Low Pass Filter Calculator - RC and RL Cutoff, Gain, dB

A low pass filter calculator returns the cutoff frequency, magnitude, phase, and dB attenuation of a first-order RC or RL low pass filter from the resistor, capacitor or inductor, and the signal frequency using fc = 1 / (2 pi R C) for RC and fc = R / (2 pi L) for RL.

• • Audio Crossover Design: Pick R and C so a subwoofer low pass stage rolls off above the desired cutoff and protects the driver from mid-range content.
• • Sensor Signal Smoothing: Size an RC network that filters switching noise from a power supply or PWM output before the analog front end sees it.
• • Anti-Aliasing Filter Sizing: Set fc just below half the ADC sampling rate so out-of-band content is attenuated before it folds into the digital signal.
• • EMI Mains Filtering: Evaluate an RL snubber or mains filter at the 50 or 60 Hz line frequency and at the conducted-emission bands.

When a coupling or bypass capacitor fixes the cutoff, the Capacitive Reactance Calculator gives the magnitude Xc = 1 / (2 pi f C) at the same frequency so you can compare the filter impedance against the source and load.

The calculator uses the textbook first-order RC and RL transfer functions to compute cutoff, time constant, magnitude, and phase at the frequency you enter.

• fc: Cutoff frequency in hertz, the -3 dB corner of the filter.
• R: Series resistance in ohms, entered with a unit selector.
• C: Shunt capacitance in farads for the RC topology.
• L: Shunt inductance in henries for the RL topology.
• f: Input signal frequency at which magnitude and phase are evaluated.
• tau: Time constant: tau = R C for RC, tau = L / R for RL. fc = 1 / (2 pi tau).

For a first-order RC low pass filter the transfer function is H(s) = 1 / (1 + s R C). Substituting s = 2 pi j f gives |H(f)| = 1 / sqrt(1 + (f / fc)^2), where fc = 1 / (2 pi R C). Above fc the magnitude falls as fc / f, the 20 dB per decade roll-off used in audio and EMI work.

According to All About Circuits, the cutoff frequency of an RC low pass filter is fc = 1 / (2 pi R C) and the magnitude response is 1 / sqrt(1 + (f/fc)^2).

According to Wikipedia, the cutoff frequency of a first order low pass filter is the frequency at which the magnitude falls to 1 / sqrt(2), corresponding to -3 dB attenuation.

The RC time constant tau = R C is also used for step-response timing. The Capacitor Charge Time Calculator takes the same tau plus a voltage threshold to estimate the charge or discharge time on the same circuit.

Four ideas appear in every first-order low pass filter design: the cutoff frequency, time constant, magnitude response, and phase shift.

Because the cutoff depends on angular frequency omega = 2 pi f, the Angular Frequency Calculator reads fc directly in radians per second instead of hertz.

Pick the topology, enter the components, and choose the signal frequency. The calculator returns fc, |H(f)|, dB attenuation, and phase shift on the spot.

1. 1 Pick the topology: Choose RC for resistor-capacitor or RL for resistor-inductor. The formula and units switch automatically.
2. 2 Enter the resistance R: Type the resistor value and pick ohm, kohm, or Mohm. Use the actual series resistor in the signal path.
3. 3 Enter C or L: For RC, type the capacitance and pick F, mF, uF, nF, or pF. For RL, type the inductance and pick H, mH, or uH.
4. 4 Enter the signal frequency: Type the frequency at which to read the filter response and pick Hz, kHz, MHz, or GHz.
5. 5 Read the cutoff and region: fc is the passband-stopband boundary. The result panel also flags whether the frequency sits in the passband, at the corner, or in the stopband.

Example: 1 kHz cutoff with a 10 kohm input impedance. Enter topology = RC, R = 10000 ohm, C = 15.9155 nF, f = 1000 Hz. The calculator returns fc = 1000 Hz, |H| = 0.7071, attenuation = 3.0103 dB, phase = -45 deg, and tags the frequency as at cutoff.

Once you know the cutoff you want, the Capacitor Size Calculator picks a standard capacitor value and tolerance that matches the closest EIA code for that capacitance.

This calculator replaces hand calculations and worksheets with a single entry form.

• • Cutoff in one pass: Reads fc = 1 / (2 pi R C) or fc = R / (2 pi L) directly from the entered components.
• • Both RC and RL: Switches between RC and RL filters without changing inputs. Useful when comparing a passive RC network with an RL snubber.
• • Gain and attenuation together: Shows magnitude as a ratio and attenuation in decibels, so you can match the result to a datasheet spec.
• • Phase shift included: Adds the -arctan(f / fc) phase lag so you can reason about pulse response and group delay.
• • Passband or stopband label: Flags whether the frequency sits in the passband, at cutoff, or in the stopband.
• • Inverts the formula: Lets you read the resistor or capacitor needed for a target cutoff, the design direction in most filter work.

The same math works for analog audio, switching power supplies, sensor front ends, and conducted EMI filters. Once you have fc, gain, and dB at your frequency, you can decide whether the filter fits the noise band or harmonic you want to suppress.

When the filter is part of a larger attenuation chain, such as a shield plus an RC stage, the Attenuation Calculator uses the same exponential form to compute the total transmitted intensity through the rest of the path.

Five practical factors decide whether the calculator result matches the bench measurement. None change the formula, but all affect the result.

• • The model assumes an ideal voltage source and open-circuit load. Real source resistance and load impedance change both fc and the Q of the filter.
• • A first-order filter rolls off at 20 dB per decade. Steep audio crossovers and EMI filters need second-order or higher topologies for 40 dB per decade or more.
• • Above the self-resonant frequency of the capacitor or inductor the textbook RC or RL transfer function no longer describes the circuit.

Once you know fc, tau, |H(f)|, and phi(f) for your circuit, you can predict the filter behavior at any frequency without re-running the full Bode plot.

According to Wikipedia, a first-order RC low pass filter has a gain roll-off of 20 dB per decade (about 6 dB per octave) above the cutoff frequency.

Once the filter is in a signal chain, the Harmonic Wave Equation Calculator takes the same frequency to confirm the wavelength, wave number, and angular frequency the low pass stage shapes.