What is the RC time constant?

The time constant tau equals resistance times capacitance (tau = R times C). It is the time, in seconds, for a charging capacitor to reach about 63.2 percent of the supply voltage, or for a discharging one to fall to 36.8 percent. It sets the speed of every RC timing circuit.

Why is full charge considered 5 tau?

Charging is exponential and never mathematically reaches 100 percent. After 5 time constants the capacitor sits at about 99.3 percent of supply, which is treated as fully charged for engineering purposes. Most timer and settling specs use the 5 tau figure.

What is the charging formula?

For charging, V(t) = Vsupply times (1 minus e^(minus t over tau)). For discharging, V(t) = V0 times e^(minus t over tau). Here e is Euler's number, t is elapsed time, and tau is R times C in seconds.

How do I size R and C for a desired delay?

Pick the delay you want, decide what voltage threshold triggers your next stage, then solve t = minus tau times ln(1 minus Vthreshold over Vsupply) for tau, and choose R and C whose product equals that tau. This tool lets you check the result instantly.

Does this account for ESR or leakage?

No. It models an ideal single-stage RC network. Real electrolytic capacitors have equivalent series resistance and leakage current that slightly alter timing, and large capacitors self-discharge. Treat the result as the theoretical baseline.

RC Circuit Charge / Discharge Time Calculator

A capacitor charging or discharging through a resistor follows a precise exponential curve set entirely by the product of resistance and capacitance. This calculator computes that time constant and the voltage at any instant, so you can predict timer-relay delays, power-supply settling, and capacitor-start motor behaviour without a scope.

How it works

The single governing quantity is the time constant:

tau (seconds) = R (ohms) × C (farads)

Capacitance entered in microfarads is converted with C_farads = uF / 1e6. Voltage then follows one of two exponentials:

charging:    V(t) = Vsupply × (1 − e^(−t / tau))
discharging: V(t) = V0      × e^(−t / tau)

To find the time to reach a target voltage fraction f while charging, the formula is inverted:

t = −tau × ln(1 − f)

The familiar milestones fall out of this: at 1 tau a charging capacitor is at 63.2 percent, and at 5 tau it is at 99.3 percent — the conventional “fully charged” mark.

Example and tips

A 100 kilohm resistor with a 47 microfarad capacitor gives tau = 100000 times 0.000047 = 4.7 seconds. Charging from 0 to a 12 V supply, the capacitor reaches about 7.6 V (63.2 percent) after 4.7 s and is effectively full at roughly 23.5 s (5 tau). When designing timer relays, choose your threshold voltage first, then read the matching time — small drift in R or C shifts the delay proportionally, so use precision parts where timing matters.