How to use this calculator
Choose charging or discharging, then enter the voltage, resistance, capacitance and the time since the switch closed.
Formulas
Time constantτ = RC
ChargingVC = V(1 − e−t/τ) i = VRe−t/τ
DischargingVC = V0e−t/τ E = ½CVC²
Worked example
9 V, 10 kΩ, 100 µF after 1 s of charging (the default)
- τ = 10,000 × 100 × 10⁻⁶ = 1 s.
- VC = 9(1 − e−1) = 5.69 V (63.2%).
- i = 9/10,000 × e−1 = 0.331 mA; stored energy ½ × 100 µF × 5.69² = 1.62 mJ.
Frequently asked questions
Why 5τ?
After five time constants the capacitor is within 0.7% of its final voltage, which engineers treat as fully charged.
Where does the equation come from?
Kirchhoff’s voltage law gives RC dVC/dt + VC = V, a first-order linear ODE. Its solution is the exponential above.