RC cutoff frequency and RC time constant
The same R and C can be described as a time constant in the time domain or as a cutoff frequency in the frequency domain.
How are RC cutoff frequency and RC time constant related?
The time constant is tau = R * C. The first-order cutoff frequency is fc = 1 / (2 * pi * R * C). A larger time constant means a lower cutoff frequency and a slower step response.
Model summary
- Time constant: tau = R * C.
- Cutoff frequency: fc = 1 / (2 * pi * R * C).
- One time constant reaches about 63.2% of a charging step; the cutoff frequency is the -3 dB point for an ideal first-order RC filter.
Worked example
For R = 10 kOhm and C = 100 nF, tau = 1 ms.
The cutoff frequency is fc = 1 / (2 * pi * 1 ms) = 159 Hz.
The same network is therefore slow on millisecond-scale edges and also attenuates signal content above the low hundreds of hertz.
Design sequence
Use the RC time constant when the question is delay, settling, charging, or discharge. Use the cutoff calculators when the question is signal bandwidth or filtering.
Common mistakes
- Treating cutoff frequency and time constant as unrelated checks.
- Using a visible resistor value instead of the effective resistance seen by the capacitor.
- Ignoring source impedance, load impedance, and capacitor tolerance.
When the approximation breaks down
- The first-order model does not cover active filters, multiple poles, op-amp stability, or ADC sampling dynamics.
- Capacitor value can move with tolerance, temperature, ageing, and DC bias.
Related calculators
RC time constant calculator
Calculate tau and capacitor voltage versus time.
Capacitor discharge calculator
Check capacitor voltage decay and time to a discharge threshold.
RC low-pass filter calculator
Calculate first-order low-pass cutoff.
RC high-pass filter calculator
Calculate first-order high-pass cutoff.