Inductive Reactance Calculator
Calculate Xl = 2πfL for AC circuits. Solve for reactance, frequency, or inductance. Log-log plot of reactance vs. frequency shows how inductors block high frequencies.
How to Use
- Pick solve target: Xl, frequency, or inductance.
- Use suffixes: k/M for ohms, nH/µH/mH for inductance, Hz/kHz/MHz for frequency.
- The log-log chart shows reactance rising linearly with frequency.
- Opposite behavior to capacitors — inductors pass DC and block high frequencies.
Show Work
Formulas
History of Inductive Reactance
Michael Faraday's 1831 law of electromagnetic induction — that a changing magnetic field induces an EMF — is the foundation of everything an inductor does. Running AC through a coil constantly changes the current, which constantly changes the coil's magnetic field, which induces a back-EMF opposing the applied voltage. That back-EMF is indistinguishable from an opposition to current, and it scales linearly with frequency: the faster the current changes, the stronger the opposition.
Heinrich Lenz formalized the direction of the induced EMF in 1834 (Lenz's law: induced current flows to oppose the change that caused it), and Heaviside in 1893 combined Faraday's and Lenz's work with Ohm's law to produce the complex-impedance formulation we still use: ZL = jωL = j·2πfL. The "j" captures the 90° phase shift between voltage and current in a pure inductor. The "2πfL" is what this calculator returns as inductive reactance in ohms.
Practically, inductive reactance is why audio crossovers can split a full-range signal between tweeters and woofers, why ferrite beads block switching noise without dissipating power, why speaker impedance is specified at 400 Hz (rising toward treble), and why transformer primaries don't short-circuit a 60 Hz line.
About This Calculator
Pick what to solve for (Xl, frequency, or inductance), enter the other two with engineering suffixes (nH, µH, mH, Hz, kHz, MHz), and this calculator returns the third via XL = 2πfL. The log-log plot shows reactance rising linearly with frequency — the characteristic behavior that makes inductors the dual of capacitors in AC circuits.
For real-world parts at very high frequencies, wire DC resistance adds a real component to impedance, and parasitic inter-winding capacitance causes self-resonance above which the "inductor" actually starts behaving capacitively. Below about 10% of self-resonance the ideal formula works within a few percent. Everything runs client-side; no values leave your browser.
Frequently Asked Questions
What is inductive reactance?
Opposition to AC current flow by an inductor, measured in ohms. Unlike resistance, no energy is dissipated — the inductor stores energy in its magnetic field during half of each cycle and returns it during the other half. At DC (f=0), Xl = 0 (short); at infinite frequency, Xl approaches infinity (open).
How does it relate to capacitive reactance?
They\'re opposites. Capacitive Xc = 1/(2πfC) decreases with frequency; inductive Xl = 2πfL increases with frequency. At a specific frequency, Xl can equal Xc — that\'s resonance, used in LC filters, antennas, and oscillators.
What's the phase shift?
Voltage leads current by 90° in an inductor. Mnemonic: ELI — E (voltage) comes before (leads) I (current) in L (inductor). Opposite of capacitors (ICE).
Is Xl the same as impedance?
No. Impedance Z combines R and X. For a pure inductor Z = +jXl (purely imaginary, +90° phase). In an RL circuit, Z = √(R² + Xl²). Use impedance for total AC analysis; reactance is just the inductive part.
Do real inductors follow this formula?
Close, but with caveats. Real inductors have DC resistance (R_DC from wire), self-resonance (when parasitic capacitance equals Xl), and core losses at high frequencies. The ideal formula Xl = 2πfL holds well from DC up to about 10% of self-resonance.
Common Use Cases
Switching Supply Inductor
Buck converter at 500kHz with 22µH: Xl = 69Ω — enough to smooth current but not block fundamental.
Audio Crossover
2-way speaker crossover at 2kHz: L for low-pass to woofer sized so Xl = R_speaker at fc.
Ferrite Bead EMI Filter
High Xl at MHz frequencies blocks switching noise while passing DC and low-frequency signals.
Loudspeaker Impedance
Voice coil inductance rises Xl at high audio frequencies — why speaker impedance is usually rated at 400Hz.
LC Resonant Tank
Oscillator tank circuit: f = 1/(2π√(LC)). Pick L for a desired resonant frequency at a given C.
Power Factor Correction
Synchronous motors can be over-excited to act like capacitors, canceling the inductive reactance of nearby motors.
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