Free calculator

RC Filter Calculator

An RC filter is a resistor and a capacitor that let some frequencies through and block others. Its cutoff frequency is f_c = 1 ÷ (2π × R × C): at that frequency the output is down to 70.7 % of the input, which is −3 dB.

Result

Cutoff frequency f_c

1.592 kHz

Gain at the cutoffalways −3 dB, the “half power” point: −3.01 dB (70.7 % of the input)
Phase at the cutoffthe output lags the input: −45.0 °
Gain at 1 kHz: −1.45 dB (84.7 % of the input)
Phase at 1 kHz: −32.1 °

A simple RC filter changes by 20 dB for every factor of 10 in frequency beyond the cutoff.

The formula

Cutoff frequency

\htmlData{sym=f_c}{f_{\mathrm{c}}} = \dfrac{1}{2\htmlData{sym=pi}{\pi }\htmlData{sym=R}{R} \htmlData{sym=C}{C}}

Low-pass gain

|\htmlData{sym=H:gain}{H}| = \dfrac{1}{\sqrt{1 + (\htmlData{sym=f}{f}/\htmlData{sym=f_c}{f_{\mathrm{c}}})^2}}

High-pass gain

|\htmlData{sym=H:gain}{H}| = \dfrac{\htmlData{sym=f}{f}/\htmlData{sym=f_c}{f_{\mathrm{c}}}}{\sqrt{1 + (\htmlData{sym=f}{f}/\htmlData{sym=f_c}{f_{\mathrm{c}}})^2}}

Low-pass phase

\htmlData{sym=phi}{\phi }= -\arctan(\htmlData{sym=f}{f}/\htmlData{sym=f_c}{f_{\mathrm{c}}})

High-pass phase

\htmlData{sym=phi}{\phi }= 90^\circ - \arctan(\htmlData{sym=f}{f}/\htmlData{sym=f_c}{f_{\mathrm{c}}})

What each letter means

$f_{\mathrm{c}}$: Cutoff frequency (Hz · hertz) : Where a filter starts to cut: the output is down to 71 % (−3 dB).
$\pi$: π (pi) ≈ 3.1416 (no unit) : A fixed number. It shows up whenever something goes round in circles, such as a sine wave.
$R$: Resistance (Ω · ohm) : How strongly something opposes current.
$C$: Capacitance (F · farad) : How much charge a capacitor stores per volt.
$H$: Filter gain |H| (no unit) : Output voltage divided by input voltage at this frequency. The bars mean "size of". No unit (shown here in dB).
$f$: Frequency (Hz · hertz) : How many times per second something repeats.
$\phi$: Phase shift φ (phi) (°) : How far the output wave is shifted in time compared with the input, as an angle: 360° is one whole cycle. A negative angle means the output lags behind.

How it works

A capacitor lets fast changes through more easily than slow ones. In a low-pass filter the resistor is in the signal path and the capacitor goes to ground, so high frequencies drain away through the capacitor and only slow signals reach the output. In a high-pass filter the two swap places: the capacitor is in the path and the resistor goes to ground, so slow changes are blocked.

Gain is the output voltage divided by the input voltage. In decibels it is 20 × log10 of that ratio: 0 dB means unchanged, −3 dB is 70.7 %, and −20 dB is one tenth. Well past the cutoff a simple RC filter falls by 20 dB for every factor of 10 in frequency. The phase says how far the output wave is shifted: −45° for a low-pass and +45° for a high-pass exactly at the cutoff.

Worked example

R = 1 kΩ and C = 100 nF. The cutoff is f_c = 1 ÷ (2π × 1 kΩ × 100 nF) = 1.592 kHz.
At the cutoff the gain is −3.01 dB and the phase is −45 ° for the low-pass, or 45 ° for the high-pass.
Ten times higher, at 15.92 kHz, the low-pass gain is −20.04 dB: about a tenth of the signal.
To design one: for a 1 kHz cutoff with C = 100 nF, R = 1 ÷ (2π × 1 kHz × 100 nF) = 1.592 kΩ. The nearest E12 value is 1.5 kΩ, which gives a cutoff of 1.061 kHz.

Common questions

What does −3 dB mean?

It is the point where the output has fallen to 70.7 % of the input voltage, which is half the power. Filter designers call it the cutoff frequency because it is where the filter starts to cut.

Should I use a low-pass or a high-pass filter?

Use a low-pass filter to remove fast noise and keep a slow signal, such as smoothing a sensor reading or a PWM signal. Use a high-pass filter to remove a steady or slowly changing part and keep the fast changes, such as blocking DC before an audio input.

Does the circuit I connect to the output change the cutoff?

Yes. A load in parallel with the capacitor (for a low-pass) or with the resistor (for a high-pass) shifts the real cutoff. This calculator assumes an unloaded filter, so make the load much bigger than R, or buffer the output with an op-amp.

Try it live

More calculators

All calculators · All lessons · How components work