Free tool · Electronics
RC Time Constant Calculator
Enter resistance and capacitance to find the time constant of an RC circuit, and how far it has charged after each multiple of it.
1τ = 1 s
63.2%
2τ = 2 s
86.5%
3τ = 3 s
95.0%
4τ = 4 s
98.2%
5τ = 5 s
99.3%
The formula
The time constant of a resistor and capacitor in series is simply their product:
R in ohms, C in farads, giving τ in seconds.
Charging voltage as a fraction of the supply follows a decaying exponential in terms of τ:
At t = τ, this gives 1 − e⁻¹ ≈ 63.2% — where the 63.2% figure the calculator's table shows comes from.
Worked example
A 10 kΩ resistor charges a 100 µF capacitor.
Convert both values to base SI units before multiplying.
τ = RC gives the time constant directly.
After one time constant, the capacitor has reached 1 − e⁻¹ of its final voltage.
Frequently asked questions
What does the RC time constant actually mean?
It's the time it takes a capacitor charging (or discharging) through a resistor to cover about 63.2% of the remaining distance to its final value. It isn't the time to reach the final value — the capacitor never quite gets there, it just gets closer with every time constant that passes.
How long does a capacitor take to fully charge?
In theory, infinitely long — charging follows a decaying exponential that only reaches 100% at infinite time. In practice, a circuit is treated as "fully charged" after about 5 time constants, by which point it has reached over 99% of its final value.
Does the time constant depend on the applied voltage?
No. τ = RC depends only on the resistance and capacitance values, not on the supply voltage or the capacitor's initial charge. A bigger supply voltage produces a bigger final voltage, reached over exactly the same time course.
What's the difference between charging and discharging time constants?
None — the same τ = RC applies to both. Charging rises from 0% towards 100% of the supply voltage; discharging falls from 100% towards 0%. Both cover 63.2% of the remaining distance in each time constant.
Where does the RC time constant show up in practice?
Debounce circuits, timing circuits, and — combined with a cutoff frequency formula — in the design of RC filters, where the same R and C set both how fast the circuit responds in time and which frequencies it passes.
Why does a smaller capacitor charge faster?
A smaller capacitor stores less charge for a given voltage, so the same current reaches that voltage sooner. Since τ = RC, halving C halves the time constant for a fixed resistance.
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