# [Inductor Impedance Calculator](https://blog.hirnschall.net/tools/inductor-impedance/) author: [Sebastian Hirnschall](https://blog.hirnschall.net/about/) meta description: Calculate inductive reactance, impedance magnitude, and phase angle. Solve for X_L, inductance, or frequency given the other two. Optional series resistance. meta title: Inductor Impedance Calculator — Reactance, |Z|, and Phase Angle date published: 11.05.2026 (DD.MM.YYYY format) date last modified: 11.05.2026 (DD.MM.YYYY format) --- Calculator ---------- Fill in any two of \( f \), \( L \), \( X\_L \) — the third is solved. \( R \) is optional: if provided, \( |Z| \) and \( \phi \) are computed as additional outputs. \( \phi \) can also be used as an input together with \( R \) to replace one of the three main variables. * Frequency (f): * Hz kHz MHz * Inductance (L): * H mH µH nH * Inductive reactance (XL): * Ω kΩ MΩ --- * Resistance (R) — optional: * Ω kΩ MΩ * Phase angle (φ) — optional: * deg rad Fill in any two of f, L, X\_L to calculate. Calculate Inductive Reactance — Explanation --------------------------------- An inductor stores energy in a magnetic field and resists any change in the current flowing through it. When an alternating current passes through an inductor, the magnetic field is constantly building and collapsing, which induces a back-EMF that opposes the driving voltage. The faster the current changes (i.e. the higher the frequency), the stronger this opposition. We quantify it as inductive reactance \( X\_L \): \[ X\_L = 2\pi f L \] Where: * \( X\_L \) is the inductive reactance (in Ohms, \( \Omega \)), * \( f \) is the frequency (in Hertz, \( \text{Hz} \)), * \( L \) is the inductance (in Henrys, \( \text{H} \)). The relationship is linear: doubling the frequency doubles \( X\_L \), and doubling the inductance doubles \( X\_L \) by the same factor. This is the opposite of a capacitor, where reactance falls as frequency rises. At DC (\( f = 0 \)) an ideal inductor has zero reactance and acts as a plain wire. At very high frequencies \( X\_L \) grows without bound, which is why inductors are used as chokes: they pass DC and low-frequency signals while increasingly blocking higher frequencies. The [capacitor impedance calculator](https://blog.hirnschall.net/tools/capacitor-impedance/) shows the complementary picture from the capacitive side. In an LC circuit, resonance occurs at the frequency where \( X\_L = X\_C \). Below that frequency the circuit is capacitive, above it the circuit is inductive. The [LC resonance frequency calculator](https://blog.hirnschall.net/tools/lc-resonance-frequency/) solves for that crossover point directly. Purpose of the Calculator ------------------------- Given any two of \( f \), \( L \), \( X\_L \), the calculator solves for the third. The rearranged formulas are: * To solve for \( X\_L \) (the most common case, checking how much a known inductor blocks at a given frequency): \[ X\_L = 2\pi f L \] * To solve for \( L \) (selecting an inductor to achieve a target reactance at a given frequency): \[ L = \frac{X\_L}{2\pi f} \] * To solve for \( f \) (finding the frequency at which a known inductor reaches a target reactance): \[ f = \frac{X\_L}{2\pi L} \] If L is made up of several inductors, compute the equivalent value first with the [inductors in series](https://blog.hirnschall.net/tools/inductors-in-series/) or [inductors in parallel](https://blog.hirnschall.net/tools/inductors-in-parallel/) calculator. Full Impedance with Series Resistance ------------------------------------- Every real inductor has winding resistance \( R \) from the copper wire. At low frequencies where \( X\_L \ll R \), this resistance dominates and the inductor looks mostly resistive. At higher frequencies \( X\_L \) takes over. The two contributions combine as perpendicular components in the complex impedance plane, giving a magnitude: \[ |Z| = \sqrt{R^2 + X\_L^2} \] and a phase angle: \[ \phi = \arctan\!\left(\frac{X\_L}{R}\right) \] The phase angle is always positive for an inductor, meaning the voltage leads the current. It runs from \( 0° \) (purely resistive, \( X\_L \ll R \)) up to \( +90° \) (purely inductive, \( X\_L \gg R \)). This is the mirror image of a capacitor, where \( \phi \) is always negative. The ratio of reactance to resistance is also the quality factor \( Q \) of the inductor: \[ Q = \frac{X\_L}{R} = \tan(\phi) \] A high \( Q \) means little resistive loss relative to the energy stored per cycle. In filter and resonator design, \( Q \) directly sets the bandwidth and insertion loss of the circuit. If \( \phi \) and \( R \) are known from a measurement (for example from an impedance analyser), the reactance can be recovered as: \[ X\_L = R \cdot \tan(\phi) \] The RL circuit also has a characteristic time constant that governs how quickly current builds up after a voltage step. That time-domain view is covered in the [RL time constant calculator](https://blog.hirnschall.net/tools/rl-time-constant/). Related Tools ------------- * [Capacitor Impedance Calculator](https://blog.hirnschall.net/tools/capacitor-impedance/) — the capacitive equivalent: \( X\_C = \frac{1}{2\pi f C} \), negative phase angle. * [LC Resonance Frequency Calculator](https://blog.hirnschall.net/tools/lc-resonance-frequency/) — find the frequency where \( X\_L \) equals \( X\_C \). * [RL Time Constant Calculator](https://blog.hirnschall.net/tools/rl-time-constant/) — time-domain view of the same RL circuit. * [Inductors in Series](https://blog.hirnschall.net/tools/inductors-in-series/) / [Inductors in Parallel](https://blog.hirnschall.net/tools/inductors-in-parallel/) — compute the equivalent inductance of a network before using it here. More calculators: [blog.hirnschall.net/tools/](https://blog.hirnschall.net/tools/).