Inductance Calculator — Coils, Solenoids, and RL Circuits
Calculate inductance, inductive reactance, and energy stored in a coil. Covers solenoid formula, RL time constants, and practical inductor applications.
An inductor resists changes in current — it's like inertia for electricity. When current tries to change quickly, the inductor's magnetic field pushes back. This property makes inductors essential in filters, power supplies, transformers, and motor drives. Understanding inductance helps you predict how circuits behave when currents switch.
The CalcHub inductance calculator computes inductance, inductive reactance, and RL time constants.
Key Formulas
Solenoid inductance: L = μ₀ × μ_r × N² × A / ℓ Stored energy: E = ½ × L × I² Inductive reactance: X_L = 2π × f × L RL time constant: τ = L / R- L = inductance (Henries, H)
- μ₀ = 4π × 10⁻⁷ H/m (permeability of free space)
- μ_r = relative permeability of core
- N = number of turns
- A = cross-sectional area (m²)
- ℓ = length of solenoid (m)
Inductance Units and Practical Values
| Component | Inductance |
|---|---|
| Small RF coil | 1 nH – 1 μH |
| Filter choke | 10 μH – 1 mH |
| Power inductor | 1 mH – 100 mH |
| Transformer primary | 0.1 H – 10 H |
| Large power line choke | 1 H – 100 H |
Inductive Reactance
Unlike resistors, inductors present increasing opposition to higher-frequency AC:
X_L = 2πfL
A 10 mH inductor at 1 kHz: X_L = 2π × 1000 × 0.01 = 62.8 Ω
At 10 kHz: X_L = 628 Ω — ten times more opposition.
This is why inductors block high-frequency signals while passing low-frequency ones — the opposite of capacitors.
Worked Example
A 50 mH inductor carries 2 A of current. How much energy is stored?
E = ½ × 0.05 × 4 = 0.1 J = 100 mJ
What is the RL time constant if it's connected to a 25 Ω resistor?
τ = L/R = 0.05/25 = 2 ms
Current reaches 63.2% of steady-state in 2 ms, and is essentially at steady-state after 5τ = 10 ms.
Why do inductors resist current changes?
Lenz's Law: changing current creates a changing magnetic field, which induces an EMF opposing the change. It's electromagnetic "inertia." The faster the current tries to change, the larger the opposing voltage generated. This self-induced EMF is described by v = L × dI/dt.
What is mutual inductance?
When two coils are near each other, a changing current in one induces a voltage in the other. This is the principle of transformers. Mutual inductance M relates the induced voltage to the rate of current change: v₂ = M × dI₁/dt.
How do inductors behave at DC steady state?
At DC (f = 0), inductive reactance X_L = 0 — a pure inductor is just a wire (zero resistance ideally). All the transient effects happen during the start-up period (5τ). This is why inductors block AC but pass DC in filter circuits.