Capacitor Energy

U = \frac{1}{2}CV^2 = \frac{Q^2}{2C}

Energy stored in charged capacitor.

Variables

Stored energy

Energy in capacitor

In SI units: kg·m²/s²

Capacitance

In SI units: A²·s⁴/(kg·m²)

Allowed values: greater than 0

Voltage

Potential difference

In SI units: kg·m²/(A·s³)

Charge

Stored charge

In SI units: A·s

Derivation

U = ∫V dq = ∫(q/C) dq = Q²/(2C) = ½CV².

Your notes

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C = 2 F (Capacitance)
V = 3 V (Voltage)

Result: U = 9 J

Other electricity & magnetism formulas with the same quantities

RC Time Constant (Capacitance) shares Capacitance
Capacitor with Dielectric (Capacitance) shares Capacitance
Ohm's Law (Electric Circuits) shares Voltage
Electric Power (Electric Circuits) shares Voltage
Inductor Energy (Electromagnetic Induction) shares Stored energy
Capacitive Reactance (AC Circuits) shares Capacitance

Where this formula is listed

Electricity & Magnetism formulas, under Capacitance, alongside Capacitors in Series, Capacitors in Parallel and Energy Density (Electric Field).
In the electricity & magnetism list it comes after Parallel Plate Capacitor and before Capacitors in Series.
Electricity & Magnetism formula sheet, one of 48 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Capacitor Energy formula?

Capacitor Energy is written U = (1/2)CV² = Q²/(2C). Energy stored in charged capacitor. It belongs to Electricity & Magnetism, under Capacitance.

What are the units in U = (1/2)CV² = Q²/(2C)?

In SI units, U is stored energy, measured in kg·m²/s²; C is capacitance, measured in A²·s⁴/(kg·m²); V is voltage, measured in kg·m²/(A·s³); Q is charge, measured in A·s.

How is the Capacitor Energy formula derived?

U = ∫V dq = ∫(q/C) dq = Q²/(2C) = ½CV². The result is U = (1/2)CV² = Q²/(2C).