RC Time Constant Calculator
τ = RC, with the charging percentages and the filter cutoff.
Work out RC Time Constant. τ = RC, with the charging percentages and the filter cutoff. States its idealisation instead of hiding it.
Time constant (τ)
1 ms
Cutoff at 159.15 Hz
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.
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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