Capacitors in Series & Parallel + Energy Calculator

Understanding the capacitors in series and parallel calculator — concept and principle

This calculator combines several capacitors into one equivalent value for a parallel bank and a series string, and shows the energy and charge the parallel bank stores at a given voltage. Use it to build a value you do not have, size a filter bank, or check how much energy a bank holds before you touch it.

How it is calculated

• Parallel: C_par = C₁ + C₂ + … + Cₙ. Capacitances simply add.
• Series: 1/C_ser = 1/C₁ + 1/C₂ + … + 1/Cₙ. The result is always smaller than the smallest capacitor.
• Energy (parallel): E = ½ · C_par · V², with C converted from µF to farads (× 10⁻⁶), giving joules.
• Charge (parallel): Q = C_par · V. With C in µF and V in volts, Q comes out in microcoulombs (µC).

Enter the capacitances as a comma-separated list in µF and the voltage in volts.

The principle

A capacitor stores charge Q = CV. In parallel, every capacitor sees the same voltage, so their charges add: Q = (C₁ + C₂ + …)V, and the total capacitance is the sum. In series, the same charge Q sits on every capacitor, while the voltages add: V = Q/C₁ + Q/C₂ + … . Dividing by Q gives the reciprocal sum. The energy formula ½CV² comes from integrating the work needed to push each extra bit of charge against the voltage already built up, which grows linearly from 0 to V.

Worked example

1. Inputs: capacitors 10, 22 and 47 µF; voltage 12 V.
2. Parallel: 10 + 22 + 47 = 79 µF.
3. Series: 1/10 + 1/22 + 1/47 = 0.1 + 0.045455 + 0.021277 = 0.166731 per µF, so C = 1 ÷ 0.166731 ≈ 5.9977 µF.
4. Energy: ½ × 79 × 10⁻⁶ F × 12² = 0.5 × 79 × 10⁻⁶ × 144 = 0.005688 J (5.688 mJ).
5. Charge: 79 µF × 12 V = 948 µC.

How to read the result

A parallel bank is larger than any single part; a series string is smaller than the smallest part. Energy grows with the square of voltage, so doubling the voltage stores four times the energy. Large electrolytic banks at hundreds of volts can store tens to hundreds of joules and give a dangerous shock.

Common mistakes

• Swapping the rules: capacitors add in parallel, unlike resistors, which add in series.
• Forgetting the µF to F conversion, which makes the energy a million times too large.
• In a series string, assuming the voltage divides equally. It divides in inverse proportion to capacitance, so the smallest capacitor takes the largest share and may exceed its rating.

Frequently asked questions

Why would I put capacitors in series?

To obtain a higher voltage rating or a smaller value than you have available. The working voltage of the string can be higher, but only if the voltages are kept balanced.

What happens to the energy if I connect two capacitors charged to different voltages?

The charge redistributes to a common voltage and some energy is lost as heat and radiation in the wires, even though the total charge is conserved.

Sources: D. Halliday, R. Resnick and J. Walker, Fundamentals of Physics, Wiley, chapter on capacitance · P. Horowitz and W. Hill, The Art of Electronics, 3rd ed., Cambridge University Press