RC Filter Calculator
Design a first-order RC filter by solving for cutoff frequency, resistor, or capacitor with instant quick stats and step-by-step breakdown.
Calculation Steps
Practical RC Design Guide
RC Filter Calculator: Cutoff Frequency, R, and C Explained
Use the RC Filter Calculator to size first-order low-pass or high-pass filters quickly and correctly. This guide explains the core equation \( f_c = \dfrac{1}{2\pi R C} \), the assumptions behind it, how each variable moves the cutoff, and how to sanity-check your design in real hardware.
Quick Start with the RC Filter Calculator
The calculator under this guide is built around the classical first-order RC cutoff: \[ f_c = \frac{1}{2\pi R C} \] It lets you solve for cutoff frequency \(f_c\), resistor \(R\), or capacitor \(C\), and shows helper metrics like time constant \(\tau = RC\) and \(5\tau\).
- 1 Choose what you want to solve for. In the Solve For dropdown, pick: Cutoff Frequency \(f_c\), Resistor \(R\), or Capacitor \(C\) depending on what is fixed in your design.
- 2 Enter the known values with realistic units. For example, use kΩ/MΩ for resistors and nF/µF for capacitors. The calculator converts everything to SI internally, so units can be mixed safely.
- 3 Pick output units that match how you think. When solving for \(f_c\), choose Hz, kHz, or MHz. When solving for \(R\) or \(C\), the output units automatically switch to Ω, kΩ, MΩ or F, µF, nF, pF.
- 4 Check the time constant \(\tau\) and \(5\tau\). The quick-stats section shows \(\tau = RC\), cutoff \(f_c\), \(\omega_c = 2\pi f_c\), and \(5\tau\) (≈ time to 99% of final value). These help you judge how “fast” your filter really is in the time domain.
- 5 Use the step-by-step view to verify the math. Hit Show Steps to see how the calculator converted your units, computed \(\tau\), and derived the final result using the same equations you would write by hand.
- 6 Do quick “what-if” sweeps. Nudge \(R\), \(C\), or \(f_c\) up and down and watch how the result and \(\tau\) change. This is often faster than running a full SPICE sweep just to get an order-of-magnitude feel.
- 7 Save or share the configuration. Use the Share menu to copy the URL or print/save to PDF when you want to attach your sizing notes to design reviews.
Tip: Start with round numbers (10 kΩ, 10 nF, 1 kHz). Once the response feels right, swap in available resistor and capacitor values from your library and re-check \(f_c\).
Watch out: The calculator assumes an ideal, first-order RC with negligible loading. Real circuits with finite input impedance or source resistance can shift the effective \(R\) and therefore the actual cutoff.
Choosing Your Method: Frequency, Components, or Time Constant
There are three common ways engineers use an RC filter calculator: start from the target frequency, start from available components, or design around a time constant.
Method A — Design from Target Cutoff \(f_c\)
You know the bandwidth you want (e.g. 1 kHz anti-alias filter), and you pick either \(R\) or \(C\) based on practical ranges.
- Direct link between spec and result: you size for the frequency you actually care about.
- Great for anti-alias filters, audio tone shaping, and sensor bandwidth limits.
- Easy to communicate in requirements (\(f_c\) at −3 dB).
- May drive inconvenient resistor or capacitor values that are not in your preferred series.
- Needs iteration to keep impedance in a safe range for noise and loading.
Method B — Design from Available R and C
You already have a resistor–capacitor pair in the library (e.g. 10 kΩ and 10 nF) and want to see what cutoff that produces.
- Perfect for reusing proven component values and BOMs.
- Helps answer “what does this existing RC actually do?” in legacy designs.
- Quick feasibility checks before re-spinning a board.
- You may end up with a cutoff that only roughly matches your ideal spec.
- Can hide issues if the loading changes between designs.
Method C — Time-Constant-First Design
Instead of thinking in frequency, you think in rise/fall time or debounce time and work from the time constant \(\tau = RC\).
- Intuitive for debouncing buttons, reset networks, and simple RC delays.
- The rule-of-thumb “≈5τ to settle to 99%” is easy to visualize in the calculator’s quick stats.
- Requires mental mapping between \(\tau\) and equivalent \(f_c\) (\(f_c \approx \dfrac{1}{2\pi \tau}\)).
- Less precise for narrow-band frequency-domain specs.
What Moves the Cutoff Frequency the Most
For a first-order RC filter, the cutoff frequency is governed by \[ f_c = \frac{1}{2\pi R C}. \] The calculator lets you manipulate each term independently. These are the main levers:
Increasing \(R\) lowers \(f_c\) and increases \(\tau\). Very large \(R\) values can reduce loading but increase thermal noise and leakage sensitivity.
Increasing \(C\) also lowers \(f_c\) and slows down the response. Extremely large capacitors can be physically bulky or have high leakage/ESR.
Tightening the bandwidth (lower \(f_c\)) for noise suppression usually pushes \(R\) or \(C\) higher; opening bandwidth (higher \(f_c\)) does the opposite. The calculator shows the trade-off cleanly.
If the source has non-zero output resistance or the load has finite input resistance, they effectively change the total \(R\) in the RC network and shift the actual cutoff from the ideal value.
Real resistors and capacitors have tolerance (±1–20%) and tempco. Your real-world \(f_c\) is really a band, not a single value. The calculator gives the nominal; you should still consider worst-case spread.
Cascading RC sections to get steeper roll-off multiplies the amplitude response and shifts the effective −3 dB point. Use the single-section calculation here as a starting point and refine with SPICE for multi-pole designs.
Worked RC Filter Examples
Example 1 — Find Cutoff Frequency from R and C
- Goal: Find \(f_c\) for an audio low-pass RC filter.
- Resistor: \(R = 10~\text{k}\Omega\)
- Capacitor: \(C = 10~\text{nF}\)
- Assumptions: Ideal first-order RC, negligible loading.
\(R = 10~\text{k}\Omega = 10{,}000~\Omega\),
\(C = 10~\text{nF} = 10 \times 10^{-9}~\text{F} = 1.0\times 10^{-8}~\text{F}\).
\[ \tau = R C = 10{,}000 \times 1.0\times 10^{-8} = 1.0\times 10^{-4}~\text{s}. \]
\[ f_c = \frac{1}{2\pi \tau} = \frac{1}{2\pi \times 1.0\times 10^{-4}} \approx 1{,}591.55~\text{Hz}. \] The calculator will display ≈ \(1.59~\text{kHz}\) when you select kHz units.
\(\tau = 100~\mu\text{s}\) and \(5\tau = 500~\mu\text{s}\). The filter significantly attenuates content much above ~1.6 kHz and settles to ≈99% of final value in about 0.5 ms.
Example 2 — Solve for C Given Target \(f_c\) and R
- Goal: Design a 1 kHz RC low-pass using a 4.7 kΩ resistor.
- Target cutoff: \(f_c = 1{,}000~\text{Hz}\)
- Resistor: \(R = 4.7~\text{k}\Omega\)
- Find: Capacitor \(C\) in nF.
\(R = 4.7~\text{k}\Omega = 4{,}700~\Omega\).
Starting from \(f_c = \dfrac{1}{2\pi R C}\), solve for \(C\):
\[ C = \frac{1}{2\pi f_c R}. \]
\[ C = \frac{1}{2\pi \times 1{,}000 \times 4{,}700} = \frac{1}{2\pi \times 4.7\times 10^{6}} \approx 3.39\times 10^{-8}~\text{F}. \]
\[ 3.39\times 10^{-8}~\text{F} = 33.9~\text{nF}. \] A standard value of 33 nF or 39 nF is usually chosen; the calculator lets you try both and see how much \(f_c\) shifts.
In the calculator, set Solve For = C, enter \(f_c = 1~\text{kHz}\), \(R = 4.7~\text{k}\Omega\), and view the result in nF.
Common RC Filter Layouts & Variations
Even though the calculator models an ideal first-order RC, that single pole shows up in many real circuits. The table below links typical layouts to reasonable cutoff ranges and practical pros/cons.
| Use Case / Layout | Typical Cutoff Range | Pros | Watch-outs |
|---|---|---|---|
| Sensor noise low-pass (RC before ADC) | 10 Hz – 5 kHz | Filters high-frequency noise, reduces aliasing, simple to implement. | Too low \(f_c\) can slow step response; source impedance interacts with ADC sampling capacitor. |
| Audio tone-shaping low-pass | 500 Hz – 20 kHz | Easy treble roll-off, very low cost, intuitive control with potentiometers. | First-order slope (−20 dB/decade) may be too gentle for some EQ curves. |
| Coupling high-pass (series C, resistor to bias) | 1 Hz – 100 Hz | Blocks DC offset between stages while preserving AC content. | Capacitor leakage and input bias currents can shift bias; too high \(f_c\) cuts low-frequency content. |
| Reset / power-on delay RC | 10 ms – 1 s | Very simple way to delay a reset or enable signal on power-up. | Strongly dependent on component tolerance and supply ramp; digital Schmitt triggers recommended. |
| Button debounce RC | 1 ms – 50 ms | Reduces chatter seen by digital inputs; easy to combine with a Schmitt buffer. | Too long of a \(\tau\) can mask short intentional presses; hysteresis design still matters. |
- Confirm whether the RC is low-pass or high-pass in the actual schematic — the calculator’s cutoff applies to either topology.
- Check that the resistor value keeps noise and loading within acceptable limits.
- Verify that the capacitor technology (ceramic, electrolytic, film) suits the voltage and frequency range.
- Run a SPICE check if you cascade multiple RC sections or interact with op-amp poles.
Specs, Logistics & Sanity Checks
The RC Filter Calculator gives you an ideal starting point. Before committing to a schematic or PCB, walk through these checks.
Component Selection
- Resistor: Use 1% metal-film for most analog work; check power dissipation if across large voltage.
- Capacitor: For small values and high frequencies, use C0G/NP0 ceramics; for larger values, X7R or film.
- Voltage rating: Ensure a comfortable margin above worst-case signal or supply voltage.
Layout & Parasitics
- Keep the R and C physically close and tied to a solid reference (ground or virtual ground node).
- Avoid long, high-impedance traces that pick up noise; route sensitive RC nodes away from fast digital lines.
- Consider stray capacitance and input capacitance of op-amps or ADCs as part of your effective \(C\).
Sanity Checks
- Compare the calculator’s \(f_c\) and \(\tau\) to similar circuits you trust.
- Evaluate worst-case with tolerance: ±R, ±C, and temperature; does the shifted \(f_c\) still meet requirements?
- Check interaction with any existing digital filtering or oversampling before finalizing the bandwidth.
A simple rule of thumb: after using the calculator to get a first design, do one quick SPICE simulation and one bench measurement on a prototype. If those agree within tolerance, your RC sizing is in a healthy range.