What is the capacitor time constant?

The time constant is resistance times capacitance, written τ = R x C. It is the time a capacitor takes to charge to 63.2% of the supply voltage through a resistor. A 10 kΩ resistor and a 100 µF capacitor give 10,000 x 0.0001 = 1 second.

Ohms times farads gives seconds, so convert kilohms and microfarads before you multiply. Each further time constant closes 63.2% of the remaining gap: the capacitor reaches 86.5% at 2τ, 95.0% at 3τ, 98.2% at 4τ and 99.3% at 5τ. The RC time constant article on Wikipedia gives the derivation.

During discharge the time constant works the other way, leaving 36.8% of the voltage after one τ. The guide to the capacitor time constant has a full table, and the capacitor charging time calculator finds τ for any values.