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.
Five time constants gets to 99.3%, which is the accepted engineering definition of settled.
f = 1 ÷ (2πRC). For 10 kΩ and 10 µF that is 1.59 Hz.
Not for tau. Only the product matters. It matters for the current drawn and the impedance the circuit presents.
Same time constant, mirrored curve. Discharge falls to 36.8% in one tau.