RC Time Constant Calculator

RC time constant: τ = R · C

The RC time constant τ = R · C sets how fast a capacitor charges or discharges through a resistor. Charging follows V(t) = Vfinal · (1 − e−t/τ); discharging follows V(t) = Vinitial · e−t/τ. At t = τ, the capacitor reaches 63 % of the target voltage; at t = 5τ, 99.3 % — the practical saturation point. Example: R = 10 kΩ, C = 100 µF gives τ = 1 s, full charge in ~5 s. The RC pair also defines a first-order low-pass filter with cutoff frequency fc = 1 / (2π · R · C). Above f_c, signals attenuate at 20 dB/decade.

Applications: debounce, filtering, timing

RC circuits provide switch debounce (τ in the 10–50 ms range smooths mechanical bounce), analog filters for audio and switching-supply ripple, antialiasing before an ADC, and form the timing element in PWM/PFM generators and 555-timer-based oscillators. Lower τ means faster response and higher cutoff frequency.

FAQ

Why 63 % at one time constant? The exponential 1 − e⁻¹ ≈ 0.632 falls out of solving the differential equation for capacitor charge — it is not arbitrary.

When is the capacitor "fully" charged? Mathematically, never — but at 5τ it is within 1 % of the final voltage, which is treated as full for most engineering purposes.

How do I pick R and C for a 100 Hz cutoff? Pick C first (e.g., 100 nF), then solve R = 1 / (2π · f_c · C) = 1 / (2π · 100 · 1e-7) ≈ 15.9 kΩ.

Does the formula change for AC? τ is defined for DC step responses; for AC use impedance X_C = 1 / (2π · f · C) and reactance analysis instead.