RC Time Constant Calculator
Enter a resistance and capacitance to get the RC time constant, the filter's cutoff frequency and how long the capacitor takes to reach each charge milestone.
How it works
The time constant tau is simply resistance times capacitance. It is the time the capacitor takes to reach about 63.2% of the way to its final voltage — not 63% of the supply, but 63% of whatever gap remains, which is why charging is exponential rather than linear.
Each further tau closes 63.2% of the remaining gap: 86.5% after 2τ, 95.0% after 3τ, 98.2% after 4τ and 99.3% after 5τ. Five time constants is the usual engineering definition of 'fully charged', because the last 0.7% rarely matters.
The same R and C define a filter. The −3 dB cutoff frequency is 1 ÷ (2πRC) — the point where the output has fallen to about 70.7% of the input in amplitude, or half the power. A slow time constant and a low cutoff frequency are the same fact stated two ways.
The formula
Time constant
τ = R × C
Charging
V(t) = V_final × (1 − e^(−t/τ))
Discharging
V(t) = V_start × e^(−t/τ)
Cutoff frequency
f_c = 1 ÷ (2π × R × C)
Worked examples
| Scenario | Working | Result |
|---|---|---|
| 1 kΩ with 1 µF | 1000 × 0.000001 | τ = 1 ms, cutoff 159.2 Hz |
| 10 kΩ with 100 µF | 10000 × 0.0001 | τ = 1 s, fully charged in ~5 s |
| Debouncing with 10 kΩ and 100 nF | τ = 1 ms | Settles in ~5 ms — longer than switch bounce |
When you'd use it
- Designing a low-pass filter for a noisy signal
- Sizing an RC debounce network for a switch
- Working out how long a capacitor takes to charge or bleed down
- Setting a delay or timing interval
Common questions
Why 63.2% rather than a round number?
It falls out of the exponential: 1 − 1/e is 0.632. Nothing chose it — it is what one time constant of exponential approach happens to equal, which is why the figure looks arbitrary but appears everywhere.
Is the capacitor ever fully charged?
Mathematically no — it approaches the final voltage asymptotically and never quite arrives. In practice 5τ gets you to 99.3%, which is closer than component tolerances and measurement error, so that is treated as done.
Does discharging take the same time as charging?
With the same resistance, yes — the curve is the mirror image and tau is identical. If the discharge path has a different resistance, which is common, the discharge time constant differs accordingly.
What is the relationship between tau and cutoff frequency?
They are reciprocal, with a factor of 2π: f_c = 1 ÷ (2πτ). A longer time constant means a lower cutoff, so a slow circuit and a filter that removes more high frequencies are the same circuit described differently.
Is anything I enter sent to a server?
No. Every calculation runs in your browser, so component values, circuit figures and measurements are never uploaded, logged or stored. There is no account and no record of what you typed.