Low Pass Filter Calculator

Enter a resistor and capacitor value plus a signal frequency to find the cutoff frequency (fc = 1/2πRC), the voltage gain, and the phase shift of a first-order RC low-pass filter.

Resistance (R)

Resistance Unit

Capacitance (C)

Capacitance Unit

Signal Frequency (f)

Frequency Unit

Quick Facts

Cutoff frequency

fc = 1 / (2πRC)

The -3 dB point, where output power drops to half (amplitude falls to 1/√2 ≈ 70.7%).

Roll-off rate

-20 dB/decade

Equivalent to -6 dB/octave above cutoff for a single first-order RC stage.

Phase at cutoff

-45°

Output lags input by 45° at fc, approaching -90° well above cutoff.

Time constant

τ = RC

Same RC product sets the filter's step-response rise time (≈2.2·RC for 10-90%).

Your Results

Calculated

Cutoff Frequency (fc)
-
fc = 1 / (2πRC)

Gain at Signal Frequency

20·log10(Vout/Vin), in dB

Voltage Ratio (Vout/Vin)

1 / √(1 + (f/fc)²)

Phase Shift at f

θ = -arctan(f/fc)

Ready

Enter resistance, capacitance, and a signal frequency, then press Calculate.

Frequently Asked Questions

What is the cutoff frequency of an RC low-pass filter?

The cutoff (or corner) frequency is the point where the filter's output drops to 1/√2 (about 70.7%) of the input amplitude, equivalent to -3 dB. For a first-order RC low-pass filter it is fc = 1 / (2πRC), where R is the resistance in ohms and C is the capacitance in farads.

Why does a low-pass filter roll off at -20 dB per decade?

A single-pole RC low-pass filter has one reactive element (the capacitor), so its magnitude response falls by 20 dB for every ten-fold increase in frequency above cutoff (equivalently 6 dB per octave, each time the frequency doubles). Cascading more RC stages steepens the roll-off by another -20 dB/decade per stage.

What is the phase shift of an RC low-pass filter?

The output lags the input by θ = arctan(f/fc). The phase shift is close to 0° well below cutoff, exactly -45° at the cutoff frequency, and approaches -90° at frequencies far above cutoff.

How do I choose R and C for a target cutoff frequency?

Pick a convenient, readily available capacitor value first, then solve for resistance: R = 1 / (2π·fc·C). Keep the stage's output impedance well below the input impedance of whatever it feeds, so the next stage doesn't load it down and shift the actual cutoff frequency.

How the RC Low-Pass Filter Calculator Works

A first-order RC low-pass filter uses a single resistor and capacitor to let low-frequency signals through largely unchanged while attenuating higher frequencies. This calculator applies the standard first-order transfer function H(jω) = 1 / (1 + jωRC) to your resistor, capacitor, and a signal frequency of interest, then reports the cutoff frequency along with the resulting gain (in dB and as a linear voltage ratio) and phase shift at that frequency.

Deriving the cutoff frequency, gain, and phase

The capacitor's impedance, 1/(jωC), forms a voltage divider with the resistor R, with the output taken across the capacitor. Solving that divider for the output-to-input voltage ratio gives H(jω) = 1 / (1 + jωRC). Setting the magnitude of this ratio to 1/√2 — the point where output power is exactly half the input power — and solving for frequency yields the cutoff frequency fc = 1 / (2πRC). At any frequency f, the magnitude of the response is |H| = 1 / √(1 + (f/fc)²), which this calculator converts to decibels via 20·log10(|H|), and the phase lag is θ = -arctan(f/fc), the angle by which the output signal trails the input.

Choosing R and C values and practical filter design notes

In practice, pick a capacitor value first (common values like 100 nF or 1 µF are easy to source), then solve for the resistor: R = 1 / (2π·fc·C). Keep R small enough that the filter's output impedance stays well below the input impedance of whatever stage it feeds — loading the filter with a low-impedance load shifts the effective cutoff frequency and adds extra attenuation. Well below fc the filter passes the signal with negligible loss (gain ≈ 0 dB); well above fc, gain falls at -20 dB per decade (-6 dB per octave) and phase approaches -90°, which is why RC low-pass filters are common as anti-aliasing filters, audio tone controls, and noise filters on sensor and power-supply lines.