RC Filter Calculator
Design a first-order RC low-pass or high-pass filter. Solve for cutoff frequency, capacitance, or resistance, and read attenuation and phase at any probe frequency.
Pick low-pass or high-pass, choose what to solve for, enter the two known values with units, and optionally probe the response at any frequency.
- f_c = 1 / (2π · R · C)
- τ = R · C
- |H(f)| = 1 / √(1 + (f/f_c)²)
- φ = −arctan(f / f_c)
- −3 dB at f_c · −20 dB/decade roll-off
How It Works
- 1
Pick a topology
Low-pass passes DC and attenuates above f_c — use it for smoothing, anti-aliasing, and audio tone shaping. High-pass blocks DC and attenuates below f_c — use it for AC coupling, DC-offset removal, and rumble filters.
- 2
Choose what to solve for
Enter two of R, C, or f_c and the calculator fills in the third. Mix units freely: Ω / kΩ / MΩ for resistance, pF / nF / µF for capacitance, Hz / kHz / MHz for frequency.
- 3
Optional: check a probe frequency
Tick the probe box and enter any frequency f to read the attenuation in dB and the phase shift in degrees at that exact point. The corner itself is always −3 dB and 45°, but off-corner numbers are what matter for sizing real filters.
First-order RC filters — the corner, the roll-off, the phase
An RC filter is the shortest path between a resistor, a capacitor, and a frequency-dependent response. Swap their positions on the signal path and the same two parts give you either a low-pass or a high-pass filter. The cutoff f_c = 1 / (2π · R · C) is exact, not approximate: at that frequency |H|² = 1/2, so half the input power reaches the output. That is the mathematical reason every textbook marks −3.0103 dB on the Bode plot. The passive filter theory behind this response was formalized at AT&T Bell Labs between 1915 and the mid-1920s, primarily by George A. Campbell and Otto J. Zobel, whose image-parameter and constant-k methods underpin classical filter design. A first-order RC gives you a gentle −20 dB per decade slope and a phase that sweeps 90° across the corner. That is enough for microphone DC-blocking, op-amp compensation, RC debouncing, and a quick anti-aliasing pre-filter, but it's usually not enough for audio crossovers or ADC anti-aliasing where aliased content must be suppressed hard. The honest upgrades are cascade stages with a buffer between them, a Sallen-Key active second-order stage, or a dedicated filter IC. For quick bench work, reach for 1% metal-film resistors and C0G or film capacitors — X7R and X5R ceramics drift enough with temperature and DC bias to move the corner by double-digit percentages, which spoils the match in precision audio and instrumentation. Time and frequency are the same thing looked at from different ends: the time constant τ = RC is 1 / (2π · f_c), so if you know either number, you know the other.
Common pitfalls
Ignoring source impedance. The effective R in f_c = 1 / (2π R C) is the sum of your filter resistor and the source's output impedance. A 10 kΩ filter fed by a 1 kΩ op-amp output actually has R_eff = 11 kΩ, pulling the corner down 9%. A signal source with 600 Ω (audio line) feeding a 1 kΩ filter shifts the corner 60%.
Ignoring load impedance. A low-pass output seen by a 10 kΩ DMM is fine; seen by a 1 kΩ next-stage input, R_filter and R_load are in parallel. Use a buffer (op-amp follower) between stages whenever the load is within 10x of the filter resistance.
Using X7R or X5R ceramics for precision filters. These Class II dielectrics lose 30-60% of their capacitance under DC bias and drift ±15% over temperature (JEDEC STD-198). A 100 nF X7R at 5 V DC can measure 50 nF. Use C0G/NP0 ceramics or film capacitors for filters that must hold the corner.
Expecting sharp cutoff from first-order. −20 dB/decade rolloff means an octave above cutoff is only 7 dB down. For anti-aliasing before a 16-bit ADC, you need 96 dB attenuation at the Nyquist frequency; a single RC cannot do that. Use a Sallen-Key second-order or dedicated filter IC (e.g. LTC1560).
Swapping low-pass and high-pass topology. Series-R with shunt-C to output = low-pass. Series-C with shunt-R to output = high-pass. Looks similar on the schematic, does the opposite thing. Verify by asking: at DC (f = 0), does the capacitor short or open the signal?
Frequently Asked Questions
What is the cutoff frequency of an RC filter?
The cutoff frequency f_c = 1 / (2π · R · C) is the point where the output power drops to half the input power, which works out to an amplitude of 1/√2 ≈ 0.707 of the input. In decibels that's exactly −3.0103 dB, which is why engineers call f_c the −3 dB point or the half-power point. Below f_c a low-pass filter passes signals through with little loss; above f_c the output falls off at −20 dB per decade, meaning a tenfold increase in frequency gives a tenfold drop in amplitude.
What's the difference between a low-pass and high-pass RC filter?
Both use one resistor and one capacitor, but the component order swaps. In a low-pass filter the resistor is in series and the capacitor goes to ground; the output is taken across the capacitor, which shorts high frequencies to ground. In a high-pass filter the capacitor is in series and the resistor goes to ground; the output is taken across the resistor, and the series capacitor blocks DC and low frequencies. Both topologies share the same cutoff formula — f_c = 1 / (2π · R · C) — and the same −20 dB/decade roll-off, just on opposite sides of the corner.
Why is the attenuation at f_c always −3 dB?
At f = f_c the magnitude of the transfer function is exactly 1/√2. Squaring that gives 1/2, so half the input power reaches the output — hence 'half-power point'. Converting 1/√2 to decibels with 20·log₁₀(1/√2) gives −3.0103 dB. This is a mathematical consequence of first-order RC behaviour, not an engineering rule of thumb, which is why it appears on every filter datasheet and textbook plot.
How do I pick R and C values for a target f_c?
Fix one value based on practical constraints, then solve for the other. For audio filters around 1–20 kHz, start with a capacitor between 10 nF and 1 µF because capacitor tolerances and values step in a coarser E-series than resistors. For RF work, pick a resistor that matches the driving impedance. A common audio tone control at f_c = 1 kHz uses R = 1.6 kΩ and C = 100 nF. The time constant τ = RC directly tells you the charge/discharge speed: one τ reaches 63%, five τ settles within 1%.
Do first-order RC filters roll off sharply enough?
Often not. A single RC pole gives only −20 dB per decade, so frequencies just above the corner leak through with noticeable amplitude. For anti-aliasing in front of an ADC, audio crossovers, or RF filtering you usually need a sharper skirt. The fix is higher-order filters: cascade several RC stages with buffers between them, or use active topologies like Sallen-Key which give −40 dB/decade per stage with no buffer needed. For the sharpest responses — Butterworth, Chebyshev, elliptic — you step up to LC or active-RC designs.
What is the phase shift of an RC filter?
A first-order low-pass filter shifts phase from 0° at DC, through −45° at f_c, and asymptotically toward −90° at very high frequencies. High-pass is the mirror: +90° at DC, +45° at f_c, approaching 0° at high frequencies. The phase changes gradually — at one decade below f_c the shift is already about 6°, and at one decade above it reaches about 84°. This phase behaviour matters in audio crossovers, control loops, and anywhere signal timing matters.
Who invented the RC filter?
The RC low-pass and high-pass topologies emerged as passive filter theory was formalized in the early 20th century. Mathematician and engineer George A. Campbell and physicist Otto J. Zobel did much of the foundational work at AT&T Bell Labs between 1915 and the mid-1920s, developing the image-parameter and constant-k designs that underlie classical filter theory. The idealised first-order RC response — the half-power corner, the −20 dB/decade slope, the 45° phase shift at f_c — falls directly out of that analysis.
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