Capacitor Energy Calculator

What the capacitor energy calculator does

A charged capacitor stores energy, and that energy depends on its capacitance and voltage. This calculator finds the energy stored from the capacitance and the voltage, and also gives the charge held on the capacitor.

Below is what stored capacitor energy is, the equations behind it, why the energy formula carries a factor of one half, and a worked example.

How to use it

1. Enter the voltage across the capacitor.
2. Enter the capacitance in farads.
3. Press Calculate for the stored energy and the charge, or Reset to clear them.

What stored energy in a capacitor is

When a capacitor is charged, it stores energy in the electric field between its plates, ready to be released when needed. This is one of the most useful things a capacitor does: it can soak up energy gradually and then deliver it in a quick burst, or hold a reserve to smooth out interruptions. The stored energy is real, usable energy, measured in joules, and it is what makes capacitors valuable for everything from camera flashes to power supplies.

The amount of energy a capacitor stores depends on two things: how much capacitance it has and what voltage it is charged to. A larger capacitance stores more energy at a given voltage, and a higher voltage stores more energy for a given capacitance. The voltage matters especially strongly, as we will see. Alongside the energy, the capacitor holds a certain amount of electric charge, the separated positive and negative charge on its two plates. This calculator finds both the stored energy and the charge from the capacitance and voltage you provide.

The equations it uses

The energy stored in a capacitor is one half of the capacitance times the voltage squared:

E = ½ × C × V²

Here E is the energy in joules, C is the capacitance, and V is the voltage. The charge held on the capacitor is simply the capacitance times the voltage:

Q = C × V

so the calculator reports both. The energy depends on the square of the voltage, which means voltage has an outsized effect: doubling the voltage quadruples the stored energy. The charge, by contrast, grows in simple proportion to the voltage. The calculator evaluates both relationships from your inputs.

Why the energy carries a factor of one half

It is natural to wonder where the factor of one half in the energy formula comes from, since charge is just capacitance times voltage with no half. The answer lies in how the capacitor charges up. When a capacitor starts empty, it takes no voltage to push in the first bit of charge, but as charge accumulates, the voltage rises, and it takes more and more effort to add each additional bit. The capacitor is only at its full voltage right at the very end.

So the energy stored is not the full charge times the full voltage, which would assume every bit of charge was pushed in at the final voltage. It is the charge times the average voltage during charging, and since the voltage rose steadily from zero to its final value, the average is half the final voltage. That is where the one half comes from. The energy is the charge times half the final voltage, which works out to one half of the capacitance times the voltage squared. The calculator builds this factor in, so the energy it reports is the true usable energy, not an overestimate.

Where stored capacitor energy is used

The ability of a capacitor to store energy and release it quickly underlies many devices. A camera flash is a classic example: a capacitor charges up slowly from the battery over a second or two, then dumps its stored energy into the flash tube in a fraction of a millisecond, producing a brilliant burst of light far brighter than the battery could manage directly. The same principle drives the powerful pulse of a defibrillator, which stores energy in a capacitor and releases it in a controlled jolt.

Stored capacitor energy also smooths power supplies, holding a reserve that fills in the gaps when the supply dips, keeping the voltage steady. Large capacitor banks store substantial energy for applications that need sudden high power, and the same idea appears in electronic timing and memory. In all these cases, knowing how much energy a capacitor holds at a given voltage is essential for design and safety, since a large charged capacitor can store a dangerous amount of energy. This calculator provides that figure directly.

Units and precision

The calculator takes the voltage in volts and the capacitance in farads, returning the stored energy in joules and the charge in coulombs. Because it works in farads, a practical capacitor value should be entered as its fraction of a farad, for instance a thousand microfarads as 0.001 farads. The relationships are exact. For small capacitors at low voltages the energy can be a tiny fraction of a joule, so the result is most informative for larger capacitors or higher voltages, where the stored energy is appreciable.

A worked example

Suppose a 1,000-microfarad capacitor, which is 0.001 farads, is charged to 12 volts.

The stored energy is E = ½ × C × V² = ½ × 0.001 × 12² = 0.072 joules, and the charge held is Q = C × V = 0.001 × 12 = 0.012 coulombs. Note the strong effect of voltage: charging the same capacitor to 24 volts instead would store 0.288 joules, four times as much, because the energy depends on the voltage squared.

Questions people ask

How do you calculate the energy stored in a capacitor?

Use E = ½ × C × V², from the capacitance and the voltage. The energy depends on the square of the voltage.

Why is there a factor of one half?

Because the capacitor charges from zero voltage up to its final voltage, so the energy is the charge times the average voltage, which is half the final value.

Why does voltage matter so much?

Because the energy depends on the voltage squared. Doubling the voltage quadruples the stored energy, while the charge only doubles.

What is the charge on a capacitor?

The separated charge on its plates, equal to capacitance times voltage, Q = C × V. It grows in simple proportion to the voltage.

References

A quick note on where the physics comes from. The energy stored in a capacitor and the charge relationship are standard physics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The units follow NIST. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 2, Section 8.3, Energy Stored in a Capacitor. https://openstax.org/books/university-physics-volume-2/pages/8-3-energy-stored-in-a-capacitor
2. HyperPhysics, Energy Stored on a Capacitor. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capeng.html
3. National Institute of Standards and Technology (NIST), SP 811, Guide for the Use of the International System of Units. https://www.nist.gov/pml/special-publication-811