What Is an RC Filter and How Is the Cutoff Frequency Calculated?
An RC filter is a first-order passive circuit built from one resistor and one capacitor that passes signals on one side of a cutoff frequency and attenuates the other. The cutoff frequency (fc) is the point where output power falls to half, or output voltage drops to 70.7% of input, which equals −3 dB.
The RC cutoff frequency formula is: fc = 1 ÷ (2π × R × C), where R is resistance in ohms, C is capacitance in farads, and fc is in hertz. The product R × C is the time constant τ in seconds, so fc = 1 ÷ (2πτ). The same formula applies to both low-pass and high-pass filters.
A first-order RC filter rolls off at 20 dB per decade (about 6 dB per octave) beyond the cutoff, and shifts phase by exactly 45° at fc. For a 10 kΩ resistor and 100 nF capacitor, fc = 1 ÷ (2π × 10,000 × 0.0000001) ≈ 159.2 Hz.
How to Use This RC Filter Calculator
Choose low-pass or high-pass, enter R and C, and the results update instantly. Here's what each field means:
- Filter type: A low-pass filter passes frequencies below fc (resistor in series, capacitor to ground). A high-pass filter passes frequencies above fc (capacitor in series, resistor to ground).
- Resistance: The resistor value in ohms (Ω), kilohms (kΩ), or megohms (MΩ).
- Capacitance: The capacitor value in picofarads (pF), nanofarads (nF), or microfarads (µF).
- Test frequency: Optional. Enter a signal frequency to see the gain in decibels, the Vout/Vin ratio, and the phase shift at that frequency.
The formulas are unit-independent, so results are identical worldwide; only the unit labels change. Capacitors and resistors are sold in standard E-series values (E12, E24, E96) defined by the International Electrotechnical Commission (IEC 60063), so pick the nearest standard values after calculating.
RC Filter Gain and Phase at Multiples of the Cutoff Frequency
The table below shows how a first-order RC filter responds at common multiples of fc. The attenuation is the same for low-pass (above fc) and high-pass (below fc) filters by symmetry.
| f ÷ fc | Low-pass gain | Low-pass phase | High-pass gain |
|---|---|---|---|
| 0.1 | −0.04 dB | −5.7° | −20.04 dB |
| 0.5 | −0.97 dB | −26.6° | −6.99 dB |
| 1 | −3.01 dB | −45.0° | −3.01 dB |
| 2 | −6.99 dB | −63.4° | −0.97 dB |
| 10 | −20.04 dB | −84.3° | −0.04 dB |
The gain magnitude is |H| = 1 ÷ √(1 + (f/fc)²) for a low-pass filter and |H| = (f/fc) ÷ √(1 + (f/fc)²) for a high-pass filter, and gain in decibels is 20 × log₁₀(|H|). According to the IEEE, the −3 dB point is the standard definition of bandwidth for first-order filters.
Frequently Asked Questions
What is the formula for the cutoff frequency of an RC filter?
The cutoff frequency of an RC filter is fc = 1 ÷ (2π × R × C), with R in ohms and C in farads. At this frequency the output is 70.7% of the input (−3 dB) and the phase shift is 45°. A 1 kΩ resistor with a 100 nF capacitor gives about 1,592 Hz.
What is the difference between a low-pass and a high-pass RC filter?
A low-pass RC filter places the resistor in series with the signal and the capacitor to ground, passing frequencies below fc. A high-pass RC filter swaps them, with the capacitor in series and the resistor to ground, passing frequencies above fc. Both share the same cutoff formula.
How accurate is this RC filter calculator?
The calculator gives exact results for ideal components using the first-order transfer function. Real parts differ: ceramic capacitors can vary ±10–20%, resistors are typically ±1–5%, and source or load impedance adds to the effective resistance, so the actual cutoff frequency will shift. Buffer the output with an op-amp when load impedance matters.
How do I choose R and C for a target cutoff frequency?
Rearrange the formula to R = 1 ÷ (2π × fc × C). Pick a practical capacitor first, such as 10 nF or 100 nF, then solve for R and round to the nearest standard E24 resistor value. Keep R well above the source impedance and well below the load impedance, typically between 1 kΩ and 100 kΩ.