RC/RL/RLC Time Constant & Resonance Calculator

A first-order RC or RL circuit's step response is governed by a single time constant: τ = RC for a resistor-capacitor circuit, or τ = L/R for a resistor-inductor circuit — the time to reach about 63.2% of the final value after a step change, with the response essentially complete after roughly 5τ. A second-order RLC circuit instead has a resonant frequency f0 = 1/(2π√(LC)) where inductive and capacitive reactance cancel, and a quality factor Q describing how sharply the circuit responds near resonance — Q = (1/R)√(L/C) for a series RLC circuit, or Q = R√(C/L) for a parallel RLC circuit, with -3dB bandwidth BW = f0/Q.

Use this for filter design (a higher Q means a narrower, more selective bandpass or notch response), for estimating how quickly a switching transient settles in an RC or RL network, or for checking a resonant LC tank circuit's frequency and selectivity.

The series and parallel Q formulas are not interchangeable — a series RLC circuit's Q rises as R falls (less series resistance means less damping), while a parallel RLC circuit's Q rises as R increases (more parallel resistance means less loading on the tank). Double-check which topology matches your actual circuit before reading the result, since using the wrong formula gives a Q value that's the reciprocal of the correct one.