# Capacitor Energy Calculator

Created by Wojciech Sas, PhD
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Jun 15, 2023

This is the capacitor energy calculator, a simple tool that helps you evaluate the amount of energy stored in a capacitor. You can also find how much charge has accumulated in the condenser. Read on to learn what kind of energy is stored in a capacitor and what is the equation of capacitor energy.

🙋 You can quickly determine any capacitance by reading the capacitor's code with Omni's capacitor calculator.

## What is the energy stored in a capacitor?

A capacitor is an electronic component commonly used in circuits. Its function is to store an electrical charge. In standard parallel plate capacitors, charges of equal but opposite values are present on adjacent plates (for a spherical capacitor, there are concentric spheres instead of plates). These charges create an electric field between them, made up of a certain amount of the circuit's energy. Because we are talking about stored charges, this is an example of potential energy. However, in this case, you cannot use the standard potential energy formula.

## Capacitor energy formula

How do you estimate the energy, E, stored in a capacitor with a capacitance, C, and an applied voltage, V? It's equivalent to the work done by a battery to move charge Q to the capacitor. The resulting equation is:

E = ½ × C × V².

Using the general formula for capacitance, C = Q / V, we can rewrite the capacity energy equation in two other analogous forms:

E = ½ × Q² / C or E = ½ × Q × V.

## Electrical energy in a capacitor – an example

How much energy can be stored in a capacitor with capacity C = 300 μF when we connect it to a voltage source of V = 20 V? Let's work it out together!

• To make our life easier, use scientific notation for the capacitance:

C = 3·10⁻⁴ F.

• Following the capacity energy formula, we can evaluate the outcome as:

E = ½ × 3·10⁻⁴ F × (20 V)² = 6·10⁻² J.

• The energy stored in the capacitor can also be written as 0.06 J or 60 mJ.

• Additionally, we can estimate the overall charge accumulated in the capacitor:

Q = C × V = 3·10⁻⁴ F × 20 V = 6·10⁻³ C = 6 mC.

• … or you can simply save time by using this capacitor energy calculator, which automatically computes all the computations for you!

By the way, if you have a system with more than one capacitor, you'd better check our capacitors in series or parallel capacitor calculators to find the total capacitance quickly because this is the value you should use in the formula for the capacitor's energy.

## Energy transformations in an LC circuit

An LC circuit is a system that is composed of an inductor and a capacitor. In practice, it can be generalized as an RLC circuit due to some resistance in the system. Once the circuit processes the signal of a resonant frequency, the potential energy of the capacitor continuously transforms into the magnetic energy produced by a current flowing through the coil. These kinds of circuits are widely used in signal processing or the sending and receiving of radio waves.

🔎 What about checking our inductor energy storage calculator to learn how to calculate magnetic energy by hand?

## FAQ

### How does a capacitor store energy?

A capacitor stores energy as the device is capable of maintaining an electric potential after being charged. The energy stored in a capacitor is electrostatic potential energy, directly associated with charges on the plates of the capacitor.

### How do I calculate the energy stored by a capacitor?

To compute the energy stored by a capacitor:

1. Find the capacitance of the component, C.
2. Measure the applied voltage V.
3. Multiply the capacitance by the square of the voltage: C · V2.
4. Divide by 2: the result is the electrostatic energy stored by the capacitor. E = 1/2 · C · V2.

### What is the energy stored by a 120 pF capacitor at 1.5 V?

The energy stored in a 120 pF capacitor at 1.5 V is 1.35 × 10-10 J. To find this result:

1. Complete the square of the voltage: V2 = 1.52 V2= 2.25 V2.
2. Multiply the result by the capacitance (we use scientific notation): C · V2 = 120 × 10-12 · 1.25 = 2.7 × 10-10 C · V2.
3. We divide by 2: E = 1/2 × C × V2 = 1/2 · 2.7 × 10-10J = 1.35 × 10-10 J.

### Why is the energy stored in a capacitor divided by two?

The formula for the energy of a capacitor may look familiar, as the electrostatic energy is given by the formula E = Q · V. In a capacitor, we must consider the nonideality of the charging process. The charge accumulated in the capacitor starts at 0 and ends at Q after a time given by the characteristic of the device. Using simple integration over the charge, we find that 0Q q dq = 1/2 Q2, which we use in the formula for the energy: 1/2 Q2 · V.

Wojciech Sas, PhD
Capacity (C)
F
Voltage (V)
V
Stored charge (Q)
C
Stored energy (E)
J
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