Find the −3 dB cutoff frequency of a first-order RC low-pass or high-pass filter, or pick the resistor or capacitor for a target cutoff with the nearest standard value. See the time constant, gain and phase at any frequency, and a Bode magnitude plot.
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Filter type
Enter your values to see the result.
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How to use the RC Filter Cutoff Calculator
Choose low-pass or high-pass.
Pick what to solve for: the cutoff from R and C, or R or C from a target cutoff.
Enter the known values with their units.
Optionally enter a test frequency to see how much the filter attenuates it.
Read the results and the Bode plot, then download the response table.
RC filter formulas
Quantity
Low-pass
High-pass
Cutoff frequency
f_c = 1 ÷ (2πRC)
Gain |H(f)|
1 ÷ √(1 + (f/f_c)²)
(f/f_c) ÷ √(1 + (f/f_c)²)
Phase
−atan(f/f_c)
90° − atan(f/f_c)
At f = f_c
−3.01 dB, −45°
−3.01 dB, +45°
Solve for R
R = 1 ÷ (2πf_cC)
Solve for C
C = 1 ÷ (2πf_cR)
Attenuation of a first-order low-pass filter
f / f_c
Gain (V/V)
Gain (dB)
Phase
0.1
0.995
−0.04
−5.7°
0.5
0.894
−0.97
−26.6°
1
0.707
−3.01
−45°
2
0.447
−6.99
−63.4°
10
0.0995
−20.04
−84.3°
100
0.0100
−40.00
−89.4°
For a high-pass filter, read the table with f_c / f instead of f / f_c. For steeper roll-off, cascade stages through a buffer or use an active (op-amp) filter; two identical passive RC stages connected directly load each other and do not give exactly −40 dB/decade at the same cutoff.
Frequently asked questions
What is the cutoff frequency formula for an RC filter?
f_c = 1 ÷ (2πRC), with R in ohms and C in farads. For R = 10 kΩ and C = 10 nF, f_c = 1 ÷ (2π × 10,000 × 10×10⁻⁹) ≈ 1,591.5 Hz. The same formula applies to both low-pass and high-pass RC filters.
What does −3 dB mean?
At the cutoff frequency the output voltage is 1/√2 ≈ 70.7% of the input, which is −3.01 dB, and the output power is half. That is why the cutoff is also called the half-power or −3 dB point.
How steep is an RC filter?
A single RC stage is a first-order filter, so beyond the cutoff its gain changes by 20 dB per decade (6 dB per octave). A low-pass filter attenuates a signal at 10 × f_c to about −20 dB (10% of the input).
What is the difference between low-pass and high-pass RC filters?
In a low-pass filter the output is taken across the capacitor, so low frequencies pass and high frequencies are attenuated. In a high-pass filter the components are swapped and the output is taken across the resistor, so DC is blocked and high frequencies pass.
How do I choose R and C?
Pick a convenient capacitor value first (capacitors come in fewer standard values), then calculate R = 1/(2πf_cC) and round to the nearest E24 resistor. Keep R well above the source impedance and well below the load impedance so they do not shift the cutoff.
What is the RC time constant?
τ = RC is the time for the capacitor voltage to reach about 63.2% of a step change. f_c = 1/(2πτ), the 10–90% rise time is about 2.2τ, and the output is within 1% of its final value after about 5τ.
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