The formula
Parallel: C = C₁ + C₂ + … · Series: 1/C = 1/C₁ + 1/C₂ + …
What it means
A capacitor stores charge on the surface of its plates, so putting them in parallel is like widening that surface: the capacitances add. In series the opposite happens, because it is like moving the plates apart: the combination stores less than the smallest one. It is exactly the resistor rule with the roles swapped, and mixing the two up is the most repeated mistake in the topic.
How to work it out by hand
- If they are in parallel, add all the capacitances
- If they are in series, work out the reciprocal of each one
- Add those reciprocals together
- Invert the result: that is the equivalent capacitance
What is worth knowing
In series there is a consequence the formula does not show: the voltage divides between the capacitors in inverse proportion to their capacitance, so the smallest one takes the most voltage and is the first to fail. That is why, when capacitors are put in series to withstand more voltage, they are chosen equal and each gets a resistor in parallel to even the share out.