RC Filter Calculator
Calculate cutoff frequency, resistance, capacitance, gain, phase shift, and output voltage amplitude for first-order RC low-pass and high-pass filters.
Calculator is for informational purposes only. Terms and Conditions
Choose what to solve for
Select the filter type and unknown value before entering known values.
Enter the known values
Use common electrical units. All values are converted to base SI units internally.
Visual Check
The circuit diagram and response curve update with the selected filter type.
Solution
Live result, quick checks, warnings, and full solution steps.
Quick checks
- Time constant—
Show solution steps See unit conversions, equation substitution, assumptions, and checks
- Enter values to see the full solution steps and checks.
Source, Standards, and Assumptions
Calculation basis, constants, assumptions, and limitations.
Uses ideal first-order passive RC filter equations for educational circuit analysis. No single governing code standard is required for this simplified calculation.
- Assumes ideal resistor and capacitor behavior.
- Assumes the filter is not significantly loaded by the next circuit stage.
- Uses standard SI conversions for ohms, farads, hertz, and volts.
On this page
Calculator Guide
How to Use the RC Filter Calculator
The RC Filter Calculator above helps calculate cutoff frequency, resistance, capacitance, gain, phase shift, and output voltage amplitude for first-order low-pass and high-pass RC filters. Use it to find the -3 dB cutoff point, solve backward for a resistor or capacitor value, or estimate what happens to a signal at a selected frequency.
An RC filter uses a resistor and capacitor to pass some frequencies while attenuating others. A low-pass RC filter passes lower frequencies and attenuates higher frequencies, while a high-pass RC filter attenuates low frequencies and passes higher frequencies. The formulas assume an ideal first-order passive RC filter, so real circuits may shift because of tolerance, loading, and parasitic effects.
Quick Answer
The core RC filter cutoff formula is \(f_c=1/(2\pi RC)\). Enter \(R\) in ohms and \(C\) in farads to calculate cutoff frequency in hertz. At \(f_c\), an ideal first-order RC filter output is about \(0.707\) of the input amplitude, or approximately \(-3.01\,dB\).
Do not rely on this simplified calculator when…
Do not use a simple RC filter result as the only basis for final high-frequency layout, precision analog design, safety-critical filtering, anti-aliasing compliance, EMC work, or production component selection. Real circuits can be affected by source resistance, load resistance, capacitor tolerance, leakage, ESR, temperature, PCB parasitics, and manufacturer limits.
Inputs and Outputs Used by the Calculator
The calculator uses the selected solve mode to decide which values are known and which value is unknown. The most common use is calculating cutoff frequency from resistance and capacitance, but the same formula can be rearranged to solve for \(R\) or \(C\).
| Type | Value | What It Means | Common Unit |
|---|---|---|---|
| Input | Filter type | Choose low-pass or high-pass behavior. | low-pass, high-pass |
| Input | Resistance, \(R\) | The resistor that works with the capacitor to set the RC time constant. | Ω, kΩ, MΩ |
| Input | Capacitance, \(C\) | The capacitor value that stores and releases charge as frequency changes. | pF, nF, µF, mF, F |
| Input | Signal frequency, \(f\) | The frequency where gain, phase, or output amplitude is evaluated. | Hz, kHz, MHz |
| Input | Input voltage amplitude, \(V_{in}\) | The input signal amplitude used to estimate output amplitude. | mV, V |
| Output | Cutoff frequency, \(f_c\) | The -3 dB point where the filter transition begins. | Hz, kHz, MHz |
| Output | Time constant, \(\tau\) | The charge/discharge time scale of the RC network. | s, ms, µs |
| Output | Gain and phase | Signal amplitude ratio and phase shift at the selected frequency. | V/V, dB, degrees |
| Output | Output voltage amplitude, \(V_{out}\) | The input amplitude multiplied by filter gain magnitude. | mV, V |
RC Filter Formula
The same cutoff frequency formula applies to an ideal first-order RC low-pass filter and an ideal first-order RC high-pass filter. The circuit layout determines which side of the cutoff is passed or attenuated.
Cutoff Frequency
Use this when resistance and capacitance are known. \(R\) must be in ohms and \(C\) must be in farads to get \(f_c\) in hertz.
Solve for Resistance
Use this when the desired cutoff frequency and capacitor value are known.
Solve for Capacitance
Use this when the desired cutoff frequency and resistor value are known.
RC Time Constant
The time constant describes transient response. A larger \(\tau\) means lower cutoff frequency and slower response.
Low-Pass Gain
High-Pass Gain
Gain in Decibels
Use this to convert voltage gain ratio into decibels. At cutoff, \(|H(f)|=0.707\), so gain is approximately \(-3.01\,dB\).
Low-Pass Phase Shift
An ideal first-order low-pass filter lags the input and has about \(-45^\circ\) phase shift at cutoff.
High-Pass Phase Shift
An ideal first-order high-pass filter leads the input and has about \(+45^\circ\) phase shift at cutoff.
Output Voltage Amplitude
This gives output amplitude magnitude. It does not describe the full time-domain waveform unless phase is also considered.
Why the formula matters
The cutoff frequency is inversely proportional to both \(R\) and \(C\). Doubling either resistance or capacitance cuts the cutoff frequency in half. This makes unit accuracy especially important because a nF-to-µF mistake changes the result by a factor of 1,000.
What the Variables Mean
Each variable must use the correct electrical unit before applying the formula. The calculator handles unit conversion, but the manual formulas below assume base SI units.
| Symbol | Meaning | How to Enter It |
|---|---|---|
| \(f_c\) | Cutoff frequency or -3 dB frequency. | Enter or read in Hz, kHz, or MHz. |
| \(R\) | Resistance in the RC network. | Enter as Ω, kΩ, or MΩ. Base formula uses ohms. |
| \(C\) | Capacitance in the RC network. | Enter as pF, nF, µF, mF, or F. Base formula uses farads. |
| \(\tau\) | RC time constant that describes charge/discharge speed. | \(\tau=RC\), measured in seconds. |
| \(f\) | Signal frequency being tested against the filter. | Use Hz, kHz, or MHz. This is not always the same as cutoff frequency. |
| \(|H(f)|\) | Gain magnitude at a selected frequency. | A value of 1 means no attenuation; 0.707 is the -3 dB cutoff point. |
| \(Gain_{dB}\) | Gain expressed in decibels. | \(Gain_{dB}=20\log_{10}(|H|)\). |
| \(\phi\) | Phase shift between input and output. | Usually reported in degrees. Low-pass lag is negative; high-pass lead is positive. |
| \(V_{in}\), \(V_{out}\) | Input and output voltage amplitude. | Use amplitude magnitude, not peak-to-peak unless the same convention is used for both. |
How to Use the Calculator
Start by choosing the filter type and solve mode. The required fields change depending on whether you are solving cutoff frequency, a component value, gain, phase, or output voltage amplitude.
Select low-pass or high-pass
Choose low-pass if you want lower frequencies to pass. Choose high-pass if you want lower frequencies or DC content attenuated.
Choose the solve mode
Use cutoff frequency when \(R\) and \(C\) are known. Use resistance or capacitance mode when designing for a target cutoff.
Check the unit selectors
Capacitor units are the biggest trap. \(10\,nF\), \(10\,\mu F\), and \(10\,pF\) produce very different cutoff frequencies.
Review gain, phase, and warnings
If you enter a signal frequency, compare the selected frequency to \(f_c\). Frequencies near cutoff experience meaningful attenuation and phase shift.
How to Interpret RC Filter Results
The cutoff frequency is a transition point, not a hard boundary. A first-order RC filter changes gradually, with a slope that approaches 20 dB per decade away from the cutoff region.
| Result Pattern | What It Means | What to Do Next |
|---|---|---|
| Frequency much below \(f_c\) | Low-pass passes strongly; high-pass attenuates strongly. | Check whether this matches the signal band you want to keep. |
| Frequency near \(f_c\) | Gain is near 0.707 V/V, or about -3 dB. Phase shift is significant. | Avoid placing critical signal content exactly at cutoff unless attenuation is acceptable. |
| Frequency much above \(f_c\) | High-pass passes strongly; low-pass attenuates strongly. | For stronger attenuation, consider multiple stages or a higher-order filter. |
| Extremely low \(f_c\) | The time constant is large and the response may be slow. | Check startup delay, settling time, and capacitor leakage. |
| Extremely high \(f_c\) | Parasitics, layout, and non-ideal component behavior may dominate. | Review capacitor type, source impedance, load impedance, and PCB layout. |
| Frequency | Low-Pass Gain | High-Pass Gain | Design Meaning |
|---|---|---|---|
| \(0.1f_c\) | About \(0.995\), or \(-0.04\,dB\) | About \(0.100\), or \(-20\,dB\) | Low-pass is mostly passing; high-pass is strongly attenuating. |
| \(f_c\) | \(0.707\), or \(-3.01\,dB\) | \(0.707\), or \(-3.01\,dB\) | This is the cutoff point for both ideal first-order filters. |
| \(10f_c\) | About \(0.100\), or \(-20\,dB\) | About \(0.995\), or \(-0.04\,dB\) | High-pass is mostly passing; low-pass is strongly attenuating. |
What to do with the result
Use the calculated cutoff frequency to decide whether your signal of interest is in the passband, transition region, or attenuated region. Then choose real resistor and capacitor values, recalculate the actual cutoff, and check whether phase shift or response delay matters for your application.
What changes the result most?
\(R\) and \(C\) affect cutoff frequency equally because \(f_c\) depends on the product \(RC\). If either value changes by 10%, the cutoff frequency changes by about 10% in the opposite direction. Component tolerance can therefore matter as much as the calculated value.
Quick sanity check
For \(R=10\,k\Omega\) and \(C=10\,nF\), the cutoff should be about \(1.59\,kHz\). If your calculator result is \(1.59\,Hz\) or \(1.59\,MHz\), you likely selected the wrong capacitor unit.
Input Quality Checklist
Before trusting the output, verify the values represent the circuit you actually plan to build. RC filters are simple, but the wrong unit or loading assumption can make the result misleading.
Check capacitor units
Confirm whether the capacitor is pF, nF, µF, mF, or F. This is the most common RC filter unit error.
Use resistance seen by the capacitor
If source resistance or another resistor contributes to the charging path, the effective \(R\) may differ from the single resistor value.
Confirm output location
Low-pass output is usually taken across the capacitor. High-pass output is usually taken across the resistor.
Account for load resistance
A low input impedance on the next stage can shift gain and cutoff behavior from the ideal result.
Step-by-Step Worked Example
The most common RC filter calculation is finding cutoff frequency from a known resistor and capacitor. A second common design task is solving for a capacitor from a target cutoff frequency.
Formula
Substitution
Final Answer
Result
The cutoff frequency is approximately 1.59 kHz. For a low-pass filter, frequencies well below this value pass more easily, while frequencies above it are increasingly attenuated.
Why this answer is reasonable
A \(10\,k\Omega\) resistor and \(10\,nF\) capacitor create an RC product of \(100\,\mu s\). Since \(f_c=1/(2\pi\tau)\), a cutoff around \(1.6\,kHz\) is expected.
Example 2: Solve for Capacitance from a Target Cutoff
Suppose you want a cutoff frequency of \(1\,kHz\) and want to use a \(10\,k\Omega\) resistor.
A practical design might use a nearby standard value such as \(16\,nF\), then recalculate the actual cutoff frequency:
Design result
A \(10\,k\Omega\) resistor with a \(16\,nF\) capacitor gives an actual cutoff of about 995 Hz, which is close to the \(1\,kHz\) target.
Engineering Diagram: Low-Pass vs High-Pass RC Filters
The component placement determines the filter behavior. A low-pass RC filter usually places the resistor in series and the capacitor to ground, while a high-pass RC filter usually places the capacitor in series and the resistor to ground.
Typical Values and Reference Checks
Practical RC values vary by application, but these ranges are useful for checking whether your result is reasonable.
| Application | Typical Cutoff Goal | Common Notes |
|---|---|---|
| Sensor smoothing | Below dominant noise frequency | Too low of a cutoff creates slow response and measurement lag. |
| PWM smoothing | Well below PWM switching frequency | A single RC stage may not reduce ripple enough for precision output. |
| Audio high-pass coupling | Often below the lowest desired audio frequency | Load impedance affects actual cutoff frequency. |
| Noise reduction | Between desired signal band and unwanted noise band | First-order rolloff is gentle, so strong attenuation may require more filtering. |
| ADC input filtering | Application-specific, often tied to sampling rate | Anti-aliasing requirements may need higher-order filtering than one RC stage. |
Common RC Filter Use Cases
Sensor Smoothing
Use a low-pass RC filter to reduce high-frequency sensor noise, but keep \(f_c\) high enough that the sensor still responds quickly.
PWM Smoothing
Use a low-pass filter with \(f_c\) well below the PWM frequency. A single RC stage may still leave ripple.
AC Coupling
Use a high-pass RC filter to block DC offset while passing changing signal content.
Audio Filtering
Use low-pass or high-pass RC filters to shape tone, reduce rumble, or remove unwanted high-frequency content.
ADC Input Filtering
Use RC filtering to reduce high-frequency content before sampling, but do not assume one RC stage is enough for strict anti-aliasing.
DC Blocking
A high-pass RC filter can remove DC bias while allowing AC variations to pass into the next circuit stage.
Reference point
At \(f=f_c\), both ideal first-order low-pass and high-pass RC filters have a gain magnitude of \(1/\sqrt{2}\), or about \(0.707\). This is the standard -3 dB cutoff reference. At the same point, low-pass phase is about \(-45^\circ\) and high-pass phase is about \(+45^\circ\).
Design Ranges and Practical Engineering Judgment
A mathematically correct RC result is only the starting point. Good RC filter design also considers standard component values, tolerance, loading, noise, current draw, and response time.
Too Much Resistance
Very high resistance can make the circuit more sensitive to leakage, noise pickup, and input bias currents.
Practical Starting Range
For many small-signal filters, \(1\,k\Omega\) to \(100\,k\Omega\) is a practical starting range, but the best value depends on the source and load.
Too Much Capacitance
Large capacitors can slow startup, increase settling time, and introduce leakage, ESR, size, and cost concerns.
Practical R and C Selection Workflow
Choose the target cutoff
Pick \(f_c\) based on the signal band you want to keep and the noise or unwanted frequency band you want to reduce.
Pick a practical resistor range
For many small-signal filters, start around \(1\,k\Omega\) to \(100\,k\Omega\), then adjust for source loading, noise, input bias current, and current draw.
Solve for capacitance
Use \(C=1/(2\pi f_cR)\), then choose a real standard capacitor value close to the calculated result.
Recalculate actual cutoff
Use the real resistor and capacitor values you can buy, then recalculate \(f_c\) instead of assuming the ideal value is available.
Standard Component Values
The exact calculated resistor or capacitor value may not exist as a standard part. Choose a nearby real component value, then recalculate the actual cutoff frequency using the values you can buy.
| Component | Common Standard Series | Practical Note |
|---|---|---|
| Resistors | E12, E24, E96 | 1% resistors are common and inexpensive, making resistor selection easier than capacitor selection. |
| Ceramic capacitors | E6, E12 | Small and inexpensive, but capacitance can vary with voltage, temperature, and dielectric type. |
| Film capacitors | E6, E12 | Often more stable for audio, timing, and precision analog filters. |
| Electrolytic capacitors | Broad preferred values | Useful for larger capacitance, but tolerance and leakage are usually worse than film or precision ceramic parts. |
Tolerance Range Example
Component tolerance can move the real cutoff frequency far from the nominal value. For example, a \(10\,k\Omega\) resistor with ±5% tolerance and a \(10\,nF\) capacitor with ±10% tolerance has a nominal cutoff of about \(1.59\,kHz\).
Using worst-case component values, the cutoff could shift roughly from:
Component tolerance matters
In this example, a nominal \(1.59\,kHz\) cutoff may behave closer to about \(1.38\,kHz\) to \(1.86\,kHz\) before considering temperature, dielectric effects, aging, or circuit loading.
Source and Load Resistance Effects
The ideal formula assumes the resistor and capacitor are the only important impedances. In a real circuit, the signal source has output resistance and the next stage has input resistance. These external impedances can change both the actual gain and the apparent cutoff frequency.
Practical loading check
For a high-pass RC filter, the effective resistance may be the filter resistor in parallel with the next stage input resistance. For a low-pass RC filter, a low load resistance can reduce output amplitude and change the response from the ideal result. If the next stage input resistance is not much larger than the filter resistor, the simple \(f_c=1/(2\pi RC)\) result may be misleading.
Unit Conversion Notes
The base RC filter formula uses ohms, farads, and hertz. The calculator can accept common engineering units, but manual calculations require consistent conversions.
| Quantity | Common Units | Conversion Reminder |
|---|---|---|
| Resistance | Ω, kΩ, MΩ | \(1\,k\Omega=1000\,\Omega\), \(1\,M\Omega=1{,}000{,}000\,\Omega\) |
| Capacitance | pF, nF, µF, mF, F | \(1\,pF=10^{-12}\,F\), \(1\,nF=10^{-9}\,F\), \(1\,\mu F=10^{-6}\,F\) |
| Frequency | Hz, kHz, MHz | \(1\,kHz=1000\,Hz\), \(1\,MHz=1{,}000{,}000\,Hz\) |
| Gain | V/V, dB | \(Gain_{dB}=20\log_{10}(|H|)\) |
| Time constant | s, ms, µs | \(\tau=RC\), measured in seconds when \(R\) is in Ω and \(C\) is in F. |
Most common unit trap
Capacitor markings and prefixes are easy to confuse. \(0.01\,\mu F\), \(10\,nF\), and \(10{,}000\,pF\) are the same capacitance, but \(10\,\mu F\) is 1,000 times larger than \(10\,nF\).
Low-Pass vs High-Pass vs RC Time Constant
The cutoff formula is the same for low-pass and high-pass RC filters, but the physical interpretation changes. The RC time constant describes time-domain response, while cutoff frequency describes frequency-domain response.
| Concept | Best Used For | Key Formula | Common Mistake |
|---|---|---|---|
| Low-pass RC filter | Smoothing, noise reduction, PWM averaging | \(f_c=1/(2\pi RC)\) | Expecting a sharp cutoff from one RC stage. |
| High-pass RC filter | AC coupling, DC blocking, low-frequency attenuation | \(f_c=1/(2\pi RC)\) | Ignoring the load resistance in the next stage. |
| RC time constant | Transient response and settling behavior | \(\tau=RC\) | Confusing time constant with cutoff frequency. |
| Band-pass from RC stages | Passing a limited middle frequency range | Uses a high-pass stage and low-pass stage | Assuming cascaded passive stages do not interact. |
| Higher-order filter | Sharper rolloff and stronger attenuation | Depends on topology | Assuming one RC stage can meet steep attenuation requirements. |
When a simple RC filter is not enough
Consider an active, buffered, or higher-order filter when you need steep rolloff, precise cutoff frequency, low loading error, gain, stable response across tolerance and temperature, or strong anti-aliasing performance.
Common Mistakes When Using an RC Filter Calculator
Most wrong RC filter results come from unit mistakes, wrong circuit assumptions, or expecting ideal behavior from a real component network.
Common Mistakes
- Entering \(10\,\mu F\) when the actual capacitor is \(10\,nF\).
- Treating cutoff frequency as a hard pass/fail boundary.
- Ignoring source resistance and load resistance.
- Choosing exact calculated values that do not exist as standard components.
- Expecting one RC stage to provide steep stopband attenuation.
- Forgetting that phase shift matters near cutoff.
Better Practice
- Convert units carefully before checking manual calculations.
- Recalculate actual \(f_c\) using real standard part values.
- Check gain and phase at the signal frequency, not just cutoff.
- Estimate tolerance range for critical filters.
- Use a buffered or active design when loading changes the response.
- Use more than one filter stage when stronger attenuation is required.
Troubleshooting Unexpected Results
If the result looks wrong, check units first. RC filter formulas are straightforward, but a single prefix error can shift the answer by several orders of magnitude.
| Problem | Likely Cause | Fix |
|---|---|---|
| Cutoff is 1,000 times too high or low | Capacitance unit error, usually nF vs µF or pF vs nF. | Recheck capacitor markings and unit selector. |
| Output voltage seems too low | Selected frequency is near or beyond the attenuated region. | Compare \(f\) to \(f_c\) and review the gain in dB. |
| Real circuit cutoff does not match | Load resistance, source resistance, tolerance, ESR, or layout effects. | Model the source/load network or measure actual response. |
| Signal is delayed too much | RC time constant is too large. | Increase cutoff frequency by reducing \(R\), reducing \(C\), or both. |
| Filtering is too weak | One first-order stage does not roll off sharply enough. | Consider cascading stages, buffering, or using an active/higher-order filter. |
| Phase shift is causing timing error | The operating frequency is too close to cutoff. | Move \(f_c\) farther away from the signal band or use a more appropriate filter topology. |
Assumptions, Sources, and Limitations
This calculator is intended for educational use, preliminary design checks, and quick engineering estimates for ideal first-order RC filters.
Ideal Components
The calculation assumes ideal resistors and capacitors with no tolerance, leakage, ESR, ESL, temperature drift, or aging effects.
No Loading Effects
The ideal result assumes the next circuit stage does not significantly load the filter output.
Small-Signal Behavior
The formulas assume linear small-signal frequency response and do not model saturation, dielectric absorption, or nonlinear behavior.
Final Design Caution
For production electronics, safety-critical circuits, high-frequency filters, or precision analog work, verify with simulation, datasheets, measurement, and engineering review.
Calculation basis
This page uses standard first-order passive RC filter relationships: \(f_c=1/(2\pi RC)\), \(\tau=RC\), gain magnitude formulas for low-pass and high-pass transfer functions, phase formulas for first-order response, and decibel conversion from \(20\log_{10}(|H|)\).
For additional background on RC low-pass cutoff frequency, transfer function, and gain/phase response, see this EEPower overview of RC low-pass cutoff frequency and transfer function.
Glossary of RC Filter Terms
These definitions help connect the calculator output to the circuit behavior.
RC Filter
A filter circuit that uses a resistor and capacitor to attenuate selected frequencies.
Cutoff Frequency
The frequency where output amplitude is about 70.7% of input amplitude, or approximately -3 dB.
Low-Pass Filter
A filter that passes lower frequencies more easily and attenuates higher frequencies.
High-Pass Filter
A filter that attenuates lower frequencies and passes higher frequencies more easily.
Time Constant
The product \(RC\), measured in seconds, describing how quickly the capacitor charges or discharges.
Gain
The ratio of output amplitude to input amplitude at a selected frequency.
Phase Shift
The timing shift between input and output waveforms, usually reported in degrees.
Roll-Off
The rate at which a filter attenuates frequencies outside the passband. A first-order RC filter approaches 20 dB per decade.
Frequently Asked Questions
What does an RC Filter Calculator calculate?
An RC Filter Calculator calculates cutoff frequency, resistance, capacitance, gain, phase shift, and output voltage amplitude for a first-order low-pass or high-pass resistor-capacitor filter.
What is the RC filter cutoff frequency formula?
The cutoff frequency formula is \(f_c=1/(2\pi RC)\), where \(R\) is resistance in ohms and \(C\) is capacitance in farads.
Is the cutoff frequency the same for low-pass and high-pass RC filters?
Yes. For an ideal first-order RC low-pass or high-pass filter using the same \(R\) and \(C\) values, the cutoff frequency is \(f_c=1/(2\pi RC)\). The difference is whether the filter attenuates frequencies above or below that cutoff.
What does -3 dB mean in an RC filter?
The -3 dB point is the cutoff frequency where the output voltage amplitude is about 70.7 percent of the input amplitude. It is not a hard stop; a first-order RC filter rolls off gradually.
How do I choose R and C values for an RC filter?
Start with a target cutoff frequency, choose a practical resistor range, solve for capacitance, select a nearby standard component value, recalculate the actual cutoff frequency, and check tolerance, loading, and response time.
Why does my real RC filter not match the calculator exactly?
Real filters can differ because resistor tolerance, capacitor tolerance, source resistance, load resistance, capacitor ESR, leakage, temperature, and circuit layout are not included in the ideal RC formula.