Inductance Calculator

Inductance governs how every coil, choke, transformer, and tuned circuit behaves — it is the reason power supplies can filter out switching noise, why radio receivers can select a single station, and why motors can start smoothly. This calculator covers the six most common inductance calculations in one tool, each with full step-by-step working you can copy straight into a lab report or design note.

How it works

An inductor stores energy in a magnetic field proportional to the current flowing through it. The fundamental relationship is:

V = L × dI/dt

A voltage V is induced across the inductor whenever the current changes at rate dI/dt. The proportionality constant L (in henries) is the inductance. Six separate calculators let you explore every consequence of this relationship.

1. Solenoid / single-layer coil inductance

The exact formula for a uniform solenoid wound with N turns over length l, each turn enclosing area A, with core permeability µr, is:

L = µ₀ × µr × N² × A / l

where µ₀ = 4π × 10⁻⁷ H/m is the magnetic constant. Because L grows with N², doubling the number of turns quadruples the inductance. For short coils (length/radius < 0.4) the Wheeler approximation replaces l with the empirical denominator (9r + 10l) for better accuracy.

2. Toroid inductance

A toroid is an axially symmetric core shaped like a ring. Because the magnetic flux stays inside the core, the mean magnetic path length is 2πr_mean rather than the coil length l:

L = µ₀ × µr × N² × A / (2π × r_mean)

Toroids achieve higher inductance per turn than solenoids of the same volume and generate far less stray field.

3. Inductive reactance

An inductor presents a frequency-dependent impedance to AC signals:

XL = 2π × f × L

At DC, XL = 0 (wire is just a wire). As frequency rises, reactance rises in direct proportion — this is the basis of high-pass RL filters and inductive chokes. Rearranging: L = XL / (2πf) and f = XL / (2πL).

4. Energy stored and self-induced EMF

The energy formula explains why inductors in switching power supplies must be properly rated — a 100 µH inductor carrying 5 A stores 1.25 mJ, and that energy must go somewhere (usually a flyback diode or snubber) when the switch opens.

5. RL circuit time constant

A resistor in series with an inductor forms a first-order RL circuit. When a step voltage is applied, the current rises exponentially:

I(t) = I_final × (1 − e^(−t/τ)) where τ = L / R

The calculator reports τ, the −3 dB corner frequency f_3dB = R / (2πL), the 10 %–90 % rise time (2.197τ), and the time to reach 99 % of final current (4.605τ).

6. Series and parallel combinations

Without mutual coupling:

• Series: L_total = L1 + L2 + … + Ln
• Parallel: 1/L_total = 1/L1 + 1/L2 + … + 1/Ln

These are exactly analogous to resistor combinations. The calculator accepts any number of inductors, shows the working equation, and flags when the result is less than the smallest (parallel) or greater than the largest (series) component.

Worked example — RF choke design

Goal: design an RF choke to block signals above 10 MHz using a standard ferrite toroid core (µr = 250) with a mean radius of 5 mm and cross-section area 3 mm².

Target XL at 10 MHz = 1 kΩ  (a common rule of thumb for effective RF blocking)

Step 1: Find required inductance from XL = 2πfL
  L = XL / (2πf)
  L = 1000 / (2π × 10×10⁶)
  L = 1000 / (6.283×10⁷)
  L ≈ 15.9 µH

Step 2: Find number of turns needed (toroid)
  L = µ₀ × µr × N² × A / (2π × r_mean)
  15.9×10⁻⁶ = 4π×10⁻⁷ × 250 × N² × 3×10⁻⁶ / (2π × 5×10⁻³)
  15.9×10⁻⁶ = (3.142×10⁻⁴ × N²) / (3.142×10⁻²)
  15.9×10⁻⁶ = 10⁻² × N²
  N² = 15.9×10⁻⁶ / 10⁻² = 1.59×10⁻³ × 10² ≈ 1.59 ... wait
  Re-checking SI carefully:
  µ₀µr = 4π×10⁻⁷ × 250 = 3.142×10⁻⁴ H/m
  A = 3×10⁻⁶ m²
  2π × r_mean = 2π × 5×10⁻³ = 3.142×10⁻² m
  L = 3.142×10⁻⁴ × N² × 3×10⁻⁶ / 3.142×10⁻²
  L = N² × 3×10⁻⁸ H
  N² = 15.9×10⁻⁶ / 3×10⁻⁸ = 530
  N ≈ 23 turns

23 turns on this core gives L ≈ 15.9 µH, presenting over 1 kΩ reactance at 10 MHz — adequate RF choking for most circuits.

Formula note

All solenoid and toroid formulas assume an ideal uniform winding with no fringing flux, no winding capacitance, and a homogeneous core. Real inductors deviate because: (a) permeability µr is frequency-dependent and non-linear near saturation; (b) winding resistance causes a real-part loss; (c) inter-turn capacitance adds a self-resonant frequency above which the component looks capacitive. For precision RF work (within 1–2 %) use the Wheeler formula or measured values; for power inductors, always check the saturation current rating and core loss datasheet.