capacitors in series calculator

What this capacitors in series calculator does

This tool finds the equivalent capacitance for any number of capacitors connected in series. In a series connection, the reciprocal capacitances add together, which means the total capacitance always ends up smaller than the smallest individual capacitor.

If you include an applied voltage, the calculator also estimates:

• Total charge stored in the series string
• Total energy stored
• Voltage across each capacitor

Formula for capacitors in series

The governing equation is:

Then:

• C_eq = equivalent capacitance (farads)
• Q = C_eqV (charge, coulombs)
• E = 0.5 C_eqV² (energy, joules)

Two-capacitor shortcut

For exactly two capacitors, you can also use:

That shortcut is fast for hand calculations, but the full reciprocal method works for any number of components.

How to use this calculator

Step-by-step

• Enter each capacitance value and select its unit.
• Add more capacitors as needed.
• Optionally enter source voltage.
• Click Calculate to get results instantly.

Use Reset to clear all values and start over.

Worked example

Suppose you have three capacitors in series: 10 µF, 22 µF, and 47 µF with a 12 V source.

• Convert to farads (or keep in µF consistently): reciprocal sum = 1/10 + 1/22 + 1/47
• C_eq ≈ 5.98 µF
• Q = C_eqV ≈ 71.8 µC
• Each capacitor sees a different voltage, with the smallest capacitor seeing the highest voltage

This is exactly why balancing and voltage rating checks matter in real designs.

Important design notes

1) Equivalent capacitance always decreases

In series, the electric field must satisfy each dielectric layer in sequence, effectively reducing charge storage ability versus any single capacitor alone.

2) Voltage rating is critical

Even if total source voltage seems safe, one capacitor may be overstressed due to tolerance and leakage differences. Always verify per-capacitor voltage in practical circuits.

3) Unit consistency prevents mistakes

Common unit conversions:

• 1 mF = 10^-3 F
• 1 µF = 10^-6 F
• 1 nF = 10^-9 F
• 1 pF = 10^-12 F

Common errors to avoid

• Adding capacitances directly (that is only for parallel)
• Mixing units without conversion
• Ignoring capacitor voltage ratings
• Assuming identical voltage split when capacitor values differ

Quick FAQ

Can I use one capacitor in this tool?

Series calculations are most meaningful with at least two capacitors. This calculator enforces that setup.

Why does the smallest capacitor get the biggest voltage?

In series, all capacitors carry equal charge. Since V = Q/C, smaller C gives larger V.

Is this useful for high-voltage stacks?

Yes, but real high-voltage designs typically require balancing resistors and careful tolerance analysis beyond the ideal math.