A capacitor charge calculator that covers two scenarios in one tool: the static case (steady-state charge, voltage and energy stored) and the dynamic case (voltage and charge at any instant during a charge or discharge transient through a resistor). Both use exact, standard formulas — no approximations.
How it works
Static charge and energy
At steady state a capacitor stores charge according to the fundamental capacitor equation:
Q = C × V
where Q is the charge in coulombs, C is the capacitance in farads and V is the voltage across the plates in volts. The tool solves for any one of the three variables given the other two.
Simultaneously it computes the energy stored in the electric field between the plates:
E = ½ × C × V²
Energy grows with the square of voltage: doubling the voltage quadruples the stored energy, which is why high-voltage capacitors are treated with particular care.
Dynamic charge and discharge in an RC circuit
When a capacitor charges through a series resistor R from a supply V₀ the voltage follows a decaying exponential:
Vc(t) = V₀ × (1 − e^(−t / τ)) τ = R × C
When it discharges back through R:
Vc(t) = V₀ × e^(−t / τ)
The quantity τ (tau) is the RC time constant in seconds. One τ after switching, the capacitor has reached 63.2 % of V₀ (charging) or dropped to 36.8 % (discharging). At exactly 5τ the capacitor is treated as fully charged or discharged — it is within 0.7 % of its final value.
The charge at any moment is Q(t) = C × Vc(t) and the instantaneous energy is E(t) = ½ × C × Vc(t)².
The calculator also solves the inverse problem: given a target voltage level (as a percentage of V₀), it returns the exact time required using t = −τ × ln(1 − Vc/V₀) for charging or t = −τ × ln(Vc/V₀) for discharging.
Worked example
A 100 µF electrolytic capacitor is connected to a 12 V supply through a 10 kΩ resistor:
| Quantity | Calculation | Result |
|---|---|---|
| Charge at full voltage | Q = 100 µF × 12 V | 1.2 mC |
| Energy at full voltage | E = ½ × 100 µF × 144 | 7.2 mJ |
| Time constant | τ = 10 kΩ × 100 µF | 1 s |
| Voltage after 1 s | Vc = 12 × (1 − e^−1) | 7.59 V (63.2%) |
| Voltage after 2 s | Vc = 12 × (1 − e^−2) | 10.38 V (86.5%) |
| Time to reach 80 % | t = −1 × ln(0.2) | 1.609 s |
| Fully charged threshold | 5τ | 5 s |
Enter these same values in the dynamic tab to verify each row — the working section shows every substitution step.
Formula reference
| Formula | Meaning |
|---|---|
| Q = C × V | Charge stored (coulombs) |
| V = Q / C | Voltage from charge and capacitance |
| C = Q / V | Capacitance from charge and voltage |
| E = ½ C V² | Energy stored (joules) |
| τ = R × C | RC time constant (seconds) |
| Vc(t) = V₀(1 − e^(−t/τ)) | Charging voltage at time t |
| Vc(t) = V₀ e^(−t/τ) | Discharging voltage at time t |
| Q(t) = C × Vc(t) | Charge at time t |
| t = −τ ln(1 − Vc/V₀) | Time to reach target voltage (charging) |
| t = −τ ln(Vc/V₀) | Time to reach target voltage (discharging) |
All calculations run entirely in your browser. No values are uploaded or stored anywhere.