RC Time Constant Calculator
Enter R and C to get the time constant τ, charge/discharge table, and cutoff frequency.
Time constant (τ)
10 ms
Cutoff frequency (−3 dB)
15.9 Hz
| Time | % charged | Duration |
|---|---|---|
| 1τ | 63.2% | 10 ms |
| 2τ | 86.5% | 20 ms |
| 3τ | 95% | 30 ms |
| 4τ | 98.2% | 40 ms |
| 5τ | 99.3% | 50 ms |
Formula
τ = R × C fc = 1 / (2π·R·C)
After one τ a capacitor reaches 63% of its final voltage; ~5τ is 'fully' charged.
The RC time constant
Charge a capacitor through a resistor and its voltage rises along the exponential curve above, not in a straight line. The time constant τ = R·C sets the pace: 63% charged at 1τ, over 99% by 5τ.
The same R and C also define a filter's −3 dB cutoff frequency, where the circuit starts attenuating signals.
Two ways to think about it
- As a timer: τ tells you how long a delay, debounce or soft-start will take.
- As a filter: fc tells you which frequencies pass and which are rolled off.
- Bigger R or C = slower response and a lower cutoff frequency.
Where it's used
Debouncing buttons, smoothing PWM into an analog voltage, low/high-pass audio and sensor filters, and the timing elements inside 555 and oscillator circuits.
Frequently Asked Questions
What is the RC time constant?+
τ = R × C. It's the time for a capacitor to charge to ~63.2% (or discharge to ~36.8%) of its final value. After 5τ the capacitor is considered fully charged (99.3%).
How does the RC circuit relate to filtering?+
An RC pair forms a first-order filter. The cutoff frequency f = 1 / (2π × R × C). Signals below this frequency pass; above are attenuated (−3 dB = half power).