RC Time Constant Calculator

Calculate and visualize the exponential charging and discharging behavior of a capacitor.

1. Mode
2. Components
Resistance (R) kΩ
Capacitance (C) μF
Supply Voltage ($V_s$) V
Time Constant (τ)
1.00
Seconds
5.00s Time to 99%
(Steady State)
7.58V Voltage at
1 Time Constant
Voltage Curve (0 to 5τ)
1τ Time Voltage

Understanding RC Circuits

A capacitor does not charge or discharge instantly. Because the resistor limits the flow of current, the voltage across the capacitor changes exponentially over time.

  • The Time Constant (τ): Calculated as $R \times C$. This is the time it takes for the capacitor to reach approximately 63.2% of its full charge, or drop to 36.8% of its initial charge.
  • The 5τ Rule: In engineering, a capacitor is considered "fully charged" or "fully discharged" after 5 time constants (5τ), at which point it has reached 99.3% of its target value.
  • Charging Formula: $V(t) = V_s(1 - e^{-t/RC})$
  • Discharging Formula: $V(t) = V_0(e^{-t/RC})$