Series RLC Circuit Calculator

$$ \begin{aligned} X_L &= 2\pi fL \\ X_C &= \frac{1}{2\pi fC} \\ Z &= \sqrt{R^2 + (X_L – X_C)^2} \\ \cos\phi &= \frac{R}{Z} \\ f_r &= \frac{1}{2\pi\sqrt{LC}} \\ Q &= \frac{1}{R}\sqrt{\frac{L}{C}} \\ BW &= \frac{f_r}{Q} \\ \alpha &= \frac{R}{2L} \\ \omega_0 &= \frac{1}{\sqrt{LC}} \\ \omega_d &= \sqrt{\omega_0^2 – \alpha^2} \end{aligned} $$
$$ \begin{aligned} X_L &= \text{Inductive Reactance} \\ X_C &= \text{Capacitive Reactance} \\ Z &= \text{Impedance} \\ \cos\phi &= \text{Power Factor} \\ f_r &= \text{Resonant Frequency} \\ Q &= \text{Quality Factor} \\ BW &= \text{Bandwidth} \\ \alpha &= \text{Damping Factor} \\ \omega_0 &= \text{Natural Angular Frequency} \\ \omega_d &= \text{Damped Natural Frequency} \end{aligned} $$