How do multi-meters measure capacitance?

Many multimeters have the ability to measure capacitance along with the ability to measure AC voltage, DC voltage, current, resistance ... The only equations I am aware of that determine capacitance at least for parallel plate capacitors are:

$$\begin{equation} C=\frac{Q}{V} \;\; \& \;\; C=\frac{\epsilon A}{d} \end{equation}$$

The only method I can think of is that the meter somehow measures the charge in the plate and then subsequently measures the potential difference. If anyone knows of a more detailed explanation I would be happy to hear it.

• You are basically right. The meter feeds a known current into the capacitor for a known length of time (i.e.it puts a known amount of charge into the cap) and then measures the voltage across the plates. In practice, it charges and discharges the capacitor repeatedly, rather than just making a single measurement. There are other methods, but if you haven't studied AC circuits yet an explanation of how they work would be too long for an answer here. – alephzero Nov 9 '18 at 14:24