RC Time Constant & Filter Calculator

One number, three uses

A resistor and a capacitor make one time constant, τ = R·C, and everything else follows from it. As a filter, the −3 dB point is fc = 1 / (2π τ). As a delay, the output reaches 63 % of a step after one τ and 99.3 % after five. As an edge, the 10 % to 90 % rise time is τ·ln 9, close enough to 0.35 / fc that the rule of thumb is what most people remember. The tool reports all three for any pair, because the same two parts turn up as a debounce, an anti-alias filter and a PWM smoother, and each is judged by a different one.

Low-pass and high-pass are the same two parts

Which one you get is decided by the wiring, not by the values. Put the resistor in the signal path with the capacitor from the output to ground and you have a low-pass filter: the capacitor is a short at high frequencies and shunts them away, so what gets through is the slow part. Swap them — capacitor in the path, resistor from the output to ground — and the same pair is a high-pass filter: the capacitor blocks DC and passes what changes. The tool has both; pick the wiring at the top and the response plot follows it.

The cutoff is the same number either way. fc = 1 / (2πRC), the point where the output is down 3 dB and 45° out of phase, and R and C swapping places does not move it. 10k and 100 n is 159 Hz as a low-pass and 159 Hz as a high-pass; the only thing that changes is which side of 159 Hz survives.

That is why the jobs they do look nothing alike. A low-pass is a PWM smoother, an anti-alias filter in front of an ADC, a debounce on a switch, the thing that stops a long cable picking up radio. A high-pass is AC coupling — the capacitor between two amplifier stages that keeps one stage’s DC bias out of the next, the input of an audio stage that has to ignore a few hundred millivolts of offset, an edge detector that only cares that something moved. Same formula, same parts bin, opposite purpose.

One asymmetry worth knowing: a low-pass has a step response you can watch settle, which is why the tool reports rise time and settling for it, and a high-pass instead has droop — hold a step at its input and the output decays back to zero with the same τ. AC-coupling a slow square wave is how a clean signal arrives at the next stage with its flat tops sagging.

Which part to pick first

Capacitors come in coarse steps. Ceramics and films are E6 or E12 — 10 n, 22 n, 47 n, 100 n — and electrolytics coarser still. Resistors come in E24 at ±5 % or E96 at ±1 %. So the sensible order is to choose the capacitor and let the resistor take up the slack, which is how the solver works: it walks every capacitor in the range you pick, finds the ideal resistor for each, snaps it to the nearest standard value, and ranks the pairs by how close the cutoff lands. For 1 kHz from E24 and E12 the best pair is 1.6k and 100 n, at 995 Hz.

The capacitor range also sets the impedance level. A 1 nF filter needs a 160k resistor for the same cutoff as 100 nF needs 1.6k; the first is quiet and easy on the source but sensitive to leakage and to whatever it drives, the second is robust but loads the source. Ten to a hundred kilohms with a few nanofarads to a few hundred is the comfortable middle for signal work.

The capacitor's tolerance is the whole error budget

The worst-case band is where the design meets reality. A ±1 % resistor next to a ±10 % capacitor gives a cutoff that can sit anywhere in a ±11 % band, and the resistor contributed one point of that. Buying a ±0.1 % resistor for the same filter changes nothing. If the cutoff has to be accurate, the money goes on the capacitor: C0G/NP0 ceramic or polypropylene film at ±5 % or better.

Worse than the tolerance is what class 2 ceramics do under voltage. X7R and X5R lose capacitance as the DC across them rises — a 100 nF 0603 X7R at half its rated voltage may be 50 or 60 nF, and Y5V is worse still. The band the tool shows is the tolerance alone; the bias effect comes on top and is not in any calculation that starts from the marked value. For a corner that matters, this is the first thing to fix.

−3 dB is not "off"

A first-order filter is gentle. At the cutoff the signal is down 3 dB, about 70 %. A decade past it, 20 dB, a tenth. Two decades, a hundredth. Anything closer than a decade to the cutoff is only partly attenuated, and the phase shift starts a decade before it. The response table makes this concrete: pick a cutoff and see what the filter does at the frequency you actually want gone. If the answer is not enough, the fix is a higher order filter — two RC stages with a buffer between them, or an active filter — not a smaller capacitor.

Settling for an ADC

The RC on an ADC input has a second job: the sample-and-hold capacitor inside the converter charges through it, and the reading is only right once the input has settled. One τ is 63 %, which is nowhere near. To be within one LSB of a 12-bit result the input must reach 99.976 % of its final value, and that takes τ·ln(2¹²) = 8.3 τ. A 10k/100n filter with τ = 1 ms therefore needs over 8 ms between selecting a multiplexed channel and reading it, or the reading carries a tail of the previous channel. The tool reports the 12-bit settling time for any pair; for 16 bits multiply τ by 11.1.

The same arithmetic covers a switch debounce. With τ = 10 ms a contact that has settled is read as clean after a few τ, and the threshold crossing time for a given logic level is timeToFraction of the step — half the supply is reached at 0.69 τ.

Source and load change the numbers

The formula's R is the total resistance the capacitor charges through. A signal source with its own impedance adds to it, so a filter fed from a potentiometer or a high-value divider has a lower cutoff than the resistor alone suggests. A load in parallel with the capacitor is a divider with R, which both shifts the corner and drops the DC level — the same loading rule the voltage divider calculator reports as output impedance. When the numbers need to hold, buffer the filter with an op-amp.

One common use is smoothing a PWM output into a DC level. The rule is to put the cutoff well below the PWM frequency and well above the rate at which the level has to change; the timer prescaler calculator gives the PWM frequency for a given timer setup, and the response table here shows how much ripple survives at that frequency.