Capacitor charge time calculator

A capacitor charging through a resistor reaches 63.2% of the supply in one time constant (R × C) and 99% after five. A 470 µF capacitor through 1 kΩ has τ = 470 ms, so it is effectively full after 2.35 seconds.

The exponential shape is the thing to internalise: charging is fastest at the start and slows continuously, so the last few per cent take as long as the first sixty. That is why inrush limiters work — a resistor in series limits the initial surge into a large reservoir capacitor, and is then shorted out by a relay once the capacitor is mostly charged. Without it, an empty capacitor looks like a dead short at the instant of switch-on, which is what welds contacts and blows fuses on large supplies.