RC time constant calculator
A capacitor charges 63.2% of the remaining gap in each time constant. After one tau it is at 63.2%, after two 86.5%, after three 95%, after five 99.3%. Nothing ever technically reaches full charge, which is why "five tau" is the universal engineering shorthand for settled — beyond that the remaining error is smaller than the component tolerances.
The RC time constant is resistance times capacitance. A 10 kΩ resistor with a 10 µF capacitor gives τ = 100 ms, so it reaches 63.2% in 100 ms and effectively settles after five time constants — half a second. The same pair is a low-pass filter with a 1.59 Hz cutoff.
How to use the RC time constant
The same RC pair is two different things depending on what you care about. In the time domain it is a delay or a debounce, characterised by tau. In the frequency domain it is a first-order filter with a −3 dB cutoff at 1/(2πRC) and a 20 dB per decade roll-off. They are the same physics viewed from two angles, and the relationship between them is why a filter that removes 50 Hz mains hum necessarily also slows the circuit response to changes.
Questions
τ = R × C. It is the time to reach 63.2% of the final voltage, and the natural time-scale of the circuit.