The RC time constant, also called tau, the time constant (in seconds) of an RC circuit, is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads), i.e.
{\displaystyle \tau =RC} \tau =RC
It is the time required to charge the capacitor, through the resistor, from an initial charge voltage of zero to ≈63.2 percent of the value of an applied DC voltage, or to discharge the capacitor through the same resistor to ≈36.8 percent of its initial charge voltage. This value is derived from the mathematical constant e, specifically {\displaystyle 1-e^{-1}} 1-e^{{-1}} or {\displaystyle e^{-1}} e^{-1}, relating to the voltage across the capacitor versus time:
Charging toward applied voltage {\displaystyle V_{0}:\quad V(t)=V_{0}(1-e^{-t/\tau })} {\displaystyle V_{0}:\quad V(t)=V_{0}(1-e^{-t/\tau })}[1]
Discharging toward zero from initial voltage {\displaystyle V_{0}:\quad V(t)=V_{0}(e^{-t/\tau })} {\displaystyle V_{0}:\quad V(t)=V_{0}(e^{-t/\tau })}