RC Time Constant Calculator

τ = RC, with the charging percentages and the filter cutoff.

τ = RC, with the charging percentages and the filter cutoff. τ = RC, and the circuit reaches 63.2% of its final value in one time constant.

Written and maintained by Mohit PatelLast checked August 4, 2026How we build these

Resistance

Capacitance

µF

Time constant (τ)

1 ms

Cutoff at 159.15 Hz

Time constant (τ)1 ms

To 63.2% (1τ)1 ms

To 95% (3τ)3 ms

To 99.3% (5τ)5 ms

Cutoff frequency159.155 Hz

Remaining after 1τ (discharge)36.788%

τ = RC. After one time constant the circuit reaches 63.2% of its final value, and that oddly specific figure is 1 − 1/e — the charging curve is exponential, so it never quite arrives. Five time constants reaches 99.3%, which is the usual working definition of "fully charged". The same τ sets the cutoff frequency of an RC filter at 1/(2πτ).

How the RC Time Constant Calculator works

τ = RC, and the circuit reaches 63.2% of its final value in one time constant. That oddly specific figure is 1 − 1/e: the charging curve is exponential, so it never quite arrives. Five time constants reaches 99.3%, which is the usual working definition of fully charged.

Also known as: time constant formula · capacitor charging time calculator · rc circuit calculator · rc filter cutoff calculator

Where 63.2% comes from

One time constant takes the circuit to 63.2% of its final value, which looks like an arbitrary number until you see it is 1 − 1/e.

Charging is exponential: the current depends on the remaining voltage gap, so as the gap shrinks the charging slows. One time constant is defined as the time for that gap to shrink by a factor of e.

Never quite finished

Because the approach is asymptotic, a capacitor never technically finishes charging. Three time constants reaches 95%, five reaches 99.3%, and ten reaches 99.995%.

Five is the usual working definition of fully charged, and it is a convention rather than a physical threshold — which is why the figure needs stating rather than assuming.

The same τ sets the cutoff frequency of an RC filter at 1/(2πτ). A 1 kΩ resistor with a 1 µF capacitor gives a 1 ms time constant and a 159.2 Hz cutoff, and those are two descriptions of one circuit rather than two facts about it.

Where to go next

The RC Time Constant question rarely arrives on its own. These are the ones that usually come with it:

Capacitor Calculator — Series and parallel, which are the reverse of resistors.
Inductance Calculator — Reactance at frequency, and where L and C cancel.
Resistor Calculator — Series and parallel totals for up to four resistors.
Speed Distance Time Calculator — Any one of the three from the other two, in four units.

Sources

Frequently asked questions

What is the RC time constant?

Resistance times capacitance. 1 kΩ with 1 µF gives 1 millisecond.

Why 63.2%?

Because it is 1 − 1/e. Exponential charging approaches its final value asymptotically, and one time constant is defined as the point where the remaining gap has shrunk by a factor of e.

How long until it is fully charged?

Five time constants, by convention — that reaches 99.3%. Strictly it never finishes, which is why a practical threshold is needed at all.

What is the cutoff frequency?

1/(2πτ). With a 1 ms time constant that is 159.2 Hz, the point where an RC filter attenuates by 3 dB.

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