Capacitor Energy Calculator

Calculator

This calculator can solve for energy \( E \), capacitance \( C \), or voltage \( V \) when you provide the other two. The stored charge \( Q \) is always shown as an additional output.

• Capacitance (C):
• F mF µF nF pF

• Voltage (V):
• V mV kV

• Energy (E):
• J mJ µJ kJ

Please fill in exactly two variables.

Calculate

Energy Stored in a Capacitor — Explanation

When a voltage \( V \) is applied across a capacitor with capacitance \( C \), charge accumulates on the plates and energy is stored in the electric field between them. The energy stored is: \[ E = \frac{1}{2} C V^2 \] Where:

• \( E \) is the stored energy (in Joules, \( \text{J} \)),
• \( C \) is the capacitance (in Farads, \( \text{F} \)),
• \( V \) is the voltage across the capacitor (in Volts, \( \text{V} \)).

The \( V^2 \) dependence is the key insight: doubling the voltage quadruples the stored energy. This is why high-voltage capacitors are so effective in pulsed energy applications like camera flashes or defibrillators.

The stored charge \( Q \) on the plates follows directly from the definition of capacitance: \[ Q = C \cdot V \] Substituting this into the energy formula gives two equivalent forms: \[ E = \frac{Q^2}{2C} = \frac{1}{2} Q V \] All three forms are equivalent — which one to use depends on what variables are known.

Purpose of the Calculator

Given any two of the three variables \( E \), \( C \), and \( V \), the calculator solves for the missing one. The rearranged formulas are:

• To solve for \( E \) (energy): \[ E = \frac{1}{2} C V^2 \]
• To solve for \( C \) (capacitance): \[ C = \frac{2E}{V^2} \]
• To solve for \( V \) (voltage): \[ V = \sqrt{\frac{2E}{C}} \]

In all cases, the stored charge \( Q = C \cdot V \) is shown as an additional output.

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