RC Time Constant Calculator — charge and discharge timing

Charge and discharge timing for an RC network, with the curve plotted and the 63%, 95% and 5τ points marked.

Example: 10 kΩ with 1 µF gives a time constant of 10 ms, settling in about 50 ms.

Formula

τ = R × C    V(t) = V₀ × (1 − e^(−t/τ))

Worked example

10 kΩ with 1 µF gives a time constant of 10 ms, settling in about 50 ms.

  1. τ = R × C

    τ = 10 kΩ × 1 µF

    τ = 10 ms

    Ohms times farads gives seconds — the units work out exactly.

  2. V(t) = V₀ × (1 − e^(−t/τ))

    at t = τ = 10 ms

    V = 3.16 V (63.2% of 5 V)

Frequently asked questions

What is the RC time constant?

τ = R × C, in seconds. It is the time for a capacitor to charge to 63.2% of the supply, or discharge to 36.8% of its starting voltage. Ohms multiplied by farads gives seconds directly — the units cancel exactly.

Why 63.2%?

It is 1 − 1/e. The charging curve is exponential, and after one time constant the remaining gap has shrunk by a factor of e. The number is not chosen; it falls out of the mathematics.

How long until the capacitor is fully charged?

Strictly, never — the curve approaches the supply asymptotically. In practice 5τ gets you to 99.3%, which is close enough for any real circuit, and that is the figure designs are built around.

How do I work out the time to a specific voltage?

Rearrange the exponential: t = −τ × ln(1 − V/V₀) for charging. Enter a target voltage above and the tool does it. This is how you size an RC delay to cross a logic threshold at a particular moment.

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