About this calculator
A resistor and a capacitor together define a time — how long the capacitor takes to charge through the resistor — and equivalently a frequency, above or below which signals are attenuated. The same two parts are a timing element in one view and a filter in the other.
This calculator gives you both readings from one R and C: the time constant τ with its charge and discharge milestones, and the −3 dB cutoff frequency with the gain and phase shift at whatever frequency you care about.
How it works
The time constant is simply τ = R × C. In one time constant a charging capacitor reaches 63.2% of its final voltage; in five it is at 99.3%, which is conventionally treated as fully settled.
Viewed as a filter, the same network attenuates by 3 dB at the frequency where the capacitor's reactance equals the resistance. That works out to fc = 1 / (2π × R × C), which is just 1 / (2πτ).
Whether it is a low-pass or a high-pass depends only on where you take the output. Across the capacitor, high frequencies are shunted away and you have a low-pass. Across the resistor, the capacitor blocks DC and you have a high-pass.
A single RC rolls off at 20 dB per decade — a tenfold frequency change gives a tenfold amplitude change. At the cutoff itself the output is 0.707 of the input and the phase has shifted by 45°.
Worked example
Filtering noise off an analogue sensor line before an ADC, where the signal itself changes no faster than about 20 Hz.
- Set the cutoff roughly 5× above the signal: fc ≈ 100 Hz
- Pick a convenient capacitor: C = 100 nF
- R = 1 / (2π × 100 × 100e-9) = 15.9 kΩ
- Nearest E24 value: 16 kΩ
- Check: fc = 1 / (2π × 16000 × 100e-9) = 99.5 Hz
- τ = 16000 × 100e-9 = 1.6 ms, so it settles in about 8 ms
16 kΩ with 100 nF gives a 99.5 Hz cutoff that passes the signal untouched while rolling off mains hum and switching noise above it.
Practical notes
- Keep the source impedance well below R, and the load impedance well above it. A filter feeding something that draws current is also a voltage divider.
- Cascading two RC stages does not simply double the roll-off slope unless you buffer between them — the second stage loads the first and the corner smears out.
- For anti-aliasing ahead of an ADC, put the cutoff at least a decade below half the sample rate. A single RC rolls off gently, so it needs plenty of margin.
- Ceramic capacitors of class 2 dielectrics (X7R, Y5V) lose capacitance under DC bias — sometimes half their nominal value. For a filter whose corner must be accurate, use C0G/NP0 or film.
- Electrolytics are polarised and leaky, which makes them poor choices for anything but bulk decoupling and very low-frequency corners.
Frequently asked questions
What is an RC time constant?
The product of resistance and capacitance, in seconds. It is the time for a charging capacitor to reach 63.2% of its final voltage, or for a discharging one to fall to 36.8% of its starting voltage.
How long does a capacitor take to fully charge?
Strictly, forever — it approaches the supply asymptotically. In practice five time constants gets it to 99.3%, which is close enough for any real circuit. Three time constants reaches 95%.
How do I calculate RC filter cutoff frequency?
Use fc = 1 / (2π × R × C). With R in ohms and C in farads the answer is in hertz. That is the −3 dB point, where output amplitude has fallen to 70.7% of input.
What is the difference between a low-pass and high-pass RC filter?
The components are identical — only the output tap moves. Take the output across the capacitor for low-pass, across the resistor for high-pass.
Why 0.707 at the cutoff frequency?
It is 1/√2. At that point the output power is exactly half the input power, and since power goes as voltage squared, the voltage ratio is the square root of a half. In decibels that is −3.01 dB, which everyone rounds to −3 dB.