guns use enormous stored magnetic energy (E = ½LI² in the rail inductance) to accelerate projectiles to km/s.
🔧
Induction Heating
A high-frequency AC coil induces eddy currents in metallic workpieces. The eddy currents generate heat via I²R — used for selective hardening, cooking (induction hobs), and sterilization.

Common Mistakes to Avoid

⚠️
Wrong unit for L

L must be in Henries. 100 mH = 0.1 H. Common values: power supplies 10–1000 μH; RF 0.1–100 μH; power transmission 1–100 mH.

⚠️
Forgetting the ½

E = ½LI², not LI². Energy builds gradually as current ramps up.

⚠️
Confusing L and C behavior

Capacitor: blocks DC, passes AC. Inductor: passes DC, blocks AC. Capacitor energy = ½CV². Inductor energy = ½LI². Their behaviors are exactly dual.

⚠️
Ignoring core saturation

Iron core inductors saturate at high current — L drops suddenly. Design to keep flux density B = μ₀μᵣNI/l below saturation (typically 1–2 T for iron).

⚠️
Using impedance Z_L for DC

X_L = 2πfL applies to AC only. At DC (f=0), X_L = 0 — ideal inductor has no impedance to DC. Only resistance (DCR) limits DC current.

Frequently Asked Questions

What is inductance? ▾
L (H) measures the magnetic flux Φ linked per unit current: L = NΦ/I. Equivalently, V = L·dI/dt — 1 henry means a 1 A/s current change induces 1 V. Higher L = more flux stored per ampere = stronger opposition to current changes.
Why does an inductor oppose current changes? ▾
By Faraday's law, a changing current creates a changing magnetic flux, inducing an EMF that opposes the change (Lenz's law). V_L = −L·dI/dt. This 'inertia' to current change is the magnetic analogue of mass's inertia to velocity change.
What is mutual inductance? ▾
When two coils are coupled magnetically: M = k√(L₁L₂), where k is the coupling coefficient (0 to 1). A changing current in coil 1 induces EMF in coil 2: V₂ = M·dI₁/dt. This is the transformer principle — M determines how efficiently energy is transferred.
What are the Q factor and efficiency of inductors? ▾
Q = ωL/R_DC (quality factor). High Q = low losses at the operating frequency. Air-core coils: Q = 50–400. Iron-core: Q = 30–200. High Q is critical for narrow-bandwidth filters and oscillator stability. At higher frequencies, skin effect and core losses reduce Q.
What is a flyback diode and why is it essential? ▾
Without protection, switching off an inductor creates V = L·dI/Δt — potentially thousands of volts in microseconds. A flyback (freewheeling) diode provides a path for the inductive current to flow harmlessly until the energy is dissipated, clamping the voltage to Vf ≈ 0.7 V (forward diode drop).
How does a buck converter work? ▾
Switch on: current builds in L (E = ½LI² increasing). Switch off: L forces current to continue through freewheeling diode into load + capacitor. Output V_out = V_in × duty_cycle. Steady-state: energy stored in L during on-time = energy delivered during off-time. Higher switching frequency → smaller L needed.
What is impedance matching with inductors? ▾
Inductors transform impedance in resonant circuits. At resonance (LC tank), the circuit appears purely resistive. A series inductor with an antenna (matching network) can transform the antenna impedance (50 Ω) to the transmitter output impedance. This maximizes power transfer.
What is self-resonance frequency? ▾
Real inductors have parasitic capacitance (between turns). At self-resonant frequency (SRF), L and C_parasitic resonate. Above SRF, the component behaves capacitively, not inductively. Choose inductors with SRF >> operating frequency for correct behavior.

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Formula Explorer connections

Interpretation: This relationship connects magnetic fields, moving charge, flux, induction or electromagnetic material response. Assumption: Specify field direction and sign convention. Uniform fields, linear materials, negligible edge effects or sinusoidal steady state may be assumed.

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