Electrical Engineering

Capacitor Energy Calculator

Calculate stored capacitor energy, capacitance, voltage, or charge using U = 1/2 C V², U = Q² / (2C), and U = 1/2 QV.

Formulas U = 1/2 C V² · U = Q² / (2 C) · U = 1/2 Q VReviewed Sep 9, 2026

A charged capacitor stores energy in its electric field. This calculator covers the three most useful equivalent forms of that relationship: U = 1/2 C V², U = Q² / (2C), and U = 1/2 QV. Choose the pair of known quantities that matches your problem, then solve for stored energy, capacitance, voltage magnitude, or charge magnitude without doing the algebra by hand.

Calculation Bench

Known Pair

Solve for

01Capacitance

C · Charge-storage capacity of the capacitor, defined by Q = CV.

02Voltage Magnitude

V · Magnitude of the potential difference across the capacitor terminals.

This is an ideal-capacitor energy calculator. It uses magnitudes only and does not check ESR losses, leakage, or voltage-rating safety margins.

Solution

Enter the required values to calculate stored energy.

U = 1/2 C V²

Formula Sheet

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

C = \dfrac{2U}{V^2}

V = \sqrt{\dfrac{2U}{C}}

UStored Energy
CCapacitance
VVoltage Magnitude
QCharge Magnitude

Variables & Units

Symbol	Variable	Description	Common Units
U	Stored Energy	Electrostatic energy stored in the capacitor's electric field.	J, mJ, kJ, ft·lbf
C	Capacitance	Charge-storage capacity of the capacitor, defined by Q = CV.	pF, nF, µF, mF, F
V	Voltage Magnitude	Magnitude of the potential difference across the capacitor terminals.	mV, V, kV
Q	Charge Magnitude	Magnitude of the stored charge on either capacitor plate.	nC, µC, mC, C

How to Use This Calculator

01Choose the known-pair form first: Capacitance & Voltage, Charge & Capacitance, or Charge & Voltage.
02Select which variable to solve for. The calculator then shows only the inputs needed for that relation.
03For real components, compare the entered voltage with the capacitor voltage rating before treating the stored-energy result as usable. Energy can be correct while the part is unsafe.
04Enter the known values with the correct units. Voltage and charge are treated as magnitudes, so enter positive values rather than signed plate polarity.
05Select Calculate to see the result in SI base units, the active formula, and the substitution using converted base-unit values.
06Use the worked examples below if you want to sanity-check the scale of the result, especially when working with microfarads, millicoulombs, or kilovolts.

How the Formula Works

For an ideal capacitor, the stored electrostatic energy can be written in several equivalent ways: U = 1/2 C V², U = Q² / (2C), and U = 1/2 QV. These are all the same relationship, connected by the basic capacitor equation Q = CV.

The squared-voltage and squared-charge forms make an important design point obvious: energy rises very quickly as voltage or charge increases. Doubling the voltage across the same capacitor multiplies stored energy by four, while doubling the capacitance at the same voltage only doubles the stored energy.

This page treats capacitance, voltage, and charge as ideal lumped quantities at a single operating point. It is useful for storage estimates, flash or pulse circuits, and textbook capacitor problems, but it does not model transient charging losses, ESR heating, leakage, or dielectric breakdown.

Worked Example 01

Stored energy from capacitance and voltage

Known

Capacitance (C): 220 µF
Voltage (V): 24 V

Formula

U = 1/2 C V²

Substitution

U = 1/2 × 220×10^-6 × 24²

Result

U = 0.06336 J (63.36 mJ)

A 220 µF capacitor charged to 24 V stores 63.36 mJ of energy.

Worked Example 02

Capacitance required for a defibrillator energy target

Known

Stored Energy (U): 400 J
Voltage (V): 10,000 V

Formula

C = 2 U / V²

Substitution

C = (2 × 400) / 10,000²

Result

C = 8.0 µF

To store 400 J at 10 kV, the required capacitance is 8.0 µF.

Worked Example 03

Charge from stored energy and capacitance

Known

Stored Energy (U): 2 mJ
Capacitance (C): 100 µF

Formula

Q = √(2 U C)

Substitution

Q = √(2 × 0.002 × 100×10^-6)

Result

Q ≈ 0.000632 C (632 µC)

A capacitor storing 2 mJ with 100 µF capacitance holds about 632 µC of charge.

Worked Example 04

Voltage from stored energy and charge

Known

Stored Energy (U): 0.45 J
Charge (Q): 15 mC

Formula

V = 2 U / Q

Substitution

V = (2 × 0.45) / 0.015

Result

V = 60 V

If 15 mC of charge stores 0.45 J, the capacitor voltage magnitude is 60 V.

Applications

01Estimating pulse or flash energy available from a charged capacitor
02Checking capacitor sizing for defibrillator, ignition, or energy-storage examples
03Solving textbook capacitor problems from any equivalent energy relation

Assumptions

01The capacitor is modeled as an ideal lumped element with a single capacitance value.
02Voltage and charge are treated as magnitudes; plate polarity and sign convention are not tracked.
03The reported energy is the electrostatic energy stored at the stated operating point.

Where This Model Stops

01Does not model ESR, leakage current, dielectric absorption, temperature effects, or capacitor aging.
02Does not check component voltage rating, ripple current, transient charging losses, or dielectric breakdown risk.
03Does not size bleeder resistors, discharge time, inrush limiting, series-balancing resistors, or capacitor-bank fault energy.
04Not intended for AC reactance, RC timing, or full capacitor-bank balancing problems.

References

[1]
8.3 Energy Stored in a Capacitor - University Physics Volume 2
OpenStax
Derives U = 1/2 CV² and gives the equivalent forms U = Q²/(2C) and U = 1/2 QV.
[2]
Energy Stored on a Capacitor
HyperPhysics, Georgia State University
Summarizes the equivalent ideal-capacitor energy expressions and links the energy to the electric field.

Frequently Asked Questions

Why are there three capacitor-energy formulas?

They are all equivalent. Starting from Q = CV, you can substitute between charge, capacitance, and voltage to rewrite the same stored-energy relation as U = 1/2 C V², U = Q²/(2C), or U = 1/2 QV.

Why does doubling voltage increase energy fourfold?

Because voltage is squared in U = 1/2 C V². If capacitance stays the same, doubling V makes V² four times larger, so the stored energy becomes four times larger as well.

Why does the calculator use charge and voltage magnitudes only?

Stored energy is always non-negative. The sign of plate charge or terminal polarity matters for circuit convention, but the amount of energy stored depends on the magnitudes in these ideal formulas.

How is this different from the RC Time Constant Calculator?

This page calculates the energy stored at a voltage. The RC Time Constant Calculator estimates how quickly a resistor-capacitor circuit charges or discharges toward that voltage.

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