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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 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 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/.
