RC Filter Calculatorfc = 1 ÷ (2πRC) · low-pass & high-pass
An RC filter’s cutoff frequency is fc = 1 ÷ (2πRC), the point where the output falls to 70.7% of the input (−3 dB). A 1 kΩ resistor with a 100 nF capacitor cuts off at 1,592 Hz. Calculate the cutoff from R and C, choose R or C for a target frequency (with the nearest standard part), or find the gain in dB and the phase shift of a low-pass or high-pass filter at any frequency, drawn on a live Bode plot.
Formula verified against OpenStax — University Physics, Volume 2 · HyperPhysics, Georgia State University
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Filter components
Low-pass: R in series, C to ground. High-pass: C in series, R to ground. Same cutoff formula for both.
Step-by-step working
What is rc filter?
An RC filter is a simple circuit of one resistor (R) and one capacitor (C) that lets some frequencies through and attenuates others. Because a capacitor’s impedance falls as frequency rises, the circuit’s output depends on frequency.
It is the most common filter in electronics: smoothing PWM into a steady voltage, removing noise from sensor readings, debouncing switches, coupling audio stages and protecting analogue-to-digital converters from aliasing.
Quick answers
How do you calculate the cutoff frequency of an RC filter?
fc = 1 ÷ (2πRC). With 10 kΩ and 10 nF: 1 ÷ (2π × 10⁴ × 10⁻⁸) = 1,592 Hz. Swap in your values in the first tab.
What capacitor do I need for a 1 kHz low-pass filter?
C = 1 ÷ (2πR × 1,000). With R = 10 kΩ that is 15.9 nF, so use 15 nF (1.06 kHz) or 16 nF from the E24 series (995 Hz).
Why is the cutoff called the −3 dB point?
At fc the output voltage is 1 ÷ √2 = 70.7% of the input, which is −3.01 dB. The power delivered is exactly half.
What is the difference between RC low-pass and high-pass filters?
They use the same two parts, just swapped. Low-pass puts the capacitor to ground and keeps slow signals; high-pass puts the capacitor in series and blocks DC. Charge behaviour is covered in the capacitor calculator.
RC filter formulas
Phase: low-pass −tan⁻¹(f/fc), high-pass 90° − tan⁻¹(f/fc). Both are −45° and +45° respectively at the cutoff.
| Symbol | Meaning | SI unit |
|---|---|---|
| fc | Cutoff (−3 dB) frequency | Hz |
| R | Resistance | Ω |
| C | Capacitance | F |
| τ | Time constant = RC | s |
| f | Signal frequency | Hz |
| |H| | Voltage gain (output ÷ input) | — |
How to design an RC filter
- Choose the cutoff: the frequency where the filter should start working, for example 1 kHz.
- Pick a convenient resistor, typically 1–100 kΩ, so the source and load aren’t strained.
- Calculate C = 1 ÷ (2πR fc) and round to the nearest standard value.
- Recheck fc with the real parts, and make sure the load impedance is at least 10× R.
Worked example: 1 kΩ and 100 nF
What is the cutoff of an RC filter built from a 1 kΩ resistor and a 100 nF capacitor?
fc = 1 ÷ (2π × 0.0001) = 1,591.5 Hz
Wired as a low-pass, a 5 kHz signal comes out at 30.3% of its amplitude (−10.36 dB, lagging 72.3°). As a high-pass, the same signal keeps 95.3% (−0.42 dB). To design for exactly 1 kHz with 10 kΩ you need 15.9 nF; the nearest E12 part, 15 nF, gives 1,061 Hz.
Common RC filter values
Ready-made combinations and their cutoffs.
| R | C | Cutoff fc | Typical use |
|---|---|---|---|
| 10 kΩ | 10 µF | 1.59 Hz | PWM-to-DC smoothing |
| 10 kΩ | 1 µF | 15.9 Hz | Audio coupling (high-pass) |
| 10 kΩ | 100 nF | 159 Hz | Switch debounce, hum filtering |
| 1 kΩ | 100 nF | 1.59 kHz | Tone control, sensor smoothing |
| 1 kΩ | 8.2 nF | 19.4 kHz | Audio anti-aliasing |
| 100 Ω | 1 nF | 1.59 MHz | RF / fast-edge filtering |
Low-pass vs high-pass at a glance
| Low-pass RC | High-pass RC | |
|---|---|---|
| Series component | Resistor | Capacitor |
| To ground | Capacitor | Resistor |
| Passes | DC and frequencies below fc | Frequencies above fc; blocks DC |
| Phase at fc | −45° (lags) | +45° (leads) |
| Roll-off | −20 dB/decade above fc | −20 dB/decade below fc |
Common mistakes to avoid
- Forgetting the 2π. 1 ÷ RC is the angular cutoff ωc in rad/s, not fc in Hz.
- Ignoring the load. A load resistance comparable to R shifts the cutoff and reduces gain. Buffer it, or keep the load above 10× R.
- Expecting a sharp cut. A single RC stage only rolls off at 20 dB per decade. Cascade stages, or use an active filter, for steeper slopes.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
RC Filter Calculator: frequently asked questions
fc = 1 ÷ (2πRC), with R in ohms, C in farads and fc in hertz.
It passes DC and low frequencies and attenuates frequencies above fc by 20 dB per decade. It is used to smooth signals, remove noise and prevent aliasing.
It blocks DC and attenuates frequencies below fc, passing higher frequencies. It is used for AC coupling and removing slow drift or hum.
−45° for a low-pass and +45° for a high-pass. Far from cutoff it approaches −90° or 0° (low-pass) and 0° or +90° (high-pass).
Cascade stages (each adds 20 dB/decade, with buffering between them), or use an active filter design such as Sallen–Key.
They are linked: τ = RC, and fc = 1 ÷ (2πτ). A bigger time constant means a lower cutoff frequency.
References & sources
- OpenStax — University Physics, Volume 2 — Ch. 10.5, RC Circuits; Ch. 15, AC circuits and reactance
- HyperPhysics, Georgia State University — RC filters and capacitive reactance
- Wikipedia — RC circuit — frequency-domain response
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.