RC Charging / Discharging Calculator

The exponential law

A capacitor charging through a resistor follows

$$v(t)=V_0\left(1-e^{-t/\tau }\right)$$

and discharges as

$$v(t)=V_0{e}^{-t/\tau }$$

with the time constant $\tau =RC$. After 1τ the capacitor reaches 63.2% of the step, after 3τ 95%, and 5τ (99.3%) is the usual "fully charged" rule of thumb. Time to an arbitrary voltage:

$$t_{\text{charge}}=-\tau \ln \left(1-\frac{V}{V_0}\right)t_{\text{discharge}}=-\tau \ln \left(\frac{V}{V_0}\right)$$

— handy for RC reset circuits and timing delays.