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Energy-Based Capacitance, Voltage and Stored Energy

Solve ideal capacitance, voltage magnitude or stored electrical energy with editable results, joule and watt-hour units, and farad prefixes.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

An ideal capacitor storing 0.002 joules at 10 volts has capacitance 0.00004 farads, or 40 microfarads.

E = ½CV²; C = 2E/V²; V = √(2E/C), choosing the positive voltage magnitude.

Worked example

Enter these known values and leave the other values blank.

Stored electrical energy
0.002 J
Voltage magnitude across capacitor
10 V
Ideal capacitance
0.00004 F

Assumptions and limitations

  • The capacitor is ideal with constant capacitance, and E is its stored electrical field energy at the evaluated voltage. The relation describes the capacitor state, not the total energy a real charging circuit draws from its source.
  • Voltage is the positive magnitude across the capacitor at the evaluated instant. The square-root inverse selects that positive magnitude. An AC RMS voltage is not automatically the instantaneous or peak capacitor voltage.
  • Enter any two known quantities and leave the third blank. All three are editable, with independent unit selectors and locks. Unit changes preserve the physical quantity.
  • This energy-based relation alone does not select an AC motor start or run capacitor. Motor characteristics, operating frequency, circuit conditions and component ratings require a separate selection method.
  • Joules and watt-hours both measure energy: 1 Wh = 3,600 J and 1 kWh = 3,600,000 J. Watt-hours are not watts of power. Voltage and farad prefixes use their exact decimal factors.
  • The captured positive-only model rejects zero or negative energy, voltage magnitude and capacitance. Zero-state inverse ambiguities are not supplied as finite results.
  • Losses, resistance, leakage, voltage-dependent capacitance, tolerances and dielectric breakdown are outside this ideal stored-energy relation. Locked inconsistent states are reported.

Common questions

Can I recover voltage from energy and capacitance?

Yes. Enter positive energy and capacitance and leave voltage blank. The inverse returns the positive magnitude √(2E/C).

Does doubling voltage double stored energy?

At fixed ideal capacitance it multiplies energy by four because energy depends on the square of voltage.

Can I use watt-hours instead of joules?

Yes. Both are energy units. One watt-hour equals 3,600 joules; the selector handles the conversion before solving.

Does this determine an AC motor’s start or run capacitor?

No. It calculates capacitance from a chosen ideal stored-energy and voltage state. It does not model a motor’s AC winding, frequency, phase shift or component selection requirements.

References

Use exact-sign positivity for energy, capacitance and voltage magnitude. Preserve the original strictly positive physical domain without treating extremely small positive quantities as zero.

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