RC & RL Time Constant Calculator
Time constant τ = RC or L/R, the charge and discharge curve at 0.5τ to 5τ, the value at any time, the time to reach any percentage, and stored energy.
How fast a capacitor or inductor circuit settles and where it is at a given instant — the exponential curve made explicit, so a delay, filter or snubber can be sized with a reason.
Example: 10 kΩ and 100 µF give τ = 1 s: 63.2 % charged at 1 s, 86.5 % at 2 s, 99.3 % at 5 s; 90 % takes 2.30 s. From 12 V the initial current is 1.2 mA and the stored energy 7.2 mJ.
63 % in one τ.
Never quite 100 %.
What the time constant is, how the curve is read, and why “five τ” is the usual definition of settled.
The time constant
A capacitor charging through a resistor, or the current building in an inductor through a resistor, follows an exponential: the remaining gap to the final value shrinks by a factor e every τ seconds, where τ = RC for the capacitor and L/R for the inductor. After one τ the value has covered 63.2 % of the way; after two, 86.5 %; after five, 99.3 % — the point most engineers call settled. Discharge and current decay are the mirror image, falling to 36.8 % after one τ.
Any time, any percentage
The page evaluates the curve at a time you name and inverts it for a percentage you name: t = −τ ln(1 − p). Give a supply voltage and the same fractions become volts (RC) or amps (RL), together with the current V ÷ R and the energy the component holds when full, ½CV² or ½LI². The cutoff frequency 1 ÷ 2πτ is listed because it is the same network seen from the frequency side.
Ideal components
The curve assumes a perfect step from a source with no resistance of its own, and parts without series resistance, leakage or saturation. A source impedance simply adds to R; an electrolytic's leakage flattens the last few percent; an inductor's winding resistance adds to R and limits the final current. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- First-order RC and RL step response, v(t) = V(1 − e^(−t/τ)) — standard circuit theory (e.g. Nilsson & Riedel, Electric Circuits, chapter 7)
Last reviewed 19 September 2026. How results are checked: How we verify.