Part of Analogue and filter calculators
RC Low-Pass Filter Calculator
Solve cutoff frequency, resistance, or capacitance for a first-order RC low-pass filter.
Inputs
Select which value to calculate from the first-order RC cutoff relationship.
Results
RC low-pass filtering attenuates frequencies above cutoff. Source and load impedance can shift the real response.
Use an RC low-pass filter for simple first-order smoothing and bandwidth limiting
An RC low-pass filter passes low-frequency content and attenuates higher-frequency content. Use this calculator to solve cutoff frequency, resistance, capacitance, and the matching time constant for a first-pass analogue filter check.
Signal smoothing
Estimate a simple RC corner before checking the real source and load impedances.
ADC input filtering
Set a first-pass anti-noise filter, then verify ADC acquisition and source-impedance limits.
Control and reference nodes
Check slow control, reference, or bias nodes where first-order filtering is acceptable.
Equations and model
The calculator uses the ideal first-order RC cutoff relationship. It assumes the resistor and capacitor are the dominant elements setting the pole.
Cutoff frequency
The -3 dB corner frequency for an ideal first-order RC low-pass filter.
Time constant
The same R and C also define the time-domain response of the network.
Rearranged values
Use the target cutoff to solve for a practical resistor or capacitor value.
fc - Cutoff frequency
Unit: hertz (Hz)
Frequency where the ideal output amplitude is about 0.707 of the passband amplitude.
R - Resistance
Unit: ohms (Ω)
The effective series resistance that works with the capacitor to set the corner.
C - Capacitance
Unit: farads (F)
The shunt capacitor value in the first-order RC low-pass network.
τ - Time constant
Unit: seconds (s)
The related time-domain settling constant of the same RC pair.
Worked example
This example matches the shared RC cutoff calculation already covered by the calculator test suite.
Design question: A 1 kΩ resistor and 100 nF capacitor form a simple low-pass filter. What is the cutoff frequency?
Inputs: R = 1 kΩ, C = 100 nF.
Time constant: τ = R × C = 100 µs.
Cutoff: fc = 1 / (2π × 1 kΩ × 100 nF) = 1.59 kHz.
Next check: confirm the source impedance, load impedance, component tolerance, and whether the filter response is acceptable at the frequencies that matter.
Source and load impedance limits
The simple equation is useful, but the real circuit decides which resistance the capacitor actually sees.
Source-side effects
- Driver output impedance can add to the filter resistor.
- Large source resistance can change cutoff and settling time.
- Sampled inputs can disturb the capacitor between acquisitions.
Load-side effects
- Finite load resistance can attenuate the passband signal.
- Input capacitance can add to the intended capacitor.
- Bias current and leakage can create DC error with large resistors.
Assumptions and limitations
First-order only
The model covers one ideal RC pole. It does not model higher-order filters or active filter behaviour.
Tolerance shifts cutoff
Capacitor tolerance, dielectric effects, and resistor tolerance can move the actual cutoff substantially.
Not a stability check
If the filter interacts with op-amp outputs, regulator loops, or ADC sampling, perform the relevant stability or settling checks.
Related calculators and next checks
Follow the next check based on whether the RC network is acting as a filter, delay, coupling network, or part of an amplifier path.
RC time constant calculator
Use when the same R and C matter as a delay, charge, or discharge network.
RC high-pass and AC-coupling calculator
Use when the capacitor is in series or you need a low-frequency cutoff.
Op-amp gain calculator
Use when the filter feeds or is embedded in an amplifier stage.
Analogue and filter hub
Follow related RC, filter, and analogue design workflows.
Engineering conversion calculator
Convert Hz, kHz, nF, µF, and SI-prefixed component values.
FAQ
What happens at the cutoff frequency?
For an ideal first-order RC low-pass filter, the output amplitude is about 70.7% of the low-frequency value, which is -3 dB. The response keeps rolling off above that point.
Does source impedance affect the cutoff?
Yes. The effective resistance is not always just the visible resistor. Source resistance, output impedance, and any series resistance can shift the real cutoff.
Does load impedance affect the cutoff?
Yes. If the load resistance is not high compared with the filter impedance, it changes gain and corner frequency. Buffering or a lower impedance filter may be needed.
Engineering reference
Equations, assumptions, and design guidance
Solves the ideal first-order RC low-pass cutoff relationship.
Equations and variables
fc = 1 / (2 * pi * R * C)tau = R * C- fc
- Cutoff frequency (Hz)
- R
- Resistance (ohm)
- C
- Capacitance (F)
Assumptions and limitations
Assumptions
- The source and load impedances do not shift the effective resistance.
- The capacitor is ideal across the frequency range of interest.
Limitations
- Component tolerance, capacitor ESR/ESL, op-amp input impedance, and source/load interaction are not included in this nominal solve.
Worked example and design use
1 kOhm and 100 nF filter
Inputs: R = 1 kOhm, C = 100 nF
Outputs: fc is about 1.59 kHz, tau = 100 us
Design guidance
- Keep the cutoff well below unwanted high-frequency content and above the wanted passband edge.
- Check R and C tolerances when cutoff placement is critical.