Explore RC behavior using flexible unit controls here. Compute tau, cutoff frequency, and timings fast. Download a clear report for labs and designs always.
The RC time constant is defined as:
τ = R × C
For a first-order RC low-pass or high-pass network, the cutoff frequency is:
fc = 1 / (2π τ)
For capacitor voltage timing, an exponential response is used. Charging approaches the supply voltage, and discharging decays toward zero.
| R | C | τ = R·C | fc = 1/(2π·τ) | 90% time (≈ 2.303τ) |
|---|---|---|---|---|
| 10 kΩ | 1 µF | 0.010 s | 15.9 Hz | 0.0230 s |
| 47 kΩ | 100 nF | 0.00470 s | 33.9 Hz | 0.0108 s |
| 1 MΩ | 10 nF | 0.010 s | 15.9 Hz | 0.0230 s |
Values are rounded for readability and match the formulas above.
Article
The time constant τ sets the speed of an RC response. After 1τ, a charging capacitor reaches 63.2% of its final step value, while a discharging capacitor falls to 36.8%. Many designs use 5τ as “settled,” which corresponds to about 99.3% completion.
Common resistors span roughly 10 Ω to 10 MΩ in signal networks, while capacitors used for timing often range from 100 pF to 1000 µF. Pairing 10 kΩ with 100 nF gives τ = 1 ms, a convenient value for fast smoothing and pulse shaping.
For first-order RC filters, the cutoff frequency is fc = 1/(2πRC). Using τ = 1 ms yields fc ≈ 159 Hz. Doubling R or C doubles τ and halves fc, making it easy to tune attenuation for noise, ripple, or audio band-limits.
Beyond the 63.2% point, the response continues predictably: at 2τ the charge is about 86.5%, at 3τ it is 95.0%, and at 4τ it is 98.2%. The 10–90% rise time of a first-order RC is about 2.197τ, useful for comparing edge speeds.
When you know a start and target voltage, the exponential equations solve for time. For discharge, t = −τ ln(Vf/Vi). If Vi=5 V and Vf=1 V, then t = −τ ln(0.2) ≈ 1.609τ. This calculator automates that step while preserving units.
RC smoothing is often chosen so τ is several times longer than the noise spikes you want to ignore. For example, if interference bursts last about 2 ms, selecting τ ≈ 10 ms strongly reduces those bursts while still tracking slower changes. The cutoff frequency view helps verify bandwidth quickly.
With a pull-up resistor and input capacitance, τ can slow logic transitions. A 100 kΩ pull-up and 20 pF input yields τ = 2 µs, usually fine. For push-button debouncing, designers may target 5–20 ms using 10–100 kΩ with 100 nF to 1 µF, balancing responsiveness and noise immunity.
Real τ varies with component tolerance and parasitics. A 5% resistor and a 10% capacitor can shift τ by roughly ±15% in worst-case stacking. Large electrolytics also have leakage and higher ESR, affecting timing at high resistance. Measure R and C, then document expected τ and fc consistently.
FAQs
It is τ = R×C, the characteristic time that sets how fast a capacitor charges or discharges through a resistor. After one τ, the response reaches about 63.2% of its final step value.
After 5τ, the exponential step response reaches about 99.3% of the final value. Many engineering tasks treat this as settled because further change is small compared with typical tolerances and noise.
For a first-order RC filter, fc = 1/(2πRC) = 1/(2πτ). The calculator reports fc directly once τ is known.
Yes. Choose “Solve R” or “Solve C” and enter the other known value plus τ. The tool converts units and computes the missing parameter in base units.
Charging uses V(t) = Vs + (Vi − Vs)e−t/τ. The calculator rearranges it to solve for time to reach a chosen Vf.
Discharge uses V(t) = Vie−t/τ. For a target Vf, time is t = −τ ln(Vf/Vi) when 0 < Vf < Vi.
Component tolerances, capacitor leakage, ESR, and stray capacitance can shift τ. Supply impedance and measurement loading also matter. Measuring actual R and C values and using realistic units improves agreement.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.