Inductor Reactance Calculator (X_L = 2πfL)
Inductive reactance X_L = 2π · f · L is how much an inductor resists current changes in a sinusoidal AC circuit. Enter the inductance L (any unit — H, mH or µH) and the frequency f (Hz, kHz or MHz); the tool returns X_L, the angular frequency ω = 2πf, the impedance magnitude |Z| and the phase — a staple tool for filter design, impedance matching, RF and power engineering.
Check inputs: L and f must be non-negative real numbers.
Inductive reactance X_L
37.70 Ω
Angular frequency ω
376.99 rad/s
Impedance magnitude |Z|
37.70 Ω
Phase ∠Z: +90°
Formula
X_L = ω · L = 2π · f · L (units: Ω) ω = 2π · f (units: rad ⁄ s) |Z| = X_L (impedance magnitude for a pure inductor) ∠Z = +90° (voltage leads current by 90°)
- · Reactance is proportional to frequency: double f, double X_L. At DC (f = 0) an inductor is a short (X_L = 0); at very high frequencies it approaches an open circuit.
- · Inductive and capacitive reactance move in opposite directions — X_C = 1 ⁄ (2π · f · C) shrinks as f grows. LC resonance occurs when X_L = X_C, giving f₀ = 1 ⁄ (2π · √(LC)).
- · Voltage across a pure inductor leads the current by 90°; power factor is zero so average real power is zero (only reactive power Q = V·I flows).
- · Typical orders of magnitude: 50 / 60 Hz mains use mH–H chokes; audio (20 Hz–20 kHz) uses mH-class crossover inductors; RF (MHz–GHz) uses nH–µH coils.
- · Real inductors have ESR (equivalent series resistance) and parasitic capacitance — above the self-resonant frequency they behave capacitively. For precision design consult the datasheet impedance-vs-frequency curve.
- · References: Sadiku, Fundamentals of Electric Circuits 6e §9.4; Hayt & Buck, Engineering Electromagnetics 8e §10.7; ARRL Handbook 2024, RF Inductors chapter.
Frequently asked
How is inductive reactance different from resistance?
Both have units of ohms (Ω), but they behave very differently. Resistance R is the same at any frequency and dissipates energy as heat (average power P = I²R > 0). Inductive reactance X_L is frequency-dependent: zero at DC, rising linearly with f, and an ideal inductor dissipates no energy — half a cycle stores energy in the magnetic field, the other half returns it, so average real power is zero and only reactive power flows. In the complex impedance Z = R + j·X_L, X_L sits in the imaginary part, which is why voltage leads current by 90°. A DC multimeter only reads the coil's ESR (usually negligible); to measure X_L you need an LCR meter or impedance analyser at the specified frequency.
When do I need impedance |Z| = √(R² + X_L²) instead of X_L alone?
X_L equals |Z| only for an ideal inductor with no series resistance. Once the circuit has any resistance (coil DCR, transformer winding resistance, series damping, etc.) you must use |Z| = √(R² + X_L²) to find the actual current I = V ⁄ |Z|, and cos φ = R / |Z| to get the power factor and real power dissipation. Example: a 1 mH coil with 10 Ω of winding resistance at 1 kHz — X_L = 2π × 1000 × 0.001 = 6.28 Ω; |Z| = √(10² + 6.28²) ≈ 11.81 Ω; phase φ = atan(6.28 ⁄ 10) ≈ 32°. RLC tank circuits, transformer design and impedance matching all need full impedance analysis. This tool reports pure-L X_L and ω; pair it with a resistor calculator and an LC resonance tool when the circuit has multiple elements.
How do I use X_L when picking an inductor?
Practical inductor-selection workflow: (1) settle on the operating frequency (switch-mode supplies 100 kHz–1 MHz; audio crossovers 1–5 kHz; RF 100 MHz+); (2) back out the target X_L from circuit needs (e.g. an EMI choke needs enough dB suppression at the noise frequency; a power inductor's X_L should be several times the load impedance); (3) use L = X_L ⁄ (2π · f) to find the required inductance; (4) pick a standard value (E12 / E24 series) and check saturation current I_sat, self-resonant frequency (SRF) and ESR; (5) keep the operating frequency well below SRF (rule of thumb: < 0.3 × SRF), or the part flips capacitive. This calculator does step (3) quickly. For RF you also need to think about Q (Q = X_L ⁄ ESR) to avoid signal loss; for power conversion factor in wire gauge, core saturation and self-heating.
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