RC Filter Calculator
Enter a resistor and a capacitor to get the cutoff frequency f_c and the time constant τ of a first-order RC filter. You can also find the C or the R needed for a target cutoff frequency.
Formulas
- Time constant τ = R × C (R in Ω, C in F, τ in seconds)
- Cutoff frequency f_c = 1 ÷ (2π R C) = 1 ÷ (2π τ) (in Hz)
- Working backward: C = 1 ÷ (2π f_c R) and R = 1 ÷ (2π f_c C)
The formulas for the cutoff frequency and the time constant are the same for a low-pass and a high-pass filter. The difference is where the output is taken from.
| Circuit | Output taken across | What it does |
|---|---|---|
| Low-pass | The capacitor | Reduces high frequencies and passes low ones |
| High-pass | The resistor | Reduces low frequencies and passes high ones |
These formulas and the placement of the output were checked against explanatory references (Wikipedia, "RC circuit", "Low-pass filter" and "High-pass filter") when the Japanese version was made.
What is the cutoff frequency?
The cutoff frequency is the frequency at which the filter reduces the signal to half its power. There, the voltage gain is 1/√2 (about 0.7) or −3 dB. For a first-order filter, well away from the cutoff, the level changes by about 20 dB for every tenfold change in frequency (one decade), which follows from an n-th order filter having a slope of 20n dB per decade.
Assumptions and limits (please read)
- This calculation assumes an ideal first-order RC circuit with no load: the source resistance is 0 and nothing is connected to the output. This is a common assumption. The references that were read do not state it explicitly; they say only that impedance matching and the load have to be considered when a filter is connected.
- In a real circuit, the source resistance and the input resistance of the connected equipment (the load) make the cutoff frequency differ from the calculated value.
- Tolerances of resistors and capacitors, temperature, frequency behavior and the choice of standard values (E series) are not covered.
Pi and "rounded" values
The cutoff frequency, and the C and R found by working backward, are calculated with an approximation of pi (60 decimal places), so they are rounded values. The time constant τ = R × C does not use pi and is exact.
Examples
| Input | Result |
|---|---|
| R = 1 kΩ, C = 1 µF | Time constant 1 ms, cutoff frequency about 159.15 Hz |
| R = 10 kΩ, C = 100 nF | Time constant 1 ms, cutoff frequency about 159.15 Hz |
| Target 1 kHz, R = 10 kΩ | C = about 15.92 nF |
Allowed ranges
R must be greater than 0 and at most 10¹² Ω, C greater than 0 and at most 10 F, and the target cutoff frequency greater than 0 and at most 10¹² Hz (checked after the unit is converted).
Electrical safety
This is a calculation for low-voltage signal circuits. Mains power (wall outlets), high voltage and large currents are not covered, and they can cause electric shock, heat and fire. The result does not guarantee the safety or the operation of a real circuit.
What is not covered
RL, RLC and second-order or higher filters, active filters, gain and phase, rounding to standard values (E series), part tolerances and frequency-response graphs are not covered. For voltage, current and resistance, see the Ohm's Law Calculator. To convert between period and frequency, see the Frequency ⇄ Period Converter. To convert between a ratio and dB, see the Decibel Calculator.
Frequently asked questions
Do I need a different calculation for a low-pass and a high-pass filter?
No. The formulas for the cutoff frequency and the time constant are the same. Taking the output across the capacitor gives a low-pass filter, and taking it across the resistor gives a high-pass filter.
Does the signal disappear completely at the cutoff frequency?
No. The cutoff frequency is the point where the power falls to half (−3 dB). It is not the frequency where the signal vanishes.
The calculated value differs from my real circuit.
The calculation is for an ideal circuit with no load. The resistance of the equipment before and after the filter, and the tolerance of the parts, change the result.