Enter a resistor and capacitor value, choose low-pass or high-pass, and get the cutoff frequency, time constant, gain, and phase shift at any signal frequency.
Quick Facts
Cutoff frequency
fc = 1 / (2πRC)
The -3 dB point, where output amplitude falls to 70.7% of input — same formula for low-pass and high-pass wiring.
Time constant
τ = RC = 1 / (2π·fc)
In a step response, the RC network reaches about 63.2% of its final value after one time constant.
Roll-off rate
≈20 dB/decade (6 dB/octave)
First-order (single R-C stage) slope beyond cutoff; cascade stages to steepen it.
Results
Calculated
Cutoff Frequency (fc)
—
fc = 1 / (2πRC), the -3 dB point
Time Constant (τ)
—
τ = RC = 1 / (2π·fc)
Gain at Signal Frequency
—
20·log10(Vout / Vin) at f
Phase Shift
—
Negative lags, positive leads the input
Ready
Enter R, C, filter type, and a signal frequency, then press Calculate.
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How the RC Filter Calculator works
An RC filter is built from a single resistor and capacitor wired in series across a signal source. Which frequencies pass through depends only on where the output is measured: take it across the capacitor and you get a low-pass filter that passes low frequencies and attenuates high ones; take it across the resistor instead and you get a high-pass filter with the opposite behavior. Both configurations share the exact same cutoff frequency formula, since it depends only on the R and C values, not on which component the output is taken from.
The formulas
The -3 dB cutoff (or "corner") frequency is fc = 1 / (2πRC), where R is resistance in ohms and C is capacitance in farads. The time constant is τ = RC (in seconds), related to the cutoff by τ = 1 / (2π·fc). For a signal at frequency f, define the ratio x = f / fc. A low-pass filter's linear gain is 1 / √(1 + x²), with the output lagging the input by φ = -arctan(x). A high-pass filter's linear gain is x / √(1 + x²), with the output leading the input by φ = arctan(fc / f). Either way, the gain in decibels is 20·log₁₀(gain), and at exactly f = fc both topologies are down 3 dB (about 70.7% of input amplitude) with a 45° phase shift.
Reading the roll-off and choosing components
A first-order (single R-C stage) RC filter rolls off at roughly 20 dB per decade (6 dB per octave) beyond the cutoff frequency — each tenfold change in frequency past cutoff changes the output by a further factor of about 10. To lower the cutoff frequency, increase R or C (or both); to raise it, decrease them, since fc depends only on the product RC. Common uses include audio tone shaping, removing DC offset or hum (high-pass), smoothing PWM or digital noise (low-pass), and AC-coupling between circuit stages. A real op-amp or transistor stage adds its own input impedance and bandwidth limits, so the practical cutoff can shift slightly from the ideal RC calculation.
Frequently Asked Questions
What is the cutoff frequency of an RC filter?
The cutoff (or -3 dB) frequency is fc = 1 / (2πRC), where R is in ohms and C is in farads. It is the same formula for both low-pass and high-pass RC filters, since only the wiring (which component the output is taken across) determines which frequencies pass. For example, a 1 kΩ resistor with a 100 nF capacitor gives fc = 1 / (2π × 1,000 × 0.0000001) ≈ 1,591.5 Hz.
What is the difference between an RC low-pass and high-pass filter?
Both use the same resistor and capacitor in series. A low-pass filter takes its output across the capacitor, so low frequencies pass through with little loss and high frequencies are attenuated. A high-pass filter takes its output across the resistor instead, passing high frequencies and attenuating low ones. The cutoff frequency formula fc = 1/(2πRC) is identical for both.
What is the time constant of an RC circuit?
The time constant is τ = RC, measured in seconds, and relates directly to the cutoff frequency as τ = 1 / (2π × fc). In a step response, the RC network reaches about 63.2% of its final value after one time constant and about 99.3% after five time constants.
How much does an RC filter attenuate a signal away from cutoff?
A first-order (single R-C stage) RC filter rolls off at about 20 dB per decade (6 dB per octave) beyond the cutoff frequency. At the cutoff frequency itself the output is already down 3 dB (about 70.7% of the input) with a 45° phase shift; one decade further into the stopband it is down roughly another 20 dB, approaching 0° or 90° of phase shift far from cutoff.