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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.
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:
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 shows the complementary picture from the capacitive side.
In a series LC circuit, resonance occurs at the frequency where \( X_L = X_C \). Below that frequency the circuit is capacitive, above it inductive. A parallel LC circuit behaves the other way round. The LC resonance frequency calculator solves for that crossover point directly.
Given any two of \( f \), \( L \), \( X_L \), the calculator solves for the third. The rearranged formulas are:
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.
More calculators: blog.hirnschall.net/tools/.
