Capacitor Stored Energy Calculator
Solve E = ½ · C · V² in any direction — stored electric-field energy from capacitance and voltage, or work backwards to find C or V. Includes a circuit diagram, the characteristic parabolic E-vs-V curve, step-by-step math, and tolerance sensitivity.
A voltage V across the capacitor pushes charge onto the plates, creating an electric field E between them. That field stores energy proportional to the capacitance C and to the square of the voltage V — so doubling the voltage quadruples the energy, even at the same capacitance.
V ↑ — quadratic growth
Energy scales with the square of voltage. Doubling V quadruples E; tripling V multiplies E by nine. This is why high-voltage energy storage is compact but dangerous — small voltage increases carry outsized energy costs.
C ↑ — linear growth
At fixed voltage, energy scales linearly with capacitance. A 2× larger capacitor stores exactly 2× the energy, and a 10× larger one stores 10× the energy.
The ½ factor
The ½ comes from integrating the instantaneous power p = C·v·(dv/dt) as the voltage ramps from 0 to V. Charging a capacitor from a fixed supply dissipates an equal amount of energy as heat in the charging path — the 50% charging loss that trips up first-time designers.
Dielectric & voltage ratings matter
Real capacitors have a maximum working voltage. Above it, the dielectric breaks down and the part fails — often short-circuit. The formula assumes the dielectric behaves linearly, which fails near the breakdown voltage.
How to Use This Calculator
The capacitor energy relation links three quantities: capacitance C, voltage V, and the stored electrostatic energy E = ½ · C · V². Pick which one you want the tool to solve, fill in the other two, then press Calculate.
1. Choose what to solve for
Pick E (stored energy from C and V), C (capacitance from E and V), or V (voltage from E and C) — the tool rearranges the formula automatically.
2. Pick a preset, or type your own values
Use the quick pills (1 nF → 1 mF, 100 mV → 1 kV, 1 nJ → 100 J) or type any custom value and choose its unit from the dropdown.
3. Press Calculate — the result takes focus
Clicking Calculate scrolls the result panel into view, focuses it for keyboard and screen-reader users, and pulses a highlight ring so your eye lands on the answer immediately.
4. Study the energy curves
The chart plots E versus V as a parabola and E versus C as a straight line, both with the current operating point marked. The parabola is the visual reason voltage dominates the energy budget.
5. Switch to Advanced for more depth
Advanced mode adds a tolerance sensitivity panel (why ±1% in V is worse than ±1% in C) plus companion metrics like charge Q, equivalent inductor current, electron count, and energy at 2× voltage.
6. Convert energy to other forms, or copy the result
Use the energy converter further down the page to express the result in joules, watt-seconds, or as a comparison to a small coin-cell battery's capacity.
What This Tool Offers
Built around the fundamental capacitor energy relation E = ½ · C · V², the electric-field result behind every energy-storage bank, snubber, defibrillator, camera flash, and bulk-decoupling calculation in electronics.
Solve all three directions
Go from C and V to E, from E and V to C, or from E and C to V — the formula is rearranged for you.
Full SI unit handling
Enter capacitance in nF → F, voltage in mV → kV, and energy in nJ → kJ. The solver auto-picks the cleanest display unit.
Focus-to-result on Calculate
Pressing Calculate scrolls the result into view, focuses it for accessibility, and plays a teal pulse so the answer is impossible to miss.
Parabolic & linear charts
See E vs V as a parabola and E vs C as a straight line, both live at your current operating point — the visual proof that voltage dominates.
Annotated field diagram
A labelled capacitor schematic with plate charges, electric field lines, and the energy formula, so you can see where the ½CV² comes from.
Companion energy metrics
Advanced mode reports charge Q = CV, energy at 2× voltage (4×), voltage for 2× energy (×√2), capacitance for 2× energy (×2), and electron count.
Reference Tables & Conversions
An energy converter, plus lookup tables for typical capacitor energies, energy vs. voltage for common capacitors, and equivalent expressions for E.
Energy unit converter
Typical Stored Energy in Real Capacitors
Representative values across common component classes. Note the enormous spread — the energy in a high-voltage pulse capacitor is many orders of magnitude above the energy in a signal-path capacitor.
| Capacitor | C | V | E = ½CV² | Typical application |
|---|---|---|---|---|
| Signal / RF cap | 100 pF | 10 V | 5 nJ | Coupling, tuning |
| Decoupling cap | 100 nF | 5 V | 1.25 µJ | IC power-rail bypass |
| Bulk decoupling | 10 µF | 12 V | 720 µJ | Supply smoothing |
| Camera flash (small) | 100 µF | 300 V | 4.5 J | Compact flash tube |
| Photoflash cap | 1000 µF | 350 V | 61 J | SLR flash |
| Defibrillator | 100 µF | 2000 V | 200 J | Medical pulse delivery |
| Railgun bank (single) | 1 mF | 10 kV | 50 kJ | Pulsed power |
| Grid-storage module | 100 F | 700 V | 24.5 MJ | Grid-scale supercapacitor |
Energy vs. Voltage — Same Capacitor
A 100 µF capacitor across its voltage range. Because energy scales with V², the last few volts hold most of the energy.
| Voltage V | E for C = 100 µF | Relative to 10 V |
|---|---|---|
| 5 V | 1.25 mJ | 0.25× |
| 10 V | 5 mJ | 1× |
| 20 V | 20 mJ | 4× |
| 50 V | 125 mJ | 25× |
| 100 V | 500 mJ | 100× |
| 200 V | 2 J | 400× |
Equivalent Expressions for Capacitor Energy
The same stored energy viewed through different electrostatic quantities — all equivalent at the terminals.
| Form | Expression | When it's useful |
|---|---|---|
| Voltage form | E = ½ · C · V² | Circuit-level calculations |
| Charge form | E = ½ · Q · V | Known charge, Q = C·V |
| Charge/capacitance | E = Q² / (2C) | When charge is known |
| Field density | E = ∫ (½ ε E²) dV | Dielectric / plate-area design |
What Does E = ½ · C · V² Measure?
It measures the electrostatic energy stored in a capacitor while voltage V appears across it. Unlike an inductor, which stores energy in a magnetic field surrounding its windings, a capacitor stores energy in the electric field between its plates. That energy is what supplies current when the source is removed, what drives a camera flash, and what makes touching a charged high-voltage capacitor dangerous even after power is cut.
The Capacitor Energy Formula
The defining relationship is:
Rearranged for the other two unknowns:
Where the ½ comes from integrating the instantaneous power delivered to the capacitor as its voltage ramps from 0 to V:
Capacitor Energy Variables
| Symbol | Meaning | Unit |
|---|---|---|
| E | Energy stored in the electric field | joules (J) |
| C | Capacitance | farads (F) |
| V | Voltage across the capacitor | volts (V) |
| Q | Charge stored, Q = C · V | coulombs (C) |
| Ef | Electric field strength in the dielectric | V/m |
Why Voltage Dominates the Energy
Capacitance enters the formula linearly but voltage enters as a square. This has practical consequences. Doubling the capacitance doubles the stored energy, but doubling the voltage quadruples it. Tripling the voltage makes stored energy nine times larger. That's why high-voltage capacitor banks are the compact-but-dangerous solution when large amounts of energy must be stored in a small volume — and why safety rules around them are so strict.
It's also why capacitor charging is only 50% efficient when done through a resistor from a fixed supply. The supply delivers C·V² of energy while the capacitor stores ½·C·V². The other half is dissipated as heat in whatever resistance is in the charging path, regardless of how small that resistance is. This "50% rule" is why switched-mode charging topologies exist for energy-critical applications.
Capacitor Energy Calculation Examples
C = 1 × 10⁻⁴ F · V = 10 V
E = ½ × 1 × 10⁻⁴ × 10²
E = 5 × 10⁻³ J = 5 mJ
C = 2 × 4.5 / 300²
C = 9 / 90,000
C = 1 × 10⁻⁴ F = 100 µF
V = √( 2 × 200 / 1 × 10⁻⁴ )
V = √( 4,000,000 )
V = 2,000 V
Frequently Asked Questions
It falls out of the integration. Power delivered to the capacitor is p = C·v·(dv/dt), and total energy is that integrated from v = 0 up to v = V. The integral of v·dv is v²/2, evaluated at V — giving ½·C·V². The same ½ appears in the inductor formula ½LI², because the underlying mathematics of ramping a linear element from zero to a final value is identical.
When a capacitor is charged from a fixed-voltage supply through any resistance, the supply delivers total energy C·V² — but only ½·C·V² ends up stored on the capacitor. The other half is dissipated as heat in the resistance, regardless of how small that resistance is. This "50% charging loss" is fundamental to the RC charging topology and is a classic exam-style gotcha. Switched-mode charging circuits exist specifically to dodge this limit.
Not directly — E = ½CV² only cares about the values C and V. But the shape determines C, so it matters indirectly. C = ε·A/d, where A is plate area, d is plate separation, and ε is the dielectric permittivity. Given a fixed voltage, a larger C (bigger plates, closer together, or a higher-ε dielectric) stores more energy.
Wherever the circuit routes it — that's the design question. In a camera flash, it discharges through a xenon tube as light. In a defibrillator, it discharges through the patient as a controlled current pulse. In a discharge through a resistor, it becomes heat. In a boost converter's switched-capacitor stage, it can be recycled back to the source. Unlike inductors, capacitors don't produce a dangerous voltage spike when disconnected — they just hold their charge until something provides a discharge path.
Both have the form ½·X·Y², but the variables differ: a capacitor stores ½CV² in an electric field, and an inductor stores ½LI² in a magnetic field. The capacitor is the "dual" of the inductor — voltage plays the role current plays, and capacitance plays the role inductance plays. Field energetics are otherwise parallel.
Substituting Q = C·V into E = ½CV² gives E = ½·Q·V, and substituting V = Q/C gives E = Q²/(2C). All three forms — ½CV², ½QV, Q²/(2C) — describe the same physical energy in different variables. Which one is convenient depends on which two quantities you already know.
Below its rated voltage, yes — to a very good approximation. Unlike ferromagnetic-core inductors, most capacitor dielectrics behave quite linearly right up to their rated voltage. Above the rated voltage, the dielectric can break down and the part usually fails short-circuit. Electrolytic capacitors also have significant leakage, so a charged electrolytic will slowly self-discharge; the formula describes the energy at the moment of charge, not indefinitely afterward.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| E | Energy | J |
| C | Capacitance | F |
| V | Voltage | V |
What it means
The energy stored in a capacitor is given by E = ½ C V², where C is the capacitance and V is the voltage across it. This energy is stored in the electric field between the plates. The formula shows that the energy depends on the square of the voltage, so doubling the voltage quadruples the stored energy. Capacitors are used as energy storage elements in power supplies, flash tubes, and dynamic memory cells. In circuits, the stored energy can be released rapidly, making capacitors useful for pulse power applications. The energy density of capacitors is much lower than batteries, but they offer much faster charge/discharge rates. Understanding the energy stored is crucial for sizing capacitors in DC‑DC converters and for ensuring safety, as charged capacitors can deliver a dangerous shock. Example: A 100µF capacitor charged to 50V stores E = 0.5 * 100e-6 * 50² = 0.5 * 100e-6 * 2500 = 0.125 joules (125 mJ).
Worked example
Energy Stored in a Capacitor – Practical Example
Real‑World| Parameter | Value |
|---|---|
| C | 1000 µF = 1×10⁻³ F |
| V | 12 V |
| Formula | E = ½·C·V² |
Common mistakes
- Units: C in farads, V in volts → E in joules.
- Energy stored: It is proportional to the square of the voltage – doubling voltage quadruples energy.
- Instantaneous: This is the energy stored at a given voltage.
- Alternative: E = ½·Q·V = Q²/(2C) – useful when charge is known.
- Sign: Energy is always positive.
Applications
Energy stored in a capacitor is E = ½·C·V², which depends on capacitance and the square of voltage. This energy is stored in the electric field between the plates and is released during discharge. Engineers use this formula to design energy‑storage capacitors, to calculate the energy available for pulsed applications, and to ensure that capacitors are safely discharged. In power supplies, the stored energy is used to smooth rectified waveforms. In defibrillators, it is the energy delivered to the patient. By understanding the energy relationship, professionals can select capacitors with adequate energy rating and predict performance. This formula is essential for capacitor selection and safety.
- Capacitor selection for energy storage applications
- Power supply filtering and bulk capacitance sizing
- Pulsed power systems (defibrillators, flash lamps)
- Energy harvesting and storage circuits
- Safety discharge calculations for service personnel
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