Free calculator
RC filter cutoff frequency calculator
An RC filter is a resistor and a capacitor that pass some frequencies and cut others. Take the output across the capacitor for a low-pass, or across the resistor for a high-pass. Both start cutting at the same cutoff frequency: find it from R and C, or pick the cutoff you want and get the part to fit.
4.7k = 4,700 Ω.
n = nano, µ or u = micro, p = pico.
Cutoff frequency, f = 1 ÷ (2πRC)
- At the cutoff
- 70.7% gets through (−3 dB)
- Time constant, τ = R × C
- 47 µs
What gets through at a frequency
The note or signal you want to check.
Low-pass output, as a share of the input
- In decibels
- −9.88 dB
- Phase
- 71.3° behind the input
The formula
R is in ohms and C in farads. At fc the capacitor's reactance equals R, and 70.7% of the voltage gets through: −3 dB. To find a part for the cutoff you want, rearrange it:
At any other frequency f, a low-pass lets through
Well above fc that's about fc ÷ f, so it falls 20 dB every time the frequency goes up ten times. A high-pass is the mirror image.
A worked example
Phone calls carry 300 Hz to 3.4 kHz. To cut the treble above 3.4 kHz with a 10 nF capacitor:
The nearest E12 value, 4.7 kΩ, puts the cutoff at 3.39 kHz. Voices at 300 Hz pass almost untouched, and hiss at 10 kHz drops to 32%, about −9.9 dB.
Choosing R and C
Pick the capacitor first, since capacitors come in fewer values (10, 15, 22, 33, 47, 68 and so on). Then work out R and round it to an E12 value. Keep R between about 1 kΩ and 100 kΩ: much lower and the filter loads whatever drives it, much higher and whatever reads the output loads the filter.
Free lesson
Now build it yourself
Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.
“Low- and high-pass filters” is lesson 4 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 24 before it first.
Or start from the very first lesson, no account neededThe ideas behind it
- Low-pass filter explainedA resistor and a capacitor that pass the bass and fade the treble, and where the cutoff sits.
- High-pass filter explainedA capacitor in series that blocks DC and the bass, passes the treble, and couples audio between stages.
- How to read a Bode plotGain in decibels against frequency on a log scale: corners, −3 dB and 20 dB per decade.
- RC time constant explainedτ = R × C: how long a capacitor takes to charge through a resistor, and the 63% rule.
Questions people ask
What is the cutoff frequency of an RC filter?
f = 1 ÷ (2π × R × C), with R in ohms and C in farads. It's where the capacitor's reactance equals the resistance, and the output is 70.7% of the input: −3 dB.
Is the cutoff the same for a low-pass and a high-pass?
Yes. The same R and C give the same cutoff either way round. Take the output across the capacitor for a low-pass, or across the resistor for a high-pass. Both let 70.7% through at the cutoff.
Why is the cutoff called the −3 dB point?
At the cutoff the output voltage is 1 ÷ √2 of the input, about 70.7%, which is −3 dB. That's half the power, because 0.707² = 0.5, so it's also called the half-power point.
How fast does an RC filter cut past the cutoff?
One RC stage falls 20 dB per decade: ten times the frequency gives a tenth of the voltage. Well above the cutoff, a low-pass passes about f_c ÷ f. For a steeper cut, use two stages or an LC filter.
More calculators
- Ohm's law calculatorAny two of V, I and R give the third, and the power.
- Electrical power calculatorWatts from any two of V, I and R, and the resistor rating that stays cool.
- LED resistor calculatorThe resistor for one LED or a string, rounded to a value you can buy.
- Resistor colour code calculatorBands to ohms, or ohms to bands, on 4- and 5-band resistors.
- Resistors in series and parallel calculatorThe total of up to eight resistors, in series or in parallel.
- Voltage divider calculatorVout from two resistors, or the resistor for the Vout you need.