Inductive Reactance Calculator - XL = 2πfL Coil Reactance Solver

An inductive reactance calculator solves XL = 2π f L for any coil in an AC circuit, taking the self-inductance in henries and the signal frequency in hertz and returning the magnitude of the coil's AC opposition in ohms, so an engineer or student can size a choke or filter without re-deriving the equation. The formula pairs with the capacitive-reactance page: a capacitor blocks DC and passes high frequencies, while an inductor blocks them.

• • AC circuit homework: Find the XL a textbook problem gives for an inductor and a chosen frequency so the rest of the circuit can be solved.
• • Audio crossover inductor sizing: Estimate the reactance of a coil at a 20 Hz to 20 kHz audio band so the corner frequency of the low-pass filter is known.
• • Switching supply choke selection: Check the XL of a power inductor at the 50 kHz to 500 kHz switching frequency when sizing the ripple current.
• • RF choke and EMI filter design: Convert a chosen inductance into a reactance at RF so a matching network can be designed.

The calculator assumes an ideal inductor with a purely reactive AC impedance, so the printed XL is the magnitude of the impedance. Real coils add a small series resistance (DCR) and a parallel parasitic capacitance that bend the impedance away from the formula above the self-resonant frequency; check the datasheet SRF for RF work.

Reactive opposition is what separates inductors from resistors in AC analysis: a resistor dissipates real power as heat, while an ideal inductor stores energy in its magnetic field during part of every cycle and returns it during the next quarter cycle, so the average real power is zero.

A coil and a capacitor in the same AC circuit react in opposite ways, and the Capacitive Reactance Calculator solves the matching Xc = 1 / (2π f C) for the capacitor half of the same analysis.

The inductive reactance calculator applies the AC-circuit equation XL = 2π f L to the inductance and frequency the user enters, with automatic conversion of the chosen unit prefixes into the SI base units the formula expects.

• L: Self-inductance of the coil in henries (H). Calculator accepts H, mH, µH, or nH prefixes and converts to henries before the formula runs.
• f: Frequency of the AC signal applied to the inductor in hertz (Hz). Calculator accepts Hz, kHz, MHz, or GHz prefixes and converts to hertz before the formula runs.
• π: The mathematical constant pi ≈ 3.14159265358979. Used to convert between angular frequency ω (rad/s) and cyclic frequency f (Hz).
• XL: Inductive reactance in ohms (Ω). Auto-prefixed to mΩ, Ω, kΩ, or MΩ so the printed value stays readable across nH inductors at GHz to H inductors at 50 Hz.

The formula is the magnitude of the complex impedance Z = j ω L of an ideal inductor, which is why XL rises linearly with both frequency and inductance and why an inductor looks like a short at DC and an open at high frequencies. Equivalently XL = ω L with ω = 2π f, and the inductive reactance calculator displays ω next to XL for reuse in a Bode plot.

Once XL is known, the next step is the AC voltage across the coil at a given current, and V = I · XL holds in phasor form just as it does for a resistor, so the calculator output drops into any AC solver that accepts V, I, and Z in phasor form.

According to HyperPhysics, the frequency dependent impedance of an inductor is called inductive reactance and equals angular frequency times inductance.

According to OpenStax, the inductive reactance of an ideal inductor at angular frequency ω is XL = ω L = 2π f L, where L is the inductance in henries and f is the signal frequency in hertz.

Once XL is known, the next step is the AC voltage across the coil at a given current, and the Ohm's Law & Basic Circuit Calculator handles V = I · Z for any voltage, current, or impedance on the same circuit.

Four ideas make the result panel easier to read: the role of frequency, the linear scaling with inductance, the short-circuit behavior at DC, and the 90° phase lag of inductor voltage.

The angular frequency ω = 2π f in rad/s is the form some sources use, with XL = ω L; the calculator displays ω alongside XL so the same value can be reused in a Bode plot or a phasor diagram. The same L that sets XL also sets the L/R time constant τ = L / R for a DC RL circuit.

The same RL time constant τ = L / R that this calculator hints at is the dual of the RC time constant τ = R C, and the Capacitor Charge Time Calculator pairs that C with a resistance and a voltage threshold to estimate the finite charge or discharge time on the same kind of circuit.

Type an inductance, pick the prefix, type a frequency, pick the prefix, and read XL in the ohm prefix the calculator picks.

1. 1 Enter the inductance: Type the coil value and pick H, mH, µH, or nH as the unit prefix. The calculator converts the value to henries before the formula runs.
2. 2 Enter the frequency: Type the signal frequency and pick Hz, kHz, MHz, or GHz as the unit prefix. The calculator converts the value to hertz before the formula runs.
3. 3 Read XL: Read the XL result in the auto-selected ohm prefix (Ω, kΩ, or MΩ). The supporting rows show the inductance in H, frequency in Hz, angular frequency ω, period T, and wavelength λ.
4. 4 Rescale for the next band: Change one unit prefix at a time to move between audio, mains, switching, and RF ranges without recomputing the formula by hand.

To find the reactance of a 100 µH switching choke at 100 kHz, pick 100 µH and 100 kHz. The inductive reactance calculator returns XL ≈ 62.832 Ω, the order of magnitude for the ripple reactance on a buck converter output.

When the matching capacitor for an LC filter or a tank circuit is not yet known, the Capacitance Calculator takes the parallel-plate geometry and dielectric material and returns the C in farads that pairs with this XL.

This calculator replaces a unit-conversion-plus-log step with a single result panel that updates as you change inputs.

• • No re-derivation of XL = 2π f L: Stops you from retyping the AC-circuit formula every time the frequency or inductance changes - the form takes the inputs, the result panel takes the arithmetic.
• • Inductance prefix library: Covers H, mH, µH, and nH so datasheet values drop in without manual conversion to henries.
• • Frequency prefix library: Covers Hz, kHz, MHz, and GHz so the form handles audio, mains, switching, and RF bands.
• • Auto-selected ohm prefix: Picks mΩ, Ω, kΩ, or MΩ so the printed XL stays readable from nH RF chokes at GHz to H chokes at 50 Hz.

The unit-prefix libraries keep the form usable straight from a coil datasheet, and the auto-selected ohm prefix keeps the inductive reactance calculator result panel readable across ten orders of magnitude.

When the LC network uses several capacitors to set its resonant frequency, the Capacitors in Series Calculator reduces the C ladder to a single equivalent capacitance so the resonant frequency f = 1 / (2π √(L C)) pairs cleanly with this L.

Two inputs drive every number: the inductance the user picks and the frequency of the AC signal applied to the coil.

• • The textbook XL = 2π f L assumes an ideal inductor with no parasitic resistance or capacitance; near and above the coil self-resonant frequency, parasitic capacitance dominates and the real impedance deviates from the formula.
• • The formula assumes a single-tone sinusoidal signal. A square wave has harmonics at higher frequencies where the reactance differs, so re-run the calculator at the dominant harmonic for non-sinusoidal inputs.

The inductive reactance calculator rejects zero or negative values for inductance and frequency because both make the formula undefined. When XL is below 1 Ω, the auto-prefix moves to mΩ so the small reactance of small RF chokes at high frequency stays readable.

According to NIST CODATA, the speed of light in vacuum is exactly 299,792,458 m/s, which the calculator uses to convert the chosen frequency into the wavelength readout.

When a printed reactance is needed but the geometry is what is actually known, the Capacitor Calculator works the other direction and returns the capacitance that pairs with a chosen L to hit a target resonant frequency.