RC and RL Time Constant and Cutoff Frequency Calculator

Pick RC or RL, enter the component values, and get the time constant, the cutoff frequency of the matching first-order filter and the time to settle within 1%.

Calculator

Time constant τ
1 ms
Cutoff frequency fc
159.2 Hz
Time to settle within 1% (5τ)
5 ms

Type numbers like 4.7, 0.002 or 2e-3. Results are rounded to 4 significant figures.

The formulas

τ=RC,τ=LR\tau = RC, \qquad \tau = \dfrac{L}{R}

τ in seconds, R in ohms, C in farads, L in henries. R is the Thevenin resistance seen by the capacitor or inductor.

fc=12πτf_c = \dfrac{1}{2\pi\tau}

The −3 dB (corner) frequency of a first-order low-pass or high-pass filter, in hertz.

x(t)=x(∞)+[x(0+)−x(∞)] e−t/τ\begin{gathered} x(t) = x(\infty) \\ {} + [x(0^+) - x(\infty)]\,e^{-t/\tau} \end{gathered}

After 5τ the response is within e⁻⁵ ≈ 0.67% of its final value.

  • Use the resistance the energy-storage element sees with every independent source turned off, not just the resistor next to it.

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