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General

Capacitor Energy & Charge Calculator

Calculate capacitor energy (E = 1/2·CV²), stored charge (Q = CV), and average charging current. Enter capacitance in μF and voltage — get energy in mJ, charge in mC, and power instantly.

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Formula

E=1/2⋅CV2,Q=CV,Iavg=Q/tE = 1/2·CV², Q = CV, I_avg = Q/t

Reference: Horowitz & Hill, The Art of Electronics

E— Stored energy (J)
C— Capacitance (F)
V— Voltage across capacitor (V)
Q— Stored charge (C)
I_avg— Average charge current (A)
t— Charge time (s)

How It Works

Capacitor energy calculator computes stored energy using E = ½CV² — essential for power supply hold-up time, energy harvesting systems, and transient suppression design. Power electronics engineers, embedded system designers, and automotive engineers use this to size bulk capacitors, supercapacitors, and energy storage banks. Per Horowitz & Hill 'Art of Electronics' (3rd ed., p.39), energy storage increases quadratically with voltage — doubling voltage quadruples stored energy, making voltage rating selection critical. Standard aluminum electrolytics provide 0.1-1 J/cm³ energy density; supercapacitors achieve 1-10 J/cm³ (10× improvement) at the cost of lower voltage ratings (2.7V typical vs. 400V+ for electrolytics). Energy discharge follows τ = RC, with 63% energy released in one time constant.

Worked Example

Design hold-up capacitance for a 12V/5A power supply requiring 20ms ride-through during input brownout. Energy needed: E = P × t = 60W × 0.020s = 1.2J. Minimum voltage at end of hold-up: 10V (allowing 83% regulation). Using E = ½C(V₁² - V₂²): 1.2J = ½ × C × (144 - 100), so C = 1.2 / 22 = 54.5mF. Select 68mF (E6 series) electrolytic capacitor rated for 16V minimum. Verify ESR: typical 68mF/16V capacitor has ESR of 20-50mΩ per manufacturer datasheet — at 5A load, this causes 100-250mV ripple. For automotive applications, this design meets ISO 7637-2 cranking transient requirements.

Practical Tips

  • ✓For hold-up time calculations, use voltage range V₁ to V₂ in E = ½C(V₁² - V₂²) — this accounts for minimum regulator input voltage requirement
  • ✓Select capacitors with ESR < V_ripple_max / I_load — for 5A load with 100mV allowed ripple, ESR must be below 20mΩ
  • ✓Supercapacitors (EDLCs) achieve 3-5 Wh/kg energy density versus 0.01-0.05 Wh/kg for aluminum electrolytics per Maxwell Technologies specifications

Common Mistakes

  • ✗Ignoring ESR losses during rapid discharge — a 100μF capacitor with 1Ω ESR loses 50% of energy as heat when discharged through a 1Ω load per P = I²R
  • ✗Using voltage rating equal to operating voltage — capacitors derate to 50% capacitance at rated voltage; design for 60-80% of rated voltage per JEDEC guidelines
  • ✗Neglecting leakage current in long-duration storage — aluminum electrolytics leak 0.01CV μA (typical), draining 10% charge in 100-1000 seconds

Frequently Asked Questions

E = ½CV² where C is capacitance in farads, V is voltage. A 1000μF capacitor at 50V stores E = 0.5 × 0.001 × 2500 = 1.25J. For comparison, a AA battery stores ~14,000J — capacitors are suited for short-duration, high-power applications.
Capacitance and voltage are primary factors — energy scales linearly with C but quadratically with V. A 100μF/100V capacitor stores 4× the energy of a 100μF/50V capacitor. Temperature affects capacitance: aluminum electrolytics lose 20-40% capacitance at -40°C per EIA-198-E.
For durations under 1 minute, supercapacitors compete with batteries at 10-100× higher power density (10kW/kg vs 0.3kW/kg for Li-ion). Supercapacitors offer 500,000+ cycles versus 500-2000 for Li-ion per Maxwell datasheet. Energy density remains 10-20× lower than batteries.
Per JEDEC JESD35, aluminum electrolytics lose 50% capacitance after 5,000-10,000 hours at rated temperature. Each 10°C above rated temperature halves lifetime (Arrhenius model). At -40°C, capacitance drops 20-40% and ESR increases 5-10×.
Charge Q = CV (coulombs) represents stored electrons; energy E = ½CV² (joules) represents work capacity. A 1F supercapacitor at 2.7V holds 2.7C charge but only 3.6J energy — the energy-to-charge ratio increases with voltage.

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