Capacitor Charge Time Calculator

A capacitor stores electrical charge and releases it rapidly. Understanding charge and discharge time is essential in electronics design — from timing circuits and power supplies to camera flashes and audio crossovers.

Formulas: Charge Voltage at Time t: V(t) = Vs × (1 − e^(−t/τ)) Discharge Voltage at Time t: V(t) = V₀ × e^(−t/τ) Time Constant: τ (tau) = R × C Time to reach X% charge: t = −τ × ln(1 − X/100)

What each variable means:

• Vs: supply voltage (volts); the voltage the capacitor is charging toward
• V₀: initial voltage on the capacitor (volts)
• R: resistance in series (ohms, Ω)
• C: capacitance (farads, F)
• τ (tau): the RC time constant; the time to reach ~63.2% of full charge
• e: Euler’s number ≈ 2.71828

The 5-tau rule: A capacitor is considered fully charged (99.3%) after 5 × τ. Engineers use this as the practical “full charge” time.

Charge percentage by time constant:

Worked example: R = 10 kΩ (10,000 Ω), C = 100 μF (0.0001 F), Vs = 9V, V₀ = 0V.

τ = R × C = 10,000 × 0.0001 = 1 second

Voltage after 1 second: V(1) = 9 × (1 − e^(−1/1)) = 9 × (1 − 0.368) = 9 × 0.632 = 5.69V Voltage after 5 seconds (full charge): V(5) = 9 × (1 − e^(−5)) = 9 × 0.9933 = 8.94V

Time to reach 90% charge: t = −1 × ln(1 − 0.90) = −ln(0.10) = 2.303 seconds

Discharge example: Capacitor starts at 9V, discharges through 10kΩ. After 2 seconds: V(2) = 9 × e^(−2/1) = 9 × 0.135 = 1.22V

Applications: RC circuits are used in audio filters, oscillators, debounce circuits, ADC sample-and-hold, and power supply smoothing.