RC High Pass Filter Calculator
Calculate cutoff frequency and output gain of a first-order RC high pass filter based on resistance, capacitance, and signal frequency.
What the RC high-pass filter calculator does
The RC high-pass filter calculator gives the cutoff frequency of a first-order high-pass filter made from one capacitor in series with the signal and one resistor to ground. Enter the resistance in ohms and the capacitance in farads and press Calculate. If you also enter a signal frequency, the tool reports the filter’s gain at that frequency in decibels and as a ratio, plus the phase shift.
The formulas
- Cutoff frequency: fc = 1 / (2π R C)
- Gain magnitude at frequency f: |H| = (2πfRC) / √(1 + (2πfRC)²)
- Gain in decibels: 20 × log10|H|
- Phase shift: φ = arctan(1 / (2πfRC)), a lead of 45° at fc
At the cutoff frequency the output is 1/√2 of the input, −3.01 dB. Below fc the gain falls at 20 dB per decade (6 dB per octave); above it the filter passes the signal almost unchanged.
Worked example with the default values
R = 10 kΩ, C = 1 µF: fc = 1 / (2π × 10,000 × 10−6) = 15.9 Hz. At a signal frequency of 1,000 Hz, 2πfRC = 62.8, so |H| = 62.8 / √(1 + 3,948) = 0.9999, essentially 0 dB, with a phase lead of 0.9°. At 10 Hz, 2πfRC = 0.628 and |H| = 0.628 / 1.181 = 0.532, which is −5.5 dB.
Response table
| Frequency relative to fc | Gain | dB | Phase lead |
|---|---|---|---|
| 0.1 × fc | 0.0995 | −20.0 | 84.3° |
| 0.5 × fc | 0.447 | −7.0 | 63.4° |
| 1 × fc | 0.707 | −3.0 | 45.0° |
| 2 × fc | 0.894 | −1.0 | 26.6° |
| 10 × fc | 0.995 | −0.04 | 5.7° |
Typical uses
- DC blocking / AC coupling. A coupling capacitor between amplifier stages with the next stage’s input resistance forms a high-pass filter. For audio, fc is set at 5 to 20 Hz so bass is untouched: 1 µF into 47 kΩ gives 3.4 Hz.
- Rumble and handling-noise filters. 20 to 80 Hz cutoffs remove turntable rumble or microphone thumps.
- Differentiators and edge detectors. With fc well above the signal frequency, the output approximates the derivative of the input, producing spikes on edges.
- Removing sensor drift. Slow baseline wander from strain gauges or ECG electrodes is filtered with cutoffs of 0.05 to 0.5 Hz.
Designing for a target cutoff
Choose C first from a standard value, then R = 1 / (2π fc C). For a 100 Hz cutoff with 100 nF: R = 1 / (2π × 100 × 10−7) = 15.9 kΩ, so 15 kΩ or 16 kΩ. Keep R between about 1 kΩ and 1 MΩ: lower values load the source, higher values pick up noise and interact with the next stage’s input impedance, which appears in parallel with R and lowers the effective resistance. The RC low-pass filter calculator uses the same RC product for the opposite response, and the RC time constant calculator relates it to the time domain, where τ = RC = 1 / (2πfc).
Limits of a single RC stage
A first-order filter rolls off gently. To attenuate 50 Hz mains hum by 40 dB while passing 1 kHz, a single stage would need fc near 5 kHz, which also cuts the wanted signal. Two cascaded RC stages give 40 dB per decade but interact unless buffered; active Sallen-Key filters or higher-order designs are the usual answer when steep roll-off is needed.
Common mistakes
- Entering capacitance in microfarads. 1 µF is 0.000001 F or 1e-6.
- Ignoring the load. A 10 kΩ resistor to ground with a 10 kΩ input stage in parallel becomes 5 kΩ and doubles fc.
- Expecting a sharp cutoff. At half the cutoff frequency, 45% of the signal still passes.
- Using electrolytic capacitors for precision. Their tolerance of ±20% and leakage make the cutoff uncertain; use film or C0G ceramic.
Related tools
The capacitive reactance calculator shows the capacitor’s impedance at any frequency, which equals R at the cutoff. The voltage divider calculator illustrates the same ratio for resistive elements, and the capacitor charge time calculator covers the step response.
External references
Frequently asked questions
Which component goes where?
The capacitor is in series with the signal path and the resistor goes from the output to ground. Swapping them gives a low-pass filter.
What is the gain above the cutoff?
It approaches 1 (0 dB). A passive RC filter never amplifies; its maximum gain is unity.
Why does the calculator show a phase shift?
The capacitor causes the output to lead the input. The lead is 45° at fc, near 90° far below it and near 0° far above it.
How do I get a steeper roll-off?
Cascade stages with a buffer between them, or use an active second-order filter. Each additional RC stage adds 20 dB per decade.
Can the same RC be used for low-pass?
Yes. The cutoff frequency is identical; only the component positions differ.