RC Time Constant Calculator
Calculate RC time constant, 20–80% and 10–90% rise time, and the 3 dB cutoff frequency from resistance and capacitance.
Convert a dB gain to a voltage ratio →
About RC timing
One time constant (τ = R × C) is the time a first-order RC circuit needs to move about 63.2% of the way from its starting voltage toward its final value. After five time constants the response is within 1% of settled.
Rise time and bandwidth
20–80% rise time = ln(4) × τ ≈ 1.386 τ
10–90% rise time = ln(9) × τ ≈ 2.197 τ
3 dB cutoff frequency f_c = 1 / (2π·R·C)
The rise-time figures describe how quickly an edge settles; the cutoff frequency is where a simple RC low-pass filter attenuates a signal by 3 dB.
Worked example: a 1 kHz low-pass filter
For a low-pass that starts rolling off around 1 kHz, try R = 1.6 kΩ and C = 100 nF: the time constant is 160 µs and the 3 dB cutoff lands at 995 Hz. An edge fed into it settles from 20% to 80% in about 222 µs.
Common questions
- What does the time constant τ actually tell me?
- It is the time for the capacitor to reach 63.2% of the way to its final voltage — not the time to get there completely. That figure is 1 − 1/e, and it comes out of the exponential rather than being chosen. After 2τ you are at 86.5%, after 3τ at 95%.
- How long until the capacitor is fully charged?
- Strictly, never: the curve approaches its target asymptotically and never quite arrives. In practice 5τ is treated as fully charged, because that is 99.3% and the remaining error is smaller than component tolerances. Some safety-critical work uses 7τ (99.9%) instead, but 5τ is the near-universal engineering convention.
- Is discharging the same curve as charging?
- It is the mirror image, with the same time constant. Discharging falls to 36.8% of the starting voltage after one τ — that is 1/e, the complement of the 63.2% figure. So the same RC pair takes the same time to fall as to rise, which is why τ characterises the circuit rather than any particular direction.
- What if the capacitor discharges through a different resistor?
- Then the discharge time constant uses that resistor instead. τ = RC always refers to whatever resistance the current actually flows through, which need not be the charging path — a common arrangement charges through one resistor and discharges through another, giving deliberately asymmetric timing. The 555 timer in astable mode does exactly this, which is why its duty cycle is never 50%.