Rc Filter Calculator - Cutoff, Magnitude, and Phase

An RC filter calculator solves fc = 1 / (2 pi R C), tau = R C, and the magnitude and phase of a single-pole filter from R, C, a signal frequency, and a topology. The same pair gives a low-pass when the capacitor sits across the load and a high-pass when it sits in series.

• • Audio low-pass: Pick R and C so the cutoff sits above the audio band and rolls off ultrasonic noise from a DAC or op-amp.
• • AC-coupling high-pass: Size R and C so the cutoff sits below the lowest frequency of interest and blocks DC bias before the next amplifier stage.
• • Power-supply decoupling: Smooth rectified DC on a small linear supply, with fc well below 100 Hz.
• • Two-stage band-pass: Cascade a high-pass and a low-pass with the same R and C for an audio tone decoder or sensor front end.

The single-pole RC network is the simplest first-order filter in electronics.

When the same R and C pair also has to answer the time-domain questions, RC circuit calculator keeps the same inputs and adds the tau and V(t) columns alongside the cutoff frequency.

The calculator takes R, C, the signal frequency f, and the filter type, and returns tau, fc, the magnitude at f in linear and dB, and the phase shift in degrees. Both topologies share the same cutoff.

• R: Resistance of the resistor in ohms. Calculator accepts ohm, kohm, and Mohm.
• C: Capacitance of the capacitor in farads. Calculator accepts F, mF, uF, nF, and pF.
• fc: Cutoff frequency in hertz, equal to 1 / (2 pi R C). The -3 dB corner of both topologies.
• f: Signal frequency for the magnitude and phase readback. Calculator accepts Hz, kHz, MHz, and GHz.
• Filter type: low-pass, high-pass, or band-pass. The low-pass uses 1/sqrt(1 + (f/fc)^2), the high-pass uses (f/fc)/sqrt(1 + (f/fc)^2), and the band-pass is the product of the two stages sharing the same fc from the single R and C pair.

The dB column uses the voltage-gain convention dB = 20 log10(|H(f)|), and the phase uses degrees so the result lines up with the textbook Bode plot.

According to Omni Calculator, RC Filter, fc = 1/(2 pi R C), the capacitor connects parallel to the load for a low-pass and in series for a high-pass, and the same formula covers both topologies.

According to Wikipedia, RC circuit, the first-order RC low-pass filter has transfer function H_lp(s) = 1/(1 + s R C), magnitude |H_lp(f)| = 1/sqrt(1 + (f/fc)^2), phase -arctan(f/fc), and the -3 dB point at fc = 1/(2 pi R C).

When the analysis needs the AC impedance of the same capacitor at the same frequency, Capacitive Reactance calculator returns Xc = 1/(2 pi f C) in ohms so the filter magnitude can be cross-checked against the reactive impedance.

Four ideas make the result panel easier to read: tau, the -3 dB cutoff, the magnitude in dB at the chosen frequency, and the symmetry between the two topologies.

Once fc is known, the magnitude and phase at any f are read directly from the first-order transfer functions.

When the capacitance value is not yet known and the design has to come from the physical part geometry, Capacitor calculator takes plate area, separation, and dielectric constant and returns C in farads so the filter inputs drop in directly.

Six short steps take you from a resistor and a capacitor to a cutoff frequency, a magnitude in dB, and a phase shift in degrees.

1. 1 Enter the resistance: Type the resistor value and pick ohm, kohm, or Mohm. The calculator converts to ohms before tau and fc run.
2. 2 Enter the capacitance: Type the capacitor value and pick F, mF, uF, nF, or pF.
3. 3 Pick the signal frequency: Type the frequency for the magnitude and phase readback, then pick Hz, kHz, MHz, or GHz.
4. 4 Pick the filter topology: Choose low-pass, high-pass, or band-pass with the same R and C.
5. 5 Read tau and fc: Read tau in the auto-prefixed seconds value (us, ms, or s) and fc in the auto-prefixed hertz value (Hz, kHz, or MHz).
6. 6 Read the magnitude and phase: Read magnitude in linear units and dB at the chosen frequency, then read the phase shift in degrees. The magnitude at fc is 1/sqrt(2) (-3.0103 dB) by definition.

Picture an AC coupling network with a 1 kohm resistor and a 100 nF capacitor. Type 1 kohm, 100 nF, 10 kHz, and high-pass. The calculator returns tau = 100 us, fc = 1591.55 Hz, |H(10 kHz)| = 0.9875, -0.108 dB, and +9.04 degrees, so the 10 kHz signal sits well into the passband.

When the next step is how long the same R and C pair takes to charge from 0 V to a chosen threshold, Capacitor Charge Time calculator solves the inverse V(t) problem and returns the time in seconds and time-constant multiples so the filter cutoff pairs with the matching RC time constant.

A small dedicated filter calculator saves time on the math and returns the cutoff, magnitude, and phase at the same time.

• • Cutoff frequency from any R and C pair: Returns fc = 1/(2 pi R C) without manual division.
• • Magnitude and phase at any frequency: Evaluates the low-pass and high-pass transfer functions, returns magnitude in linear and dB, and phase in degrees.
• • Low-pass, high-pass, and same-corner band-pass in one form: Covers the three single-pole topologies used in audio, power-supply, and sensor designs, with the band-pass branch sharing fc from one R and C pair.
• • Resistance and capacitance prefix library: Accepts ohm, kohm, and Mohm for R and F, mF, uF, nF, and pF for C so reel values drop in without conversion.
• • Frequency prefix library: Accepts Hz, kHz, MHz, and GHz so the same form covers sub-audio coupling, audio band-pass, and RF low-pass filters.
• • Auto-prefixed tau and fc: Picks us, ms, or s for tau and Hz, kHz, or MHz for fc so values stay readable from RF to long-period pairs.

Reading both magnitude and phase from one panel lets you sketch the Bode plot.

When the filter output feeds a resistive load and the steady-state current or power dissipation has to be checked, Ohm's Law calculator returns V = I R for any combination so the filter magnitude pairs with the load-side voltage and current.

Four inputs drive the result panel: R, C, f, and the filter topology. Each shifts tau, fc, and the magnitude at f.

• • The single-pole transfer function assumes an ideal resistor and ideal capacitor with source impedance much lower than R. Real capacitors add ESR and ESL, so the measured magnitude at high frequency rolls off faster than the ideal curve.
• • The dB formula dB = 20 log10(|H|) assumes voltage gain. For power gain, use 10 instead of 20; the column then reads half that value.

The band-pass branch models a same-corner cascade where both stages share fc; a textbook band-pass with separate corners needs a unity-gain buffer so the second stage does not load the first.

According to Wikipedia, Decibel, voltage magnitude ratios are converted to decibels by dB = 20 log10(|H|), so a low-pass filter with |H(fc)| = 1/sqrt(2) reads -3.0103 dB at the cutoff frequency.

When the bench magnitude at fc reads a few tenths of a dB off the predicted -3.0103 dB point, Attenuation calculator takes the same R and C pair in dB terms so the cut-in shape, slope, and corner can be cross-checked against the predicted low-pass response.