Energy Stored in Capacitor Calculator

Physics Electricity and Magnetism • Electric Potential and Capacitance

Written by STEM Calculators Team Published January 12, 2026 Updated February 24, 2026

8. Energy Stored in Capacitor Calculator

Compute stored energy using $U=\tfrac12CV^2=\tfrac12QV=\dfrac{Q^2}{2C}$ , plus a discharge preview through a resistor and a field-energy-density estimate $u=\tfrac12\,\varepsilon E^2$ .

Inputs support: pi, e, sqrt(), sin, cos, exp, log. Use * for multiplication. Example: 10e-6 means 10 μF.

Mode + Inputs

Mode: Capacitance $C$ (F): Voltage $V$ (V): Charge $Q$ (C): Dielectric handling: Relative permittivity $\kappa=\varepsilon_r$: $\varepsilon_0$ (F/m): Plate area $A$ (m²) [geom]: Separation $d$ (m) [geom / $E=V/d$]: Field magnitude $E$ (V/m) [optional]: Discharge resistor $R$ (Ω): Time $t$ for discharge readout (s): Target energy fraction $f_U=U/U_0$: Discharge plot: Plot variable: Plot span $t_{\max}$ (s): Time cursor $t_c$ (s): Play speed:

Energy bar $U(t_c)/U_0$

If you choose geometry mode, $C_0=\varepsilon_0A/d$ and $C_{\mathrm{eff}}=\kappa C_0$. Otherwise, you may treat $C$ as already effective.

Ready

Steps

Enter values and click Solve.

Discharge plot (pan/zoom)

Drag to pan • wheel to zoom • double-click resets view

Hover: (t, y)=… Cursor: …

The time cursor $t_c$ controls the highlighted point and the energy bar.

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8. Energy Stored In Capacitor Calculator — Theory

1) Stored energy in a capacitor

A capacitor stores electrostatic energy. Common equivalent expressions are:

\[ U=\frac12CV^2=\frac12QV=\frac{Q^2}{2C}. \]

These are equivalent because $Q=CV$.

2) Dielectric effect

Inserting a dielectric increases capacitance by a factor $\kappa=\varepsilon_r$: $C_{\mathrm{eff}}=\kappa C_0$ .

\[ \varepsilon = \kappa \varepsilon_0, \qquad C_{\mathrm{eff}}=\kappa C_0. \]

3) Parallel-plate geometry

For a parallel-plate capacitor (ignoring fringing):

\[ C_0=\varepsilon_0\frac{A}{d}, \qquad C_{\mathrm{eff}}=\kappa \varepsilon_0\frac{A}{d}. \]

4) Discharge through a resistor

A capacitor discharging through a resistor $R$ has time constant $\tau=RC$. The voltage decays exponentially:

\[ \tau = RC, \qquad V(t)=V_0e^{-t/\tau}, \qquad Q(t)=Q_0e^{-t/\tau}, \qquad U(t)=U_0e^{-2t/\tau}. \]

Energy decays twice as fast in the exponent because $U\propto V^2$.

5) Field energy density

The energy density in an electric field is $u=\tfrac12\varepsilon E^2$ . For parallel plates, $E\approx V/d$.

\[ u=\frac12\,\varepsilon E^2, \qquad E\approx \frac{V}{d}. \]

In advanced treatments, total energy can be written as the field integral $U=\dfrac{\varepsilon_0}{2}\int E^2\,dV$ (in vacuum).

Steps

Discharge plot (pan/zoom)

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