RC High-pass Filter Calculator
This RC High-pass Filter Calculator determines cutoff frequency, time constant, angular frequency, voltage gain, attenuation, frequency ratio, and phase shift for an ideal first-order passive filter.
Enter resistance, capacitance, and an analysis frequency to check how the filter rejects DC and lower-frequency content while passing higher-frequency signals. Common applications include AC coupling, audio inputs, sensor interfaces, and DC offset removal.
The model assumes an unloaded output and ideal components. Source impedance, load resistance, capacitor leakage, ESR, tolerance, dielectric behavior, and bias conditions should be included in the final circuit analysis.
Engineering tool
RC High-pass Filter Calculator
Calculate cutoff frequency, time constant, voltage gain, attenuation, frequency ratio, and phase for an ideal first-order RC high-pass filter.
Shunt resistance from Vout to ground.
Series coupling capacitance between Vin and Vout.
Frequency used for gain and phase calculation.
Cutoff frequency (fc)
159.155 Hz
fc = 1 / (2πRC)
Result console
- Time constant (τ)
- 1ms
- Angular frequency (ω)
- 6,283.185rad/s
- Frequency ratio (f / fc)
- 6.283185
- Voltage gain |H|
- 0.98757V/V
- Gain
- -0.109dB
- Attenuation
- 0.109dB
- Phase shift
- 9.043°
At the selected analysis frequency, the ideal output amplitude is 98.76% of Vin and leads the input by 9.043°.
RC High-pass Filter Diagram
The series capacitor blocks DC and low-frequency content. The output is taken across the resistor connected from Vout to ground.
Formula reference
RC High-pass Filter Formulas
A high-pass filter attenuates lower frequencies and approaches unity gain at frequencies well above cutoff. At fc, gain is approximately -3.01 dB and phase lead is 45 degrees.
Time constant: τ = RCCutoff: fc = 1 / (2πRC)Angular frequency: ω = 2πfVoltage gain: |H| = (f / fc) / √(1 + (f / fc)²)Gain: 20 log10(|H|)Phase: φ = atan(fc / f)Variable definitions
- τ
- Time constant in seconds (s)
- fc
- Cutoff frequency in hertz (Hz)
- f
- Analysis frequency in hertz (Hz)
- |H|
- Output-to-input voltage magnitude ratio
- Gain
- Signed amplitude response in decibels (dB)
- φ
- Positive output phase lead in degrees
How to Use This Calculator
- Enter the shunt resistance and choose Ω, kΩ, or MΩ.
- Enter the series capacitance and choose pF, nF, µF, mF, or F.
- Enter the signal frequency where gain and phase should be evaluated using Hz, kHz, or MHz.
- Select Calculate and compare f / fc, voltage ratio, dB attenuation, and phase lead with the circuit requirements.
Worked Example
10 kΩ and 100 nF Filter
R = 10 kΩ = 10,000 Ω
C = 100 nF = 100 × 10⁻⁹ F
τ = RC = 0.001 s = 1 ms
fc = 1 / (2π × 10,000 × 100 × 10⁻⁹)
fc ≈ 159.15 Hz
At 1 kHz, f / fc ≈ 6.283 and |H| ≈ 0.988.
Gain ≈ -0.11 dB and phase ≈ 9.04°
Engineering Notes
Blocks DC and low frequencies
The series capacitor prevents steady-state DC transfer and increasingly attenuates AC components as frequency falls below fc.
Coupling capacitors form high-pass filters
An audio or signal coupling capacitor combines with amplifier input resistance and source impedance to create a practical high-pass response.
Both R and C set cutoff
Increasing resistance or capacitance lowers fc. Use the effective resistance seen by the capacitor, not only the labeled load resistor.
Cutoff gain is about -3 dB
At fc, ideal voltage magnitude is 0.707 of the passband value and phase lead is 45 degrees.
Real capacitor behavior matters
Tolerance, ESR, leakage, dielectric absorption, voltage coefficient, polarity, and temperature can shift low-frequency response and transient behavior.
Common Mistakes
- Ignoring source and load resistances that change the effective R.
- Choosing fc too close to the lowest wanted signal frequency.
- Confusing positive phase lead with positive dB gain.
- Using nominal capacitance without checking tolerance and bias effects.
- Ignoring startup transients and capacitor polarity in coupled circuits.
Support reference
FAQ
What is an RC high-pass filter?
An RC high-pass filter uses a series capacitor and a resistor to ground to attenuate DC and lower frequencies while passing frequencies above its cutoff.
How do you calculate the cutoff frequency of an RC high-pass filter?
Use fc = 1 / (2πRC), with resistance in ohms and capacitance in farads. The same cutoff equation applies to ideal first-order RC low-pass and high-pass filters.
What happens below the cutoff frequency?
Below cutoff, output amplitude decreases at approximately 20 dB per decade as frequency falls. At DC, an ideal series capacitor blocks the signal completely.
Why is the gain -3 dB at cutoff?
At cutoff, the ideal output voltage ratio is 1 / √2, approximately 0.707. This corresponds to 20 log10(0.707), or about -3.01 dB.
How do you choose R and C for an audio coupling capacitor?
Use the effective input resistance seen by the capacitor and choose C so fc is below the lowest required audio frequency. Then verify capacitor tolerance, bias, leakage, source impedance, and startup transients.
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This calculator provides an ideal unloaded first-order RC response for engineering reference. Verify effective source and load resistance, capacitor parasitics, tolerance, bias, leakage, polarity, signal range, and measured frequency response before using the result in production.