🎛️ Filter Diagnostics

RC Filter Capacitor Calculator — High-Pass, Low-Pass, Band-Pass Cutoff Frequency & Gain

Solve C = 1/(2πfR) for all four RC filter topologies, read the attenuation at any frequency, and watch the Bode curve move as you type.

RC Filter Capacitor Calculator

C = 1/(2πfR) — live capacitor values, gain readout and Bode plot for all four filter types.

Filter type

Cutoff frequency fc (Hz)

Resistor R

Check gain at frequency f (Hz)

Quick presets

Filter capacitor C

15.9nF

Formula: C = 1/(2π·fc·R) = 0 F

Roll-off: −6 dB/octave (−20 dB/decade), single pole

Gain at your check frequency

10000 Hz

Gain

-20 dB

Voltage

10%

🎛️ Read it right. The dB figure is amplitude relative to the pass band, and the % figure is output voltage — at −3 dB exactly 70.7% of the input voltage remains, which is why the corner is also called the half-power point. A gain check inside the pass band returning 0 dB confirms the wiring, not a fault.

Live RC Bode plot — magnitude from 0.01× to 100× the cutoff frequency

Defaults verify: 1 / (2π × 1 000 Hz × 10 000 Ω) = 15.9 nF, and the low-pass gain at 10 kHz reads ≈ −20.0 dB (10% voltage). Switch modes to cross-check the band-pass and twin-T outputs against the worked examples below.

Failure deconstruction

Four Real-World Filter Failures, Deconstructed

Filter faults rarely announce themselves as filter faults — they arrive as hum, jagged waveforms or dull audio. Each card below follows the same diagnostic chain: the observed symptom, the root cause expressed in the transfer function, and the fix stated as new R and C values. Every number on these cards comes from the same two equations the calculator runs — fc = 1/(2πRC) and −10·log10(1+(f/fc)²) — so you can verify any of them by typing the values in above. Type a keyword to highlight the scenario that matches your bench symptom, or reset the view to compare all four side by side.

4 of 4 scenarios match

Common IssueCritical Failure

“50 Hz hum leaks through my low-pass”

Symptom: Mains hum is clearly audible (and visible on a scope) even though the low-pass filter was built exactly to spec with fc = 1.6 kHz for the wanted audio band.
Root cause: The corner sits more than 1.5 decades above the interference. At 50 Hz, a 1591 Hz low-pass attenuates −10·log10(1+(50/1591)²) = −0.004 dB — the hum passes at 99.9% amplitude, effectively untouched.
Fix: Move fc to ~10 Hz (160 kΩ + 100 nF): 50 Hz then drops −14.2 dB. If you must keep the 1.6 kHz band intact, add a 50 Hz twin-T notch instead of lowering fc — never both corners at once.

Residual 50 Hz hum at the output99.9%

Common Issue

“My PWM looks jagged after smoothing”

Symptom: A PWM DAC running a 980 Hz carrier was smoothed with an RC low-pass at fc = 500 Hz, yet the output still shows visible steps and an audible whine.
Root cause: The corner is less than one octave below the carrier. At 980 Hz the filter manages only −10·log10(1+(980/500)²) = −6.8 dB — 45.4% of the carrier ripple survives to the output.
Fix: Push fc two decades under the carrier: R = 1 kΩ with C = 10 µF gives fc = 15.9 Hz, cutting the 980 Hz carrier by −35.8 dB so only 1.6% of the ripple remains.

Carrier ripple remaining at fc = 500 Hz45.4%

Common Issue

“Audio sounds muffled after my filter”

Symptom: Speech survives but music sounds dull after the low-pass: cymbals, consonants and the whole 8 kHz region have collapsed into the noise floor.
Root cause: With fc = 1 kHz, the 8 kHz overtone sits three octaves up the roll-off: −10·log10(1+8²) = −18.1 dB, so only 12.4% of that content reaches the output.
Fix: Raise fc to ≥ 15 kHz: the 8 kHz band then sits below the corner and loses just −1.1 dB (77.8% passes), restoring the treble without touching the design impedance.

8 kHz overtone remaining at fc = 1 kHz12.4%

Common Issue

“My notch won't kill 60 Hz”

Symptom: A single series-R plus shunt-C network was tuned to 60 Hz to 'notch out' hum on a sensor line, but the interference barely moved.
Root cause: One RC pole cannot produce a null. Best case, a low-pass tuned to 60 Hz gives −3.0 dB at 60 Hz (70.7% remains) while destroying everything above it — a 1 kHz signal loses −24.4 dB.
Fix: Build a twin-T: R = 26.5 kΩ (×2), R/3 = 8.83 kΩ, C = 100 nF (×2), 2C = 200 nF → f0 = 60 Hz with a genuine null, while 1 kHz content passes at ≈ 0 dB.

60 Hz residual with a single pole tuned to 60 Hz70.7%

Reference

Common RC Filter Corner Frequency vs R × C Pairs

The same four numbers keep reappearing in filter work because the R×C product — not the individual values — sets the corner. Every row below solves fc = 1/(2πRC) exactly; type any pair into the calculator above to confirm it. Note how the same 1 591 Hz corner appears from a 1 kΩ × 100 nF pair and a 10 kΩ × 10 nF pair: choose the row whose impedance your source can drive without sagging.

R Value	C Value	fc (Hz)	Filter Type Suggestion	Typical Application
1 kΩ	100 nF	1591 Hz	LPF	Audio output filter
10 kΩ	10 nF	1591 Hz	LPF	PWM output smoothing
100 kΩ	1 µF	1.59 Hz	HPF	AC coupling
1 kΩ	10 µF	15.9 Hz	HPF	Subsonic filter

The corner and the time constant are the same R×C product seen from two sides: fc = 1/(2πτ). Build any pair above and watch it charge and settle in the RC time constant calculator, then compare how each row's corner shifts when the source impedance stops being negligible — that failure mode is dissected in the loading-effect section below.

Topology

High-Pass vs Low-Pass: One Formula, Two Topologies

Every RC filter is a frequency-dependent voltage divider. The capacitor's reactance falls as frequency rises — Xc = 1/(2πfC) — so wherever the capacitor sits in the divider decides what passes and what gets shunted away. That single fact generates both filter families from the same parts bin.

Inside the low pass filter capacitor calculator: series R, shunt C

The resistor is in series with the signal; the capacitor shunts the output node to ground, and the output is taken across the capacitor. At low frequencies Xc is huge, so nearly all the input appears across the capacitor and DC passes freely. At high frequencies Xc collapses toward a short, and the highs are dumped to ground. This is the PWM smoothing, DAC-reconstruction and rail-decoupling workhorse.

Inside the high pass filter capacitor calculator: series C, shunt R

Swap the positions: the capacitor now sits in the series path and the resistor shunts the output to ground, with the output taken across the resistor. DC is blocked outright — a capacitor is an open circuit at 0 Hz — while high frequencies cross the small Xc almost unattenuated. This is the AC-coupling stage between amplifier blocks, the subsonic filter that protects woofers, and the edge-differentiator in timing circuits. If you are sizing an inter-stage coupling cap specifically, the coupling and decoupling capacitor calculator extends this math with load-line considerations.

The capacitor filter frequency calculator formula is position-blind

Both calculators above solve the identical equation for the identical corner. Only the placement of R and C in the divider changes — and with it, which side of fc survives.

💡 Key relation. The -3 dB cutoff frequency formula fc = 1/(2πRC) is the same for both high-pass and low-pass — only the resistor/capacitor positions in the circuit differ.

Engineering sketches of resistor and capacitor RC filter networks on a designer's workbench

Same parts, swapped positions, opposite filtersPhoto: Unsplash

Property	Low-Pass	High-Pass
Series element	Resistor R	Capacitor C
Shunt element	Capacitor C	Resistor R
Output taken across	Capacitor C	Resistor R
DC (0 Hz) behavior	Passes	Blocked
Below fc	Passes	Attenuates
Above fc	Attenuates	Passes

Attenuation math

The Gain Table: What Each Decade of Separation Costs You

Design failures are usually spacing failures: the wanted signal and the interference sit too close together on the frequency axis for a single pole to separate them. This table converts that spacing into a hard attenuation number. Read each row as listed for a low-pass; for a high-pass, read it bottom-up — the responses are perfect mirror images.

A filter capacitor calculator online, frozen into a table

The physics anchor is reactance: at fc, Xc = 1/(2πfcC) equals R exactly, which is why the divider splits 70.7/29.3 there. You can watch Xc sweep across the band in the capacitor reactance calculator — the −3 dB point is simply where its curve crosses your resistor value.

f / fc	Gain	Voltage Remaining	Where You Are
0.1×	−0.04 dB	99.5%	Deep in the pass band (low-pass); deep in the stop band (high-pass)
0.5×	−1.0 dB	89.1%	Approaching the corner — the roll-off has already begun
1×	−3.0 dB	70.7%	The corner itself: capacitive reactance exactly equals R
2×	−7.0 dB	44.7%	One octave past the corner
10×	−20.0 dB	10.0%	One full decade out — the 20 dB/decade slope is established

Reading the RC Bode plot by hand

On a log-frequency axis the single-pole response is two straight lines: flat through the pass band, then falling at exactly −20 dB per decade above the corner, with the two lines meeting at the −3 dB point. The Bode plot in the calculator draws the true curve — not the asymptotes — from 0.01× to 100× your reference frequency, with the dashed amber line marking −3 dB. In band-pass mode the curve becomes the product of the high-pass and low-pass stage responses; in notch mode it shows the twin-T dip plunging below −40 dB at f0.

💡 Tip. Memorize the spacing rule hidden in the table: every decade of separation between your signal and the interference is worth 20 dB of free attenuation, and every octave is worth 6 dB. If your unwanted tone sits only half a decade away, a single RC cannot save you — you need more poles or a notch, no matter how carefully you pick the capacitor.

Cascading

How to Calculate Capacitor Size for Bandpass Filter Designs

A passive RC band-pass is nothing more than a high-pass stage feeding a low-pass stage. The high-pass sets the lower corner fL by blocking everything below the band; the low-pass sets the upper corner fH by shunting everything above it. Size each capacitor exactly as you would for a standalone filter, using the stage's own corner frequency.

How to calculate capacitor size for bandpass filter stages, step by step

Worked example — a 300 Hz to 3.4 kHz voice band at R = 10 kΩ in both stages. First, the high-pass stage: C_HP = 1/(2π × 300 × 10 000) = 53.1 nF, so the standard value 47 nF sits at fL = 339 Hz. Second, the low-pass stage: C_LP = 1/(2π × 3400 × 10 000) = 4.68 nF, so 4.7 nF lands at fH = 3.39 kHz. The derived figures follow directly: BW = fH − fL = 3.06 kHz, center f0 = √(fL·fH) = 1 010 Hz, and Q = f0/BW ≈ 0.33 — a wide, gentle band, which is exactly what a speech filter should be.

Pairing a low pass filter resistor capacitor calculator with its high-pass mirror

Two cautions decide whether the built circuit matches those numbers. First, isolation: without a buffer between the stages, the low-pass input impedance loads the high-pass output and drags both corners inward — an op-amp voltage follower costs one cent of board space and removes the interaction entirely. Second, geometry: when fH is at least 10× fL the stages barely overlap and the response is a wide trapezoid; as the corners converge, Q rises past 0.5, a resonant hump appears at f0, and you have left the plain RC world and entered the land of bridged-T and active band-pass design.

🎛️ Roll-off reality. Single-pole RC filters have a gentle 6 dB/octave (20 dB/decade) roll-off. For sharper filtering (24 dB/octave), cascade multiple stages or use an active filter.

The null

Twin-T Notch Filter: a True Null From Three Resistors and Three Capacitors

Scenario card four established the bad news: no two-particle RC network produces a notch. The good news is that six of them do. The twin-T runs two T-shaped paths in parallel between source and load — a low-pass arm of two series resistors R with a shunt capacitor C at their junction, and a high-pass arm of two series capacitors C with a shunt resistor R at theirs. A third resistor R/3 and a third capacitor 2C complete both junctions to ground.

Away from f0, one arm leads and the other lags, and their combination passes the signal. At exactly f0 = 1/(2πRC), the two paths arrive with equal amplitude and opposite phase and cancel to a genuine null. For 50 Hz mains rejection with R = 26.5 kΩ, the base capacitor is C = 1/(2π × 50 × 26 500) = 120 nF, giving legs of R, R = 26.5 kΩ; R/3 = 8.83 kΩ; C, C = 120 nF; 2C = 240 nF — all standard or trimmable values, and the notch mode in the calculator above outputs these legs directly.

Depth and sharpness are set by execution, not topology. With 1% parts expect roughly −40 dB of rejection; with 5% parts the arms mismatch and the null shallows toward −26 dB. The unloaded twin-T has a low Q of about 0.25, meaning the dip spans a wide band — bootstrapping the R/3–2C ground node with a voltage follower raises the effective Q dramatically and narrows the notch around 50 or 60 Hz where it belongs.

⚠️ Warning. Do not round the leg values to the nearest E12 step and expect a deep null — a 5% error in the R/3 arm alone can eat 15–20 dB of rejection. Buy the R and C pairs from the same batch (their ratios then track) and make R/3 a trimmable pot if the notch must disappear into the noise floor.

❌ Don't. Don't try to deepen a notch by stacking ordinary RC low-pass stages at the same corner — you will trade 60 Hz rejection for the entire signal band. A pole can only slope; only the twin-T (or an active notch) creates a true zero. For a line-frequency kill on a measurement front-end, the twin-T is the correct and cheapest instrument.

Twin-T notch filter prototyped on a solderless breadboard with a digital multimeter

The twin-T's signature: a null, not a slopePhoto: Unsplash

The silent killer

The Loading Effect: What Every RC Capacitor Filter Calculator Omits

The formula fc = 1/(2πRC) is exact — the problem is that the R in a built circuit is almost never the resistor you soldered. The capacitor responds to the Thevenin resistance it sees: the source's output impedance adds in series with your design resistor, and the load impedance sits in parallel with the shunt element. Both shift the corner, always in the direction that makes the filter worse for your plan.

Quantified both ways. Add a 1 kΩ source impedance in front of a 10 kΩ + 10 nF low-pass and the total series resistance becomes 11 kΩ, dropping fc from 1 591 Hz to 1 447 Hz — a 9% error before the filter is even connected to its load. Now hang a 10 kΩ load across the capacitor: the effective shunt resistance falls to the parallel combination 5 kΩ and fc doubles to 3.18 kHz, which for a PWM smoothing filter means the carrier escapes. The defense is impedance hygiene: keep the source impedance under 1% of the design R, and keep the load at least 20× the design R (which holds the corner shift under 5%). Between those limits, buffer.

⚠️ Warning. Cascading two RC stages directly — high-pass into low-pass with no buffer — is a loading problem in disguise. The second stage's input impedance becomes the first stage's load, dragging both corners toward each other by 20–40% in typical voice-band designs. One op-amp follower between stages restores the calculated corners exactly; without it, re-derive every value with the loaded impedances.

❌ Don't. Don't verify a filter's corner with a high-impedance signal generator set to 50 Ω output and then wire it to a 1 kΩ load on the bench — the measurement conditions and the real circuit disagree by more than the tolerance of your parts. Measure with the actual source and load attached, or the number you confirm is not the number you ship.

fc = 1 / (2π · R_th · C) — where R_th is what the capacitor actually sees

If the filter feeds a coupling stage downstream, the same Thevenin logic decides the coupling cap's value — the coupling & decoupling capacitor calculator handles that side of the chain, including the high-pass corner the coupling cap itself forms with the load.

Questions About RC Filter Capacitors

How do I calculate the capacitor for a low-pass filter?▼

For the standard series-R, shunt-C low-pass, the capacitor is C = 1/(2π·fc·R). Pick the corner you need and a practical resistor, then divide. Example: fc = 1 591 Hz with R = 10 kΩ gives C = 1/(2π × 1591 × 10 000) = 10.0 nF. Any R×C product equal to 1/(2π·fc) — here 10 µs — hits the same corner, so the split between R and C is yours to make based on the impedance level your source and load can tolerate.

How does a high-pass filter capacitor calculator differ?▼

The formula does not change at all: it is still C = 1/(2π·fc·R). What changes is the wiring — the capacitor moves into the series path and the resistor becomes the shunt element, with the output taken across the resistor. The gain math mirrors too: below the corner the attenuation is −10·log10(1+(fc/f)²) instead of −10·log10(1+(f/fc)²). A high-pass therefore blocks DC completely and passes everything above fc, while the low-pass does the opposite with the identical equation.

What capacitor size do I need for a bandpass filter?▼

Two capacitors — one per stage. Cascade a high-pass stage whose corner is the lower limit fL and a low-pass stage whose corner is the upper limit fH. With the same R in both stages: C_HP = 1/(2π·fL·R) and C_LP = 1/(2π·fH·R). For a 300 Hz to 3.4 kHz voice band at R = 10 kΩ, that is C_HP = 53 nF and C_LP = 4.7 nF, giving BW = 3.1 kHz, f0 = √(300 × 3400) ≈ 1 010 Hz and Q ≈ 0.33. Buffer the two stages with an op-amp follower so the corners stay independent.

What does −3 dB mean?▼

It marks the frequency where output power has fallen to half the pass-band value, which corresponds to the output voltage dropping to 1/√2 ≈ 70.7% of its low-frequency or high-frequency level. Physically, −3 dB is where the capacitor's reactance Xc exactly equals the resistor R in a first-order RC network. It is the conventional boundary of the pass band — not silence: two-thirds of the voltage is still getting through at the corner.

Why does my RC filter only cut 6 dB per octave?▼

A single resistor and capacitor create one pole, and one pole always rolls off at 20 dB per decade, which is 6.02 dB per octave. Doubling the frequency past the corner costs only about 6 dB forever. To double that slope you must add poles: cascade a second RC stage (with a buffer between them so they don't load each other) for 12 dB/octave, or use an active topology such as a Sallen-Key or multiple-feedback filter for 24 dB/octave or more.

Can I build a notch filter from resistors and capacitors?▼

Yes — the twin-T notch filter uses exactly six passive parts: two resistors R in the low-pass arm, a third resistor R/3 to ground, two capacitors C in the high-pass arm and a fourth capacitor 2C to ground. The notch frequency is f0 = 1/(2πRC), where the two signal paths cancel. Realistic null depth with 1% parts is roughly −40 dB; trimming the R/3 leg with a pot and bootstrapping the R/3–2C node raises both depth and selectivity.

Does the load resistance change my cutoff?▼

Yes, and it is the most common reason a built filter misses its calculated corner. The correct formula is fc = 1/(2π·R_th·C), where R_th is the Thevenin resistance the capacitor actually sees — source impedance in series, load impedance in parallel. Feed a 10 kΩ design from a 1 kΩ source and fc drops 10% to 1 447 Hz; hang a 10 kΩ load across the shunt element and the effective resistance halves, doubling fc from 1.59 kHz to 3.18 kHz. Keep the load at least 20× the design R to stay within 5%.

Ceramic or film for RC filters?▼

Use C0G/NP0 ceramics or film (polyester, polypropylene) for anything timing- or frequency-critical. High-K class 2 ceramics such as X7R lose 20–50% of their capacitance under DC bias, which silently drags fc upward, and Y5V/Z5U are unusable for filters. For a 50/60 Hz twin-T, matching between the two arms matters more than the absolute value — buy 2% or 1% film parts from the same batch, and trim the R/3 leg for depth.

This RC filter capacitor calculator is one tool in a family of capacitor design utilities. The capacitor calculator home page covers code decoding, energy storage and unit conversion, while the calculators hub lists every tool — from time constants and reactance to coupling and motor-run sizing — so you can chain an entire signal chain's worth of values in one session.

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