High-Pass Filter Calculator: RC and RL Cutoff Frequency, Component Values and Attenuation
Find the cutoff frequency of an RC or RL high-pass filter, or the capacitor, inductor or resistor for a target cutoff, plus gain, dB attenuation and phase at any frequency.
How it works
RC: f_c = 1 ÷ (2πRC) · RL: f_c = R ÷ (2πL) · gain = f ÷ √(f² + f_c²) = R ÷ √(R² + X_C²) · attenuation (dB) = 20 log₁₀(gain) · phase = arctan(f_c ÷ f), output leads · X_C = 1 ÷ (2πfC), X_L = 2πfL · n identical buffered stages: gain = (single-stage gain)ⁿ, overall −3 dB point = f_c ÷ √(2^(1/n) − 1)
A passive high-pass filter blocks low frequencies and passes high ones. In the RC version a capacitor sits in series with the signal and the output is taken across a resistor to ground; at low frequencies the capacitor’s reactance is large, so little signal gets through. In the RL version the resistor is in series and the output is taken across an inductor, whose reactance is small at low frequencies and shorts them to ground. Either way the cutoff (corner) frequency is where the reactance equals the resistance: the output is 1/√2 = 70.7% of the input (−3 dB) and leads it by 45°. Below the cutoff the output falls by 20 dB for every tenfold drop in frequency. Pick what you want to find: the cutoff from the parts, or the capacitor, inductor or resistor that gives a target cutoff, rounded to the nearest E12 or E24 standard value with the cutoff that value really gives. Enter a test frequency to see the gain, dB attenuation, output voltage and phase there, and read the full response from the table and Bode plots. Under More options you can cascade up to three identical buffered stages for a steeper slope. This is the mirror image of the RC low-pass filter calculator: the same cutoff formula, but the gain rises with frequency instead of falling. Results assume an ideal source and a load much larger than R.
Worked example
With R = 3.3 kΩ and C = 47 nF, f_c = 1 ÷ (2π × 3,300 Ω × 47 × 10⁻⁹ F) = 1.026 kHz and the time constant is RC = 155.1 µs. At 100 Hz the capacitor’s reactance is 1 ÷ (2π × 100 × 47 nF) = 33.86 kΩ, so the gain is 100 ÷ √(100² + 1,026²) = 0.0970: the filter passes 9.7% of the signal, an attenuation of −20.27 dB, and the output leads the input by 84.4°. To aim for exactly 1 kHz instead, choose “RC: capacitor for a target cutoff”: C = 1 ÷ (2π × 3.3 kΩ × 1 kHz) = 48.23 nF, and the nearest E12 part, 47 nF, gives the 1.026 kHz above.
Sources: Omni Calculator: High-pass filter (3.3 kΩ, 47 nF → 1.0261 kHz) · Electronics Tutorials: Passive RC high-pass filter (82 pF, 240 kΩ example; cascading) · Redcrab Software: RC high-pass filter formulas (gain, attenuation, phase)
Frequently asked questions
How do you calculate the cutoff frequency of a high-pass filter?
For an RC filter use f_c = 1 ÷ (2πRC); for an RL filter, f_c = R ÷ (2πL). For example, 3.3 kΩ and 47 nF give 1 ÷ (2π × 3,300 × 0.000000047) = 1.026 kHz.
How do I choose the capacitor for a high-pass filter?
Pick a resistor first, then C = 1 ÷ (2π × R × f_c). For a 100 Hz cutoff with 10 kΩ, C = 1 ÷ (2π × 10,000 × 100) = 159 nF; the nearest standard value, 150 nF, gives 106 Hz.
What happens at the cutoff frequency?
The output is 70.7% of the input (−3 dB, half the power) and leads the input by 45°. Far above the cutoff the signal passes almost unchanged; below it the output drops by 20 dB per decade for a single stage.
What is the difference between a high-pass and a low-pass RC filter?
The same two parts swapped: in a low-pass filter the resistor is in series and the output is across the capacitor, so high frequencies are shorted to ground. In a high-pass filter the capacitor is in series and the output is across the resistor, so low frequencies, including DC, are blocked.
How do I make the roll-off steeper?
Cascade stages. Each identical, buffered RC or RL stage adds 20 dB/decade, so two give 40 dB/decade. Without buffers the stages load each other; a common rule is to make each later resistor about 10 times larger and capacitor 10 times smaller.
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This calculator is for educational purposes. Double-check important results before acting on them.