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?
What is the difference between an RC low-pass and high-pass filter?
What is the time constant of an RC circuit?
How much does an RC filter attenuate a signal away from cutoff?
Common Tip Percentages
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| Category | % of Net Income | Examples |
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Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|---|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |