How this calculator works
At the cutoff of an ideal first-order filter, reactance magnitude equals resistance. The output amplitude is 1/sqrt(2) of the passband value, corresponding to half the power for the same load. The RC time constant is RC, while the RL time constant is L/R. Source and load resistances change the effective resistance and should be included when they are significant.
Formula
RC: fc = 1/(2 pi R C). RL: fc = R/(2 pi L). The angular cutoff is omega_c = 2 pi fc.
Worked example
An RC filter with R = 1000 ohm and C = 1 microfarad has fc = 159.15494 Hz. An RL filter with R = 10 ohm and L = 0.1 H has fc = 15.91549 Hz.
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Frequently asked questions
Is cutoff a complete stop?
No. A first-order filter rolls off gradually; cutoff marks a specified amplitude ratio.
Does this work for high-pass and low-pass filters?
Yes for the basic first-order RC or RL topology. The output connection determines which side of cutoff is attenuated.
Does an RLC circuit use this formula?
No. Resonant or higher-order filters need their own transfer function and bandwidth calculation.