Last updated: 2026-06-15

RC time constant

When a resistor and a capacitor are connected in series, the capacitor charges and discharges along a smooth exponential curve. The speed of that curve is set by a single number, the time constant $\tau = R \cdot C$. With resistance $R$ in ohms and capacitance $C$ in farads, the product has units of seconds.

This calculator solves for the time constant, the resistance or the capacitance, and also reports the practical settling time and the half-life.

What the time constant means

After one time constant, a charging capacitor has reached $63.2\%$ of the supply voltage; a discharging one has fallen to $36.8\%$. Each further time constant covers the same fraction of the remaining gap, so the approach to the final value is exponential rather than linear.

By convention a capacitor is treated as fully charged after $5\tau$, which this calculator reports as the settling time.

Formula

The half-life $t_{1/2}$ is the time for the voltage to change by half. Rearranging the defining equation gives $R = \tau / C$ and $C = \tau / R$ for the other two solve modes.

Worked example

A $10\ \text{k}\Omega$ resistor charges a $100\ \mu\text{F}$ capacitor. The time constant is:

So the capacitor reaches 63.2 % of the supply in 1 second and is essentially fully charged after 5 seconds. Its half-life is $0.693 \times 1 = 0.693\ \text{s}$.

Time constant and filter cutoff

The same resistor and capacitor also form a first-order filter. Its cutoff frequency is related to the time constant by $f = 1/(2\pi\tau)$. A larger time constant gives a lower cutoff frequency, so the choice of $R$ and $C$ fixes both how quickly the circuit responds to a step and which frequencies it passes or blocks.

Limitations

The $\tau = R\cdot C$ result assumes a single resistor and a single ideal capacitor with no leakage and a source with negligible internal resistance. Real circuits with several resistors or capacitors combine them into an equivalent $R$ and $C$ first; capacitor leakage and tolerance, and any load drawing current, will shift the actual timing from the ideal value.