Series RLC impedance calculator

Enter resistance in ohms, inductance in henries, capacitance in farads, and frequency in hertz. The result includes the real and imaginary impedance components, inductive and capacitive reactance, total magnitude, and phase in both degrees and radians. It also identifies whether the circuit behaves inductively, capacitively, or as a purely resistive load at that operating point.

Enter consistent component values and frequency

Use SI base units for every input: resistance in ohms, inductance in henries, capacitance in farads, and frequency in hertz. Convert common prefixes before submitting values. For example, 100 millihenries is 0.1 henry, 1 microfarad is 0.000001 farad, and 1 kilohertz is 1000 hertz. Resistance may be zero for an ideal lossless series LC circuit, but inductance, capacitance, and frequency must all be greater than zero. The calculation models ideal lumped components at a single sinusoidal frequency. It does not include an inductor's winding resistance, a capacitor's equivalent series resistance, parasitic capacitance, skin effect, dielectric loss, or frequency-dependent component tolerances unless those effects have already been represented in the resistance you enter. For a practical design, use measured or datasheet values at the intended operating frequency when available. Keeping units consistent is especially important because a prefix error can shift reactance by factors of thousands or millions while still producing a numerically valid result.

Understand the impedance calculation

The calculator first converts frequency to angular frequency using ω = 2πf. It then computes inductive reactance as XL = ωL and the positive magnitude of capacitive reactance as XC = 1/(ωC). In complex impedance notation, the resistor contributes the real part R, the inductor contributes +jXL, and the capacitor contributes −jXC. Their series sum is therefore Z = R + j(XL − XC). The returned net reactance is XL − XC, so a positive value means inductive behavior and a negative value means capacitive behavior. The impedance magnitude is obtained from the right triangle formed by the real and imaginary components: |Z| = √(R² + X²). Phase is computed with atan2(X, R), which preserves the sign of the reactance and handles zero resistance correctly. Phase is positive for an inductive load, negative for a capacitive load, and zero when the two reactances cancel. Both degree and radian values are provided so the output can be used directly in engineering calculations or software.

Apply magnitude and phase correctly

Impedance magnitude tells you the ratio between RMS voltage magnitude and RMS current magnitude for the ideal series branch: |I| = |V|/|Z|. The phase tells you the current and voltage timing relationship. With the impedance angle convention used here, a positive phase means voltage leads current, as in an inductive circuit; a negative phase means current leads voltage, as in a capacitive circuit. At series resonance, XL and XC are equal, net reactance is zero, and the impedance reduces to the resistance. Real component values and finite precision may leave a very small nonzero reactance near that point, so inspect the component values rather than assuming an exact zero. This tool evaluates one frequency per request; it does not generate a sweep, bandwidth, quality factor, transient response, power factor under nonsinusoidal excitation, or component ratings. Use the detailed real and imaginary fields when passing results to another complex-number calculation, and use the magnitude and phase fields when working with polar-form phasors. Automated API requests cost $0.002 per item.