Capacitor Calculator
Capacitors store energy in an electric field. This calculator handles charge, stored energy and the RC time constant that governs charging and discharging.
Formula
τ = R × C · charging: V(t) = V₀(1 − e^(−t/τ)) · discharging: V(t) = V₀e^(−t/τ)
- τ is the time constant in seconds, R in ohms, C in farads
- 10 kΩ with 100 µF gives τ = 1 second
After one time constant a capacitor reaches 63.2% of the supply
Charge and Energy
Charge: Q = C × V — coulombs from farads and volts
Energy: E = ½CV² — joules
A 1,000 µF capacitor at 12 V holds 0.012 C and stores 0.5 × 0.001 × 144 = 0.072 J.
Energy scales with the square of voltage, so doubling the voltage quadruples the stored energy — which is why voltage rating matters as much as capacitance.
The RC Time Constant
τ = R × C
One time constant is the period to charge to about 63% of the supply, or discharge to 37%. After five time constants the capacitor is treated as fully charged.
10 kΩ with 100 µF gives τ = 1 second, so roughly 5 seconds to full charge.
This is the basis of timing circuits, debouncing and filters.
Series and Parallel Are Backwards
Capacitors combine the opposite way to resistors, which catches people out constantly:
- Parallel: capacitances add. C = C₁ + C₂
- Series: reciprocals add. 1/C = 1/C₁ + 1/C₂
So series capacitors give less total capacitance, though the arrangement shares voltage and raises the effective voltage rating.
Safety: large capacitors hold a dangerous charge long after power is removed. Discharge through a resistor before handling.
Quick Reference
| Time | Charged to | Discharged to |
|---|---|---|
| 1τ | 63.2% | 36.8% |
| 2τ | 86.5% | 13.5% |
| 3τ | 95.0% | 5.0% |
| 4τ | 98.2% | 1.8% |
| 5τ | 99.3% | 0.7% |
Frequently Asked Questions
- How much energy does a capacitor store?
- Half of capacitance times voltage squared. A 1,000 µF capacitor at 12 V stores 0.072 joules.
- What is the RC time constant?
- Resistance times capacitance. It is the time to reach about 63 per cent of full charge, with five time constants treated as fully charged.
- Do capacitors add in series like resistors?
- No, the opposite. Capacitors add in parallel and combine reciprocally in series, so series capacitors give less total capacitance.
- Are charged capacitors dangerous?
- Large ones can be, and they retain charge long after power is removed. Discharge through a suitable resistor before handling equipment.