How to Calculate RC Filter Cutoff Frequency
An RC filter's cutoff frequency is f_c = 1 / (2 × π × R × C), with R in ohms and C in farads. For example, with R = 1 kΩ and C = 100 nF: f_c ≈ 1,591 Hz ≈ 1.6 kHz. At this frequency the output falls to 0.707× the input (−3 dB).
An RC filter is the most basic filter circuit, using a resistor (R) and a capacitor (C) together to pass some frequencies and attenuate others. The single number that defines its behaviour is the cutoff frequency (fc) — the frequency where the signal power drops to half (−3 dB).
RC filter cutoff formula: fc = 1 / (2πRC)
The cutoff frequency depends only on the resistor and capacitor values:
fc = 1 / (2 × π × R × C)
| Symbol | Meaning | Unit |
|---|---|---|
| fc | Cutoff (corner) frequency | Hertz (Hz) |
| R | Resistance | Ohms (Ω) |
| C | Capacitance | Farads (F) |
This formula is the SAME for both first-order low-pass and high-pass RC filters — only the arrangement of R and C differs.
Low-pass or high-pass?
The same two parts make two different filters depending on the layout:
- Low-pass: R in series, C to ground at the output. Passes frequencies BELOW fc. Used for supply-noise cleanup, PWM→analog.
- High-pass: C in series, R to ground at the output. Passes frequencies ABOVE fc. Used for DC blocking (capacitor coupling), bass cut.
How to calculate it, step by step
- Determine R and C — convert units to base SI (kΩ→Ω, nF→F).
- Apply fc = 1 / (2πRC).
- To hit a target cutoff, solve in reverse: R = 1/(2π·fc·C) or C = 1/(2π·fc·R).
- Pick the nearest standard value and re-check fc.
Worked examples
- R = 1 kΩ, C = 100 nF: fc = 1 / (2π × 1000 × 100×10⁻⁹) ≈ 1,591 Hz ≈ 1.6 kHz.
- R = 10 kΩ, C = 10 nF: fc ≈ 1,591 Hz (same RC product → same fc).
- Target 1 kHz, C = 100 nF: R = 1/(2π × 1000 × 100×10⁻⁹) ≈ 1.59 kΩ → standard 1.6 kΩ.
What happens at the cutoff? (−3 dB)
At fc the output amplitude falls to 0.707× the input (i.e. −3 dB, half the power) and the phase shifts by 45°. Beyond fc, a first-order filter rolls off at −20 dB/decade (10× attenuation per 10× frequency). For a sharper transition, cascade filters or use an active (op-amp) filter.
Relation to the time constant (τ = RC)
The same RC product gives the time-domain time constant (τ = R × C). The two are linked by fc = 1/(2πτ): a fast circuit (small τ) corresponds to a high cutoff. See also frequency and period.
Common mistakes
- Unit mix-ups: not converting nF/µF and kΩ to base units (1 nF = 10⁻⁹ F).
- Forgetting 2π: it is NOT fc = 1/(RC); the angular frequency ω = 1/(RC), but f = ω/2π.
- Loading: a low-impedance load on the output shifts fc — a buffer may be needed.
Use the calculator
Enter R and C to find the cutoff frequency instantly with our RC Filter Calculator.