RC Time Constant

Formula

Description

The RC time constant defines how quickly a capacitor charges or discharges through a resistor. After one time constant (1τ), the capacitor reaches approximately 63.2% of its final voltage when charging, or drops to 36.8% when discharging. After 5τ the capacitor is considered fully charged or discharged (99.3%). The exponential charging curve follows V(t) = Vfinal × (1 - e^(-t/τ)), making the time constant the key parameter for timing circuits, filters, debounce circuits, and power supply soft-start designs.

Variables

• τ — Time constant in seconds (s)
• R — Resistance in ohms (Ω)
• C — Capacitance in farads (F)

Practical Notes

The RC time constant also defines the -3dB cutoff frequency of a simple RC low-pass or high-pass filter: f_cutoff = 1/(2πRC) = 1/(2πτ). For debouncing mechanical switches, a typical RC of 10-50ms works well.