Energy Storage in a Capacitor — Formula, Examples & PV Reference
Energy storage capacitor reference: the ½·C·V² formula that governs every capacitive energy storage system from a 1 µF coupling capacitor to a megajoule pulsed-power bank, the trade-offs between capacitors as energy storage vs batteries (cycle life vs energy density), the role of the DC-link capacitor in a solar PV inverter, and the standard equation for solar energy buffering. Reviewed by a licensed PE.
Capacitor energy calculator
The embedded calculator covers every capacitive energy storage workflow: enter capacitance and voltage to get stored energy in joules and watt-hours, or solve for the required capacitance given an energy target. For battery-side storage sizing see the related battery calculator and the dedicated battery capacity sizing tool.
The energy-storage formulas
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- E = stored energy in joules (J)
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- C = capacitance in farads (F)
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- V = voltage across the capacitor in volts (V)
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- Q = stored charge in coulombs (C); Q = C · V
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- C_Ah = nameplate capacity in ampere-hours
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- V = nominal voltage
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- For LFP at 80 % DoD: usable Wh = nameplate × 0.8
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- P_rated = panel STC rated power in kWp
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- η = derate (typical 0.75 = inverter loss + soiling + cable + temperature)
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- H_solar = peak-sun-hours per day at site (3.5 in UK, 5–6 in southern US, 7+ in Sahara)
Standards governing energy storage
| Standard / body | Scope |
|---|---|
| IEEE 1547-2018 | Interconnection of distributed energy resources (including BESS) to the utility grid |
| UL 9540 / UL 9540A | Energy storage system safety; thermal-runaway propagation testing |
| NFPA 855 | Installation of stationary energy storage systems — fire and life safety |
| IEC 60896 | Stationary lead-acid battery design, performance, and safety |
| IEC 62619 | Lithium-based stationary battery safety |
| IEC 60384 / EIA-198 | Fixed capacitor specifications and reliability |
| IEEE 1679 | Recommended practice for the characterisation and evaluation of emerging energy-storage technologies |
Reference: energy density across storage technologies
| Technology | Energy density (Wh/kg) | Power density (W/kg) | Cycle life | Round-trip η |
|---|---|---|---|---|
| Ceramic capacitor | ~ 0.0001 | 10⁶ | unlimited | 99 % |
| Electrolytic capacitor | ~ 0.05 | 10⁴ | 10⁵+ | 95 % |
| Supercapacitor (EDLC) | 5–10 | 5 000–10 000 | 10⁶+ | 90–95 % |
| Flywheel | 5–100 | 1 000–10 000 | 10⁵+ | 85 % |
| Lead-acid battery | 30–40 | 75–300 | 500–1 000 | 75–85 % |
| LiFePO₄ (LFP) | 90–160 | 200–500 | 3 000–5 000 | 90–95 % |
| NMC / NCA Li-ion | 200–270 | 500–2 000 | 1 000–2 000 | 90–95 % |
| Solid-state Li (emerging) | 300–500 (target) | ~ 2 000 | 10 000+ | 90–95 % |
| Pumped hydro | ~ 0.3 (incl. reservoir mass) | N/A | unlimited | 70–85 % |
| Compressed-air (CAES) | 5–60 (incl. cavern) | N/A | unlimited | 40–70 % |
- Identify the load and the duty profile. Decide what the storage must deliver: short pulse (capacitor / supercap, milliseconds to seconds), bridging (battery, minutes to hours), long-duration (battery bank, hydro, CAES, days). The duty profile sets the technology.
- Compute the energy required. Energy = power × time. A 1 kW load for 4 hours = 4 kWh. For a single-shot pulse: E = ½ · C · V² (capacitor) or E = m · c · ΔT (thermal). Convert all numbers to consistent SI units (joules) before sizing.
- Pick the storage technology by energy density and cycle life. Energy density (Wh/kg): supercap 5–10, lead-acid 30–40, LFP 90–160, NMC 200–270, Tesla pack 250+. Cycle life: supercap 1 000 000+, lead-acid 500–1 000, LFP 3 000–5 000. Pick the chemistry whose Wh/kg meets the size budget AND whose cycles meet the replacement budget.
- Size the storage element. For a capacitor: C = 2·E / V². For a battery: nameplate Ah = (load_W × hours) / V / DoD, then add a 20–25 % safety margin. Round up to standard module sizes (100 Ah / 200 Ah / 400 Ah modules; standard capacitor values per IEC 60063).
- Add power-electronics interface. Capacitor banks need a controlled discharge resistor or current-limited driver. Battery banks need a charger / inverter / BMS. Supercaps in vehicle KERS need a DC-DC converter to match the bus voltage.
Worked example — DC-link capacitor for a 5 kW solar PV inverter
A residential 5 kW string inverter uses a DC-link capacitor between the MPPT stage and the H-bridge to absorb the 100 Hz (or 120 Hz in 60 Hz mains) ripple from single-phase output. Required: keep DC bus ripple ≤ ±5 % around 400 V nominal.
Step 1 — peak ripple energy: ΔE per half-cycle = P × T/2 = 5 000 × (0.01 / 2) = 25 J at 50 Hz mains.
Step 2 — relate to capacitor parameters: ΔE = ½·C·(V_max² − V_min²) = ½·C·(420² − 380²) ≈ ½·C·32 000 = 16 000·C.
Step 3 — solve for C: C = 25 / 16 000 = 1.56 × 10⁻³ F = 1 560 µF.
Step 4 — pick the part: choose a 2 200 µF, 450 V electrolytic (e.g. Nippon Chemi-Con KMR series) for ~ 40 % design margin. Verify ripple-current rating ≥ 8 A RMS at 100 Hz.
Step 5 — verify life: at 65 °C ambient and 6 A ripple, a 105 °C electrolytic lasts ~ 50 000 hours = 5.7 years continuous, ≥ 10 years at typical 50 % duty. Acceptable for the 10-year warranty class of residential PV inverters.
Capacitor vs battery vs flywheel — when each one wins
| Use case | Best technology | Why |
|---|---|---|
| Camera flash, defibrillator | Capacitor (electrolytic) | Millisecond pulse; needs high power, low energy |
| Vehicle KERS / regen braking | Supercapacitor | 10⁶ cycle life; seconds-scale energy capture |
| UPS bridging (5 min) | Battery (sealed lead-acid or LFP) | Watt-hours per kg matter more than peak power |
| Off-grid solar 1–5 day storage | LFP battery bank | Cycle life × DoD economics dominate |
| Grid-scale 4 hour storage | BESS (LFP) — Tesla Megapack class | Modular, fast-deploy, falling cost |
| Grid-scale 8+ hour storage | Pumped hydro (where geography permits) | $/kWh much lower at long durations |
| Grid-scale frequency response | Supercap or BESS in fast-response mode | Sub-second response time |
Variants and edge cases
Energy — units and conversions
Energy is measured in joules (J) in SI and in watt-hours (Wh) in electrical practice. 1 Wh = 3 600 J; 1 kWh = 3.6 MJ. For comparison: 1 g of TNT releases 4.184 kJ; 1 g of gasoline 47 kJ; 1 kg of LFP battery 320–580 kJ. The energy in 1 litre of diesel ≈ 38 MJ, equivalent to ~ 10.5 kWh — about 10 % of a Tesla Model 3 75 kWh pack.
Solar PV systems and the energy storage capacitor
Every grid-tie solar PV inverter uses a capacitive energy storage stage on its DC bus to handle the 100 Hz / 120 Hz ripple inherent in single-phase output. The same capacitor also rides through brief grid sags (10–100 ms). For three-phase inverters the ripple is much smaller (300 Hz / 360 Hz) so the DC-link capacitance can drop by 5–10×. Off-grid solar PV systems add a battery-side BESS for true 24-hour energy storage.
Pulsed-power capacitor banks
For high-power pulsed applications — railguns, plasma research, electromagnetic forming — capacitor banks at 50–100 kV reach megajoules per cabinet. The Z Machine at Sandia uses a 36-bank Marx generator storing 22 MJ at 80 kV for inertial-confinement fusion experiments. Energy storage scaling: E = ½·C·V² makes voltage the dominant variable — doubling V quadruples stored energy.
Frequently asked questions
- How is energy storage in a capacitor calculated?
- The energy storage of a capacitor is given by E = ½ · C · V², where C is capacitance in farads and V is voltage in volts. A 1 000 µF capacitor at 400 V stores ½ × 0.001 × 160 000 = 80 J. Capacitive energy storage scales with the square of voltage, so doubling V quadruples stored energy — for the same C. This is why high-voltage pulsed-power capacitors at 50–100 kV reach megajoules per cabinet.
- Why are capacitors used as energy storage instead of batteries?
- Capacitors as energy storage win on power density and cycle life: a supercapacitor releases its full charge in milliseconds (10⁵+ W/kg) and survives a million-plus charge-discharge cycles, while batteries deliver their energy slowly (10²–10³ W/kg) and last hundreds-to-thousands of cycles. The trade-off is energy density: a battery stores 50–100× more energy per kilogram. Hybrid storage (battery + supercap) gets both — a battery for endurance, a capacitor for peak power.
- What is the equation for solar energy stored in a capacitor?
- The equation for solar energy stored in a capacitor is the same as any capacitor: E = ½ · C · V². In a solar PV system, the DC-link capacitor on the inverter buffers the gap between the panel's instantaneous output and the inverter's 50/60 Hz output. The capacitor is sized so the bus-voltage ripple stays below ±5 % at the worst-case load — typically a few mF for a 5 kW residential string inverter.
- What does passive energy meaning refer to?
- In storage terminology, "passive" energy meaning is contrasted with "active": passive storage holds energy without conversion or active control (a charged capacitor, a flywheel, a thermal mass), while active storage converts energy on demand (a battery via electrochemistry, pumped hydro via a turbine). Most pulsed-power and ride-through systems use passive storage because no conversion latency is acceptable.
- What is the energy stored in a 1 farad capacitor at 12 V?
- E = ½ × 1 × 12² = 72 joules. By comparison, a 100 Ah lead-acid battery at 12 V holds 100 × 12 × 3 600 = 4.32 megajoules — sixty thousand times more energy. This is why batteries dominate bulk storage and capacitors fill the high-power-pulse niche.
- What is the energy density of a supercapacitor vs a battery?
- Supercapacitor: 5–10 Wh/kg (Maxwell BCAP series), with peak power 5–10 kW/kg. Lithium-ion battery: 200–270 Wh/kg (NMC), with peak power 0.5–2 kW/kg. So a supercap stores 20–30× less energy per kg but delivers 10× more peak power. Used in regenerative braking (Maxwell, Skeleton), grid frequency response (CSIRO Hornsdale supercap+battery), and pulsed-power weapons research.
- How does a battery energy storage system (BESS) compare to capacitive storage?
- A grid-scale BESS (Tesla Megapack, BYD Cube Pro) uses lithium-iron-phosphate batteries to store hundreds of MWh per facility — the dominant grid-scale technology since 2020. Capacitor banks at the same scale would be physically impossible (energy density is too low). Capacitor / supercap installations at the grid scale are limited to ride-through, voltage support, and fast frequency-response duties measured in seconds.
Faraday on the storage of electric charge
The capacity of a conductor for receiving electricity, when other circumstances remain the same, is found to be in proportion to the quantity of insulating matter, or dielectric, interposed between it and surrounding bodies. The amount of electricity which a body can hold for a given degree of intensity, or, as we now express it, for a given electrical tension, depends not on the conductor itself but on the substance separating it from neighbouring conductors.
Related calculators and references
Sources and further reading
- Faraday, M. Experimental Researches in Electricity, Volume I (Series I–XIV). London, 1839. The foundational work on capacitance and dielectrics.
- IEEE. IEEE Std 1547-2018 — Standard for Interconnection and Interoperability of Distributed Energy Resources with Associated Electric Power Systems Interfaces.
- UL. UL 9540 — Standard for Energy Storage Systems and Equipment; UL 9540A — Test Method for Evaluating Thermal Runaway Fire Propagation in Battery Energy Storage Systems.
- NFPA. NFPA 855 — Standard for the Installation of Stationary Energy Storage Systems, 2023 edition.
- Sandia National Laboratories. DOE/EPRI Electricity Storage Handbook, 2020. The reference document for grid-scale storage technology comparison.
- Lawrence Berkeley National Lab. Energy Storage Technology and Cost Characterisation Report, annual update. Technology-by-technology cost and performance benchmarks.