What this calculator does
A low pass filter lets signals below a certain frequency through largely unchanged while attenuating everything above it. The simplest version, an RC low pass filter, needs just one resistor and one capacitor, and its cutoff frequency is fixed entirely by their values: f = 1 / (2πRC).
This calculator runs that formula either direction. Given a resistor and capacitor already on hand, it returns the resulting cutoff frequency. Given a target cutoff frequency and one component value, it solves for the other component, which is the more common design question when building a low pass filter circuit from scratch.
The formula
The cutoff frequency, also called the -3 dB point, is 1 divided by 2π times resistance times capacitance. Rearranging that same equation solves for resistance (given a target frequency and capacitance) or capacitance (given a target frequency and resistance), since all three quantities sit in one fixed relationship.
| Term | Meaning |
|---|---|
| f | Cutoff frequency: the point where the output has fallen to 1/√2 (about 70.7%) of the input, roughly -3 dB. |
| R | Resistance in the RC circuit, in ohms. |
| C | Capacitance in the RC circuit, entered here in nanofarads. |
| Angular cutoff frequency | The cutoff expressed in radians per second, ω = 2πf, the form used directly inside the underlying equations. |
The inputs explained
| Field | What to enter |
|---|---|
| Solve for | Choose whether to work out the cutoff frequency from known R and C, or solve for the resistor or capacitor needed to hit a target cutoff frequency. |
| Resistance (Ω) | Resistance in ohms. Used directly when solving for frequency or capacitance; ignored when solving for resistance. |
| Capacitance (nF) | Capacitance in nanofarads (nF). Used directly when solving for frequency or resistance; ignored when solving for capacitance. |
| Target cutoff frequency (Hz) | The target cutoff frequency in hertz. Only used when solving for resistance or capacitance. |
When to use it
Checking a filter already built
With a resistor and capacitor already chosen, solving for cutoff frequency confirms where the filter actually rolls off before it goes into a circuit.
Designing a low pass filter circuit from a target frequency
Picking a common capacitor value and solving for resistance (or the reverse) is the usual starting point when a specific cutoff frequency is the design requirement, such as filtering noise above a known signal bandwidth.
Comparing component choices
The same cutoff frequency can be reached with many different resistor-capacitor pairs; solving for one component across a few candidate values of the other shows the trade-offs, such as very high resistances being noisier and very small capacitances being harder to source accurately.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How cutoff frequency changes with capacitance, at a fixed resistance
A fixed 1,000 Ω resistor, across a range of common capacitor values.
| Capacitance | Cutoff frequency (-3 dB point) |
|---|---|
| 10 nF | 15,915.49 Hz |
| 47 nF | 3,386.28 Hz |
| 100 nF | 1,591.55 Hz |
| 220 nF | 723.43 Hz |
| 470 nF | 338.63 Hz |
| 1000 nF | 159.15 Hz |
How cutoff frequency changes with resistance, at a fixed capacitance
A fixed 100 nF capacitor, across a range of resistor values.
| Resistance | Cutoff frequency (-3 dB point) |
|---|---|
| 100 Ω | 15,915.49 Hz |
| 500 Ω | 3,183.10 Hz |
| 1,000 Ω | 1,591.55 Hz |
| 5,000 Ω | 318.31 Hz |
| 10,000 Ω | 159.15 Hz |
| 47,000 Ω | 33.86 Hz |
Questions
What does the cutoff frequency actually mean?
It is the frequency at which the filter output has dropped to about 70.7% of the input signal amplitude, commonly described as the -3 dB point. Frequencies well below it pass through largely unaffected; frequencies well above it are increasingly attenuated.
Why is capacitance entered in nanofarads?
Nanofarads are the typical unit for the small ceramic and film capacitors used in this kind of RC low pass filter circuit; the underlying formula uses farads, and the calculator converts automatically.
How steep is the roll-off past the cutoff frequency?
A simple single-stage RC low pass filter attenuates at roughly 6 dB per octave (about 20 dB per decade) above the cutoff. Steeper roll-off needs additional filter stages, which this single-resistor, single-capacitor calculation does not cover.
How is this different from an RC time constant calculation?
The RC time constant, τ = RC, describes how quickly a capacitor charges or discharges over time in the time domain. Cutoff frequency describes the same RC pair in the frequency domain, and the two are directly related: f = 1 / (2πτ).
For the same R and C pair described in the time domain instead of frequency, see the RC circuit charge and discharge calculator. For a related resonant circuit built from a resistor, inductor and capacitor, see the RLC resonant frequency calculator.