RLC Impedance Calculator

Enter Calculation

Resistance R (Ω)

Inductance L (H)

Capacitance C (F)

Frequency f (Hz)

Formula

Show calculation steps (1)

1. Phase Angle

   

   Phase angle in degrees between voltage and current

Results

Total Impedance

153.1985

ohms (Ω)

Inductive reactance XL	6.2832 Ω
Capacitive reactance XC	159.1549 Ω
Net reactance X	-152.8718 Ω
Phase angle φ	-86.26°

What is the RLC Impedance Calculator?

This tool computes the total impedance (Z) of a series RLC circuit — a circuit containing a resistor (R), an inductor (L) and a capacitor (C) driven at a frequency f. Impedance is the AC equivalent of resistance: it tells you how much the circuit opposes alternating current, measured in ohms (Ω). The calculator also returns the inductive and capacitive reactances and the phase angle between voltage and current.

A series RLC circuit: resistor (R), inductor (L) and capacitor (C) driven by an AC source.

How to use it

Enter the resistance in ohms (Ω), the inductance in henries (H), the capacitance in farads (F), and the source frequency in hertz (Hz). Click calculate to see the total impedance along with X_L, X_C, the net reactance and the phase angle. Use SI base units — for example, 1 µF = 0.000001 F and 1 mH = 0.001 H.

The formula explained

The inductive reactance is \(X_L = 2\pi f L\) and the capacitive reactance is \(X_C = \frac{1}{2\pi f C}\). Because the inductor and capacitor push current in opposite phase, their net reactance is \(X = X_L - X_C\). Combining with resistance using the Pythagorean theorem gives $$Z = \sqrt{R^2 + X^2}$$ The phase angle is \(\varphi = \arctan(X / R)\): positive means inductive (current lags), negative means capacitive (current leads). When \(X_L = X_C\) the circuit is at resonance and \(Z = R\), its minimum value.

The impedance triangle relates R, net reactance (X) and total impedance Z by the phase angle θ.

Worked example

For R = 10 Ω, L = 0.001 H, C = 0.000001 F and f = 1000 Hz: \(\omega = 2\pi \cdot 1000 \approx 6283.19\). \(X_L = 6283.19 \cdot 0.001 \approx 6.2832\ \Omega\); \(X_C = \frac{1}{6283.19 \cdot 0.000001} \approx 159.155\ \Omega\). Net reactance \(\approx -152.872\ \Omega\), so $$Z = \sqrt{10^2 + 152.872^2} \approx 153.2\ \Omega$$ and \(\varphi \approx -86.26^\circ\) (strongly capacitive).

FAQ

Is this for series or parallel circuits? This calculator models a series RLC circuit, where R, L and C carry the same current.

What units should I use? Ohms, henries, farads and hertz. Convert µF and mH to base units first.

What happens at resonance? When \(X_L = X_C\), the reactances cancel, impedance equals R and the phase angle is zero.