Passive filter calculator

Low-pass and high-pass RC filter calculator

Solve a first-order passive RC filter for cutoff frequency, resistance or capacitance. Then evaluate ideal voltage gain and phase at a frequency that matters to your circuit.

Calculated response

Resistance

10 kΩ

Capacitance

10 nF

Cutoff (−3.01 dB)

1.592 kHz

Gain at 10 kHz

-16.072 dB

Voltage ratio

0.15718

Phase

-80.96°

Time constant: 100 µs

Choose the right calculation

The same time constant sets the pole; component placement determines the response.

01
Find cutoff
Enter R and C to calculate the cutoff frequency. This is useful when checking a schematic or evaluating available component values.
02
Find resistance
Enter capacitance and the required cutoff to solve resistance, then compare the result with the nearest E12 starting value.
03
Find capacitance
Enter resistance and the required cutoff to solve capacitance, including a practical E12 starting value and its shifted cutoff.

Filter equations

This page models one ideal passive RC pole with no source or load interaction.

Cutoff frequency

f_c = 1 / (2πRC)

Low-pass magnitude

|H| = 1 / √(1 + (f/f_c)²)

High-pass magnitude

|H| = (f/f_c) / √(1 + (f/f_c)²)

At f = f_c, either response has a magnitude of approximately 0.7071, or −3.0103 dB. A first-order response changes at 20 dB per decade on the attenuated side of the corner.

Include the driving source resistance in the effective series resistance and the receiving load in the circuit model. When loading is not negligible, the simple unloaded formula can predict the wrong corner frequency and passband gain.

From ideal values to a working circuit

Use the calculated pole as the beginning of design verification, not the end.

Account for source and load

The low-pass resistor may include output resistance from the driver. A finite load can form an additional divider. Buffering may be needed when the next stage loads the node.

Check component behavior

Capacitance can vary with tolerance, temperature, frequency and DC bias. Resistor tolerance and parasitic capacitance also move the actual pole.

Define attenuation at real frequencies

A cutoff target alone does not specify rejection. Use the response result to check the signal band and the unwanted-noise or switching frequency.

Use a higher-order design when required

One pole provides a gradual roll-off. Tight transition bands, anti-aliasing and precision phase requirements generally need a properly designed multi-pole network.

Frequently asked questions

What does the RC cutoff frequency mean?

For an ideal first-order RC filter, cutoff is the frequency where the output magnitude is 1/√2 of the passband value, approximately −3.01 dB. It is not a brick-wall boundary.

Do low-pass and high-pass RC filters use the same cutoff equation?

Yes. Both use f_c = 1/(2πRC). The component order and the node used for the output determine whether low or high frequencies are passed.

Why might the measured cutoff differ from the result?

Component tolerance, capacitor bias and temperature effects, source resistance, load impedance, wiring and parasitic reactance all change the effective resistance and capacitance seen by the circuit.

Can this calculator design an anti-aliasing or active filter?

It models a single unloaded passive RC pole only. Anti-aliasing, reconstruction and active filters often require multiple poles, a defined source/load model and an amplitude or phase specification.