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RC Filter Cutoff Frequency Calculator

Calculate the minus three decibel cutoff frequency of an RC low-pass or high-pass filter from resistance and capacitance

Frequently Asked Questions

What is the cutoff frequency of an RC filter?

It is the minus three decibel point, where the output power drops to half the input power. Above or below it, depending on the topology, the signal rolls off at six decibels per octave.

Do low-pass and high-pass filters share the same cutoff?

Yes. The same resistor and capacitor values give the same minus three decibel cutoff frequency whether wired as a low-pass or a high-pass filter. Only the component arrangement differs.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How This Calculator Works

A passive RC filter uses a single resistor and capacitor to pass some frequencies and attenuate others. The cutoff frequency is the point at which the output power drops to half of the input, known as the minus three decibel point. Above or below that frequency, depending on the topology, the signal rolls off at six decibels per octave.

Low-Pass and High-Pass Share the Same Cutoff

The same resistor and capacitor values give the same minus three decibel cutoff frequency whether you wire them as a low-pass or a high-pass filter. The only difference is which component sits in series with the signal. A low-pass filter passes slow signals and blocks fast ones, while a high-pass filter does the reverse.

How To Use It

Enter the resistance in kilohms and the capacitance in microfarads. The calculator returns the cutoff frequency in hertz and kilohertz. Adjust either value to move the cutoff: larger components push the cutoff lower.

Tips

Doubling either R or C halves the cutoff frequency.
The rolloff is a gentle six decibels per octave for a single stage.
Cascade stages for a steeper rolloff if needed.

Filter Response and Phase Shift

Understanding what happens at and around the cutoff frequency is essential for proper filter design. At the cutoff frequency fc = 1/(2π⋅R⋅C), the output voltage is 70.7% of the input (a -3 dB power reduction, since power goes as V²). The phase relationship between input and output also shifts at this frequency: for a low-pass RC filter, the output lags the input by exactly 45 degrees at fc. Well below fc, the phase shift approaches 0 degrees; well above fc, it approaches -90 degrees. This phase shift is continuous and frequency-dependent, which is important in feedback circuits and in systems where multiple signal paths are summed - unexpected phase shift can turn negative feedback into positive feedback.

The amplitude roll-off above (or below, for high-pass) the cutoff frequency is 20 dB per decade, which is the same as 6 dB per octave. In practical terms, this means that at 10x the cutoff frequency, a low-pass filter attenuates the signal by 20 dB (a factor of 10 in voltage, 100 in power). This is a relatively gentle slope - it is often called a "first-order" response. Many applications require more aggressive attenuation just outside the passband, which is where multi-stage and higher-order filter designs become necessary.

Multiple Stages

Cascading two identical RC filter stages doubles the roll-off rate to 40 dB per decade (12 dB per octave), giving a "second-order" response. However, the -3 dB cutoff frequency shifts lower than the single-stage value because the second stage loads the first. When identical RC sections are cascaded without buffering, the actual response differs from the theoretical product of two independent sections because each stage's source impedance interacts with the next stage's input impedance. The result is a Butterworth-like low-pass response only if the stages are isolated with unity-gain buffers. Cascading also doubles the phase shift: two stages produce up to -180 degrees of phase lag, which is relevant in feedback systems where 180 degrees of phase shift at a frequency with gain greater than unity will cause oscillation.

RC Filters in Real-World Circuits

The RC filter appears in virtually every analog circuit in one form or another:

Anti-aliasing before ADC: Analog-to-digital converters alias signals above the Nyquist frequency (half the sample rate) back into the passband as spurious artifacts. An RC low-pass filter set well below Nyquist prevents this. For a 10 kHz sample rate ADC, a cutoff of 4-5 kHz is typical, with a higher-order active filter often used instead of a single RC for sharper rolloff.
Audio tone controls: Simple treble and bass controls in guitar amplifiers and vintage hi-fi equipment use RC networks as frequency-selective voltage dividers. The Baxandall tone control topology uses two RC networks in a feedback loop to create shelving filters with flat boost and cut responses.
Power supply decoupling: Every IC power pin should have a small ceramic capacitor (100 nF) to the ground plane, forming an RC filter with the board trace inductance and the power supply source impedance. This provides a local charge reservoir and suppresses high-frequency noise on the supply rail.
Sensor signal conditioning: Thermistor circuits, strain gauge bridges, and Hall effect sensors often produce noisy analog signals that benefit from an RC low-pass filter before the ADC to reduce measurement noise without adding active circuitry.
I²C and SPI bus speed: Digital communication buses have parasitic capacitance from the PCB traces and pin capacitance of each connected device. This parasitic capacitance, combined with the pull-up resistor, forms an RC low-pass filter that limits the maximum usable clock speed. I²C specifies maximum pull-up resistor values and total bus capacitance limits (400 pF for standard mode) for this reason.

Passive vs. Active Filters

A passive RC filter has one significant limitation: it loads the source (the output impedance of whatever drives it) and is loaded by the sink (the input impedance of whatever it drives). This loading shifts the actual cutoff frequency away from the calculated value and reduces the output voltage even within the passband. Adding an op-amp buffer between stages eliminates inter-stage loading. The Sallen-Key topology uses a single op-amp with RC feedback to implement a true second-order filter with no inter-stage loading, providing 40 dB/decade rolloff with a controlled Q factor. This is the most common building block for audio and instrumentation filter design. The op-amp version requires a power supply but provides gain (or unity gain with no signal loss in the passband), higher input impedance, and lower output impedance.

RC Time Constant Applications

The time constant τ = R⋅C appears in many applications beyond frequency filtering. The time constant is the time for the voltage across a capacitor to rise to 63.2% (1 - 1/e) of its final value when charged through a resistor, or fall to 36.8% (1/e) of its initial value when discharged. After five time constants, the capacitor is more than 99% charged or discharged, which is the practical "fully settled" criterion for timing circuits.

RC timing circuits: A comparator with an RC network forms a one-shot timer. When the capacitor voltage crosses the comparator's threshold (typically set at 63% with a resistor divider), the output changes state. A 555 timer IC uses two comparators with thresholds at 1/3 and 2/3 of the supply voltage to build astable (oscillator) and monostable (one-shot) circuits around an external RC network.
Camera flash charge: A camera flash stores energy in a large electrolytic capacitor (200-400 μF at 300-350 V). The charge time through the current-limiting resistor is an RC process; typical full charge times of 3-8 seconds correspond to several RC time constants with the internal resistance of the charging circuit.
Relay coil snubber: A relay coil is an inductor, not a capacitor, but an RC snubber (resistor and capacitor in series, placed across the coil) absorbs the voltage spike when the relay is de-energized. The snubber RC time constant is chosen to match the coil's inductance and internal resistance for optimal spike suppression.

Debounce Circuits

Mechanical switches bounce - when pressed or released, the contacts make and break contact many times in the first few milliseconds before settling to a stable state. A microcontroller polling the switch at high speed will see many transitions instead of one clean edge. An RC debounce circuit adds a capacitor across the switch contacts: the capacitor cannot charge or discharge instantly, so the bounce-induced transitions are smoothed out before reaching the digital input. A Schmitt trigger input (which has hysteresis between its logic-high and logic-low thresholds) further cleans up the slow edges that result. Typical component values are 1-10 kΩ and 10-100 nF, giving time constants of 10-1000 μs - much longer than a bounce event (1-10 ms is considered very conservative) but shorter than the minimum time between intentional key presses.

Frequently Asked Questions

How do I choose R and C values?

Start with the required cutoff frequency and then choose the resistor value first. Pick R large enough that it does not significantly load the source (typically R ≥ 1 kΩ, or at least 10 times the source impedance), but small enough that the required capacitor value is physically achievable and not excessively affected by capacitor tolerances. From fc and R, calculate C = 1/(2π⋅fc⋅R). For example, a 1 kHz cutoff with R = 10 kΩ gives C = 1/(2π⋅1000⋅10000) = 15.9 nF, which you would round to 15 nF or 22 nF from standard values. Always use a capacitor tolerance of at least 5% for filter circuits; standard ceramic capacitors are 10-20% tolerance, so the actual cutoff frequency will vary accordingly.

Why does my filter not attenuate as much as expected?

Two loading effects are the most common culprits. Source impedance in series with R raises the effective resistance seen by C, shifting the cutoff frequency lower than calculated and reducing attenuation at the target frequency. Load impedance in parallel with C (the input impedance of the next stage) lowers the effective capacitance, shifting the cutoff higher. The solution is to buffer both sides of the filter with op-amp stages, or to design the R value to be much smaller than the load impedance and much larger than the source impedance. In practical circuits, keeping source impedance less than R/10 and load impedance greater than 10⋅R keeps the actual response within a few percent of the calculated ideal.