Skip to content
STEMForge Tuition

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.

Time constant (τ = RC)1 s
Charge reached after

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:

τ=RC\tau = RC

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:

V(t)=V0(1et/τ)V(t) = V_0 \left(1 - e^{-t/\tau}\right)

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.

R=10000 Ω,C=100×106 FR = 10\,000\ \Omega,\quad C = 100 \times 10^{-6}\ \text{F}

Convert both values to base SI units before multiplying.

τ=10000×100×106=1 s\tau = 10\,000 \times 100 \times 10^{-6} = 1\ \text{s}

τ = RC gives the time constant directly.

At t=τ=1 s, V63.2% of V0\text{At } t = \tau = 1\ \text{s}, \ V \approx 63.2\% \text{ of } V_0

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.

Want this explained live?

No charge for the first call.