How to Use the RC Filter Calculator
An RC filter uses a single resistor and capacitor to shape a signal's frequency content. Depending on where the output is tapped, the same two-component network can be either a low-pass filter (passes low frequencies, attenuates high ones) or a high-pass filter (passes high frequencies, attenuates low ones). This calculator takes your resistance, capacitance, filter type, and a signal frequency, then reports the cutoff frequency along with the exact voltage gain, attenuation in decibels, and phase shift the filter produces at that frequency.
Deriving the low-pass and high-pass response
A capacitor's impedance falls as frequency rises: X_C = 1/(2πfC). In a low-pass RC filter the output is taken across the capacitor, which forms a voltage divider with the resistor. Treating the network as a complex divider gives a transfer function H(f) = 1/(1 + jf/f_c), where the cutoff frequency is f_c = 1/(2πRC) — the point where X_C equals R. Taking the magnitude gives the gain |H(f)| = 1/√(1+(f/f_c)²), and the phase angle is φ = −arctan(f/f_c), meaning the output increasingly lags the input as frequency rises. Swap the resistor and capacitor positions (output across the resistor instead) and the roles invert: the high-pass transfer function is H(f) = (jf/f_c)/(1 + jf/f_c), giving gain |H(f)| = (f/f_c)/√(1+(f/f_c)²) and phase φ = 90° − arctan(f/f_c). Both filters share the same cutoff formula and both cross |H| = 1/√2 ≈ 0.707 (equivalently −3.01 dB) exactly at f = f_c, but they approach that point from opposite directions.
Practical design notes
- Rolloff is gradual, not a hard wall: a single RC stage attenuates at roughly 6 dB per octave (about 20 dB per decade), so a low-pass filter still passes a meaningful fraction of a signal one octave above cutoff (about 45%, or −7 dB) rather than blocking it outright. Cascading multiple RC stages (or using an active filter topology) steepens the rolloff for applications that need sharper separation.
- Loading matters: the formulas above assume the filter drives a high-impedance load and is driven by a low-impedance source. A load comparable to R, or a source impedance comparable to X_C, shifts the effective cutoff frequency — buffer the filter with an op-amp follower when the downstream impedance is not much larger than R.
- Component tolerance and rounding: standard resistors and capacitors carry ±1% to ±20% tolerance, and common capacitor values (e.g. 0.1 µF, 100 nF) are rounded from the exact calculated value. Recompute the cutoff with the nearest real-world part values before finalizing a design.
- Common uses: low-pass RC filters remove high-frequency noise and anti-alias signals before an ADC; high-pass RC filters (also called AC-coupling or DC-blocking capacitors) strip DC offset from audio and sensor signals while passing the frequencies of interest.