Calculate the Voltage Across a Capacitor (RC Charging)

This calculator gives the voltage across a capacitor that charges through a resistor from a DC supply. Enter the supply voltage, the resistance, the capacitance and the time since the switch closed; you get the capacitor voltage, the percent of full charge and the RC time constant.

Formula

For a capacitor that starts empty and charges through resistor R from voltage Vs: V(t) = Vs × (1 − e^(−t ÷ τ)), with time constant τ = R × C (ohms × farads = seconds). Here R is entered in kΩ (× 1000) and C in µF (÷ 1,000,000).

• Vs: supply voltage, V
• R: series resistance, kΩ
• C: capacitance, µF
• t: time since charging started, s

Worked Example

12 V supply, 10 kΩ, 100 µF, after 1 s.

1. τ = 10,000 Ω × 0.0001 F = 1.000 s
2. t ÷ τ = 1; e^(−1) = 0.367879
3. V = 12 × (1 − 0.367879) = 7.585 V
4. 7.585 ÷ 12 = 63.21% of the supply
5. 5τ = 5.000 s to reach about 99%

Limits and common mistakes

• The formula assumes the capacitor starts at 0 V. For discharge use V = V0 × e^(−t ÷ τ).
• After one τ the capacitor is at 63.2%, after 3τ at 95%, after 5τ at 99.3%.
• Real capacitors have tolerances of ±10-20%, so τ can differ by as much.
• Keep within the capacitor’s rated voltage.