Enter each capacitance as a numerical value in microfarads (µF), from 0.001 to 1,000,000. Enter the voltage magnitude across the complete network in volts (V), from 0 to 1,000. These are calculation bounds, not component ratings. All three capacitors must be present and have positive capacitance.

The results compare connecting the same three capacitors entirely in series or entirely in parallel, using the same total voltage. Stored energy is reported in microjoules (µJ); divide by 1,000,000 to obtain joules.

The calculator uses normalized numerical inputs: c = C/(1 µF) and v = V/(1 V). Enter only the numerical values in these fixed units; unit conversion is not automatic.

\[C_{\mathrm{s}}=\left(\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}\right)^{-1},\qquad C_{\mathrm{p}}=C_1+C_2+C_3\]
\[E=\frac{1}{2}C_{\mathrm{eq}}V^2,\qquad \frac{E}{1\,\mu\mathrm{J}}=\frac{1}{2}\frac{C_{\mathrm{eq}}}{1\,\mu\mathrm{F}}\left(\frac{V}{1\,\mathrm{V}}\right)^2\]

For initially uncharged ideal capacitors with isolated intermediate junctions, series capacitors carry equal charge magnitude: Q = Cs × V. Each capacitor then has voltage Vi = Q/Ci = (Cs/Ci) × V. A smaller capacitance receives a larger voltage; equal voltage division requires equal capacitances. In parallel, every capacitor has the full applied voltage.

This model excludes leakage effects, balancing resistors, capacitance tolerances, dielectric losses and parasitic resistance or inductance. It does not predict long-term voltage sharing in a real series bank or determine permissible operating voltage. Results describe stored energy, not charging losses.

Zero total voltage gives zero stored energy. A result marked unavailable is not zero; invalid arithmetic or a numeric-range failure can make dependent outputs unavailable.

Worked examples using the same total voltage for both connections
C1, C2, C3 (µF)Total voltage (V)Series capacitance (µF)Parallel capacitance (µF)Series energy (µJ)Parallel energy (µJ)
10, 20, 30125.4545454560392.727272734320
6, 6, 6921881729
10, 20, 3005.454545456000

For 10, 20 and 30 µF, Cs = 1/(1/10 + 1/20 + 1/30) = 60/11 µF, while Cp = 60 µF. At 12 V, series energy is ½ × (60/11) × 12² = 392.72727273 µJ; parallel energy is ½ × 60 × 12² = 4,320 µJ.

Ideal series voltages are approximately 6.545455 V, 3.272727 V and 2.181818 V, which sum to 12 V. For the equal-capacitance example, each series capacitor has 3 V across it.

Formula sources

  1. OpenStax, University Physics Volume 2, section 8.2: series and parallel capacitance and equal-charge voltage division.
  2. OpenStax, University Physics Volume 2, section 8.3, equation 8.10: stored capacitor energy.

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