RC Time Constant Calculator

How to use this calculator

1. Enter or choose resistance.
2. Enter or choose resistance unit.
3. Enter or choose capacitance.
4. Enter or choose capacitance unit.
5. Enter or choose capacitor is.
6. The time constant τ updates as you type. Use Copy result or Share to keep it.

Method

τ = R × C; charging: V(t) = V × (1 − e^(−t/τ)); discharging: V(t) = V × e^(−t/τ); f_c = 1 ÷ (2πRC)

R

resistance in ohms

C

capacitance in farads

τ

time constant in seconds

V

supply voltage (charging) or starting voltage (discharging)

t

time since the switch

Worked example

1. τ = 10,000 Ω × 0.0001 F = 1 s.
2. After t = 1 s = 1τ: V = 5 × (1 − e⁻¹) = 5 × 0.63212 = 3.1606 V.
3. f_c = 1 ÷ (2π × 1) ≈ 0.1592 Hz.

A 10 kΩ resistor with a 100 µF capacitor has τ = 1 s; after one second the capacitor has charged to 3.16 V of 5 V.

What the result means

After 1τ the capacitor has covered 63.2% of the change, after 3τ 95%, and after 5τ 99.3%, which is the usual “fully charged” rule. The same τ sets the −3 dB corner of a first-order RC filter.

Assumptions and limits

• Ideal resistor and capacitor driven by a step from a stiff voltage source.
• Discharging starts from the voltage entered and decays towards zero.
• Capacitor leakage, ESR, source resistance and tolerance (often ±10–20% for electrolytics) change the real timing.