Capacitor Energy & Charge Calculator

Using the capacitor energy and charge calculator

Type the capacitance and pick its unit (picofarads up to farads), then type the voltage across the capacitor and pick its unit (nanovolts up to gigavolts). Two further menus decide how the answers are displayed: Charge unit runs from pC to MC, and Energy unit offers joules with metric prefixes, watt-hours, kilowatt-hours, electronvolts, calories and foot-pounds.

Press Calculate and you get two rows: Capacitor Energy and Capacitor Charge. Both inputs must be positive numbers. Mixed units are fine, for example 4.7 µF on a 5 V supply or 2,200 mF at 0.9 kV, because everything is converted to farads, volts, coulombs and joules internally before the answer is converted back.

• The energy conversions use these rounded factors: 2.77778 × 10^-4 Wh per joule, 6.242 × 10¹⁸ eV per joule, 0.2390057 Cal per joule and 0.737562 ft-lb per joule. Because the electronvolt factor has only four significant digits, eV and keV answers are good to about four digits.
• A very small result can round to 0 because answers are rounded to eight decimal places; switch to a smaller unit (nJ instead of J, for example) to see it.

Capacitance, charge, voltage and stored energy

A capacitor is two conductors separated by an insulating layer, the dielectric. Connect it to a voltage source and electrons pile up on one plate while the other plate loses the same number, so the two plates carry equal and opposite charge. The capacitance says how much charge the device holds for each volt across it. One farad is one coulomb per volt, which is a very large capacitance: ordinary parts are measured in picofarads, nanofarads, microfarads or millifarads, and only supercapacitors reach hundreds or thousands of farads.

The charge is not the only thing stored. Pushing more charge onto plates that already repel it takes work, and that work stays behind as energy in the electric field between the plates. It can be recovered later, which is why capacitors power camera flashes, smooth power rails and ride through short power cuts.

Capacitor charge and energy formulas

Q = C × Vcharge in coulombs, capacitance in farads, voltage in volts

E = ½ × C × V² = ½ × Q × V = Q² ÷ (2 × C)energy in joules

The factor of one half appears because the voltage is not constant while the capacitor charges. The first sliver of charge moves against almost no voltage, the last sliver against the full V, so the average opposing voltage is V ÷ 2. Multiplying the total charge Q by that average gives ½QV, and substituting Q = CV gives ½CV².

Charge is proportional to voltage, but energy follows the square of voltage. A 1 mF capacitor at 5 V holds 5 mC and 12.5 mJ; at 10 V it holds 10 mC but 50 mJ. Doubling the voltage therefore quadruples the energy.

Worked examples

A small electrolytic capacitor. A 10 µF capacitor is connected across 12 V. Q = 10 × 10^-6 F × 12 V = 1.2 × 10^-4 C, or 120 µC. E = ½ × 10 × 10^-6 × 12² = 7.2 × 10^-4 J, or 720 µJ. That charge corresponds to about 7.5 × 10¹⁴ elementary charges (120 µC divided by 1.602 × 10^-19 C).

A camera flash. A 100 µF capacitor charged to 330 V stores Q = 100 × 10^-6 × 330 = 0.033 C (33 mC) and E = ½ × 100 × 10^-6 × 330² = 5.445 J. Released in a few milliseconds, that is a power of well over a kilowatt, even though the amount of energy is tiny compared with a battery.

A supercapacitor. A 3,000 F cell at 2.7 V holds Q = 3,000 × 2.7 = 8,100 C and E = ½ × 3,000 × 2.7² = 10,935 J, which is 3.0375 Wh. Choose Wh as the energy unit to read that figure directly.

A high-voltage bank. 2.2 mF charged to 3.3 kV stores 7.26 C and 11,979 J, or about 3.33 Wh. Notice how voltage drives the energy: the same capacitor at 330 V would hold only 119.79 J.

Energy and charge units

Charge units are plain powers of ten: 1 mC = 10^-3 C, 1 µC = 10^-6 C, 1 nC = 10^-9 C and 1 pC = 10^-12 C. The Cal option converts with 0.2390057 calories per joule, i.e. the thermochemical calorie of 4.184 J; it is not the dietary Calorie, which is the kilocalorie.

Capacitors in series and in parallel

If you have a bank of capacitors, combine them into one equivalent capacitance first and enter that value. Capacitors in parallel simply add: C = C₁ + C₂ + …. Capacitors in series combine like resistors in parallel: 1 ÷ C = 1 ÷ C₁ + 1 ÷ C₂ + …. Two 10 µF capacitors give 20 µF in parallel and 5 µF in series. Series strings also share the voltage, which is how several low-voltage parts can be used on a higher rail.

Assumptions and limits

• The formulas describe an ideal capacitor. Real parts leak a little charge, have series resistance and inductance, and change capacitance with voltage, temperature and age.
• The voltage must stay below the rating printed on the component; beyond it the dielectric can break down.
• How fast a capacitor charges or discharges depends on the resistance in the circuit: the time constant is τ = R × C, so 10 µF behind 1 kΩ has τ = 10 ms. Use the Ohm's law calculator for the resistor side of that circuit.

Results are idealised calculations, not design or safety advice. Large capacitors can hold a dangerous charge long after a circuit is switched off. See the disclaimer.