Why are motor capacitors huge in physical size even though their values are in uF range?

Motor capacitors are not plain electrolytics, because the voltage across them reverses at the mains frequency.

The larger value ones are start capacitors - usually bipolar electrolytic, and rated to the peak mains voltage - but not for continuous operation. They are usually disconnected by a centrifugal switch in the motor, which operates when the motor is up to speed. Consider that not only is the voltage high, and continually reversing, but the ripple current is high too (especially when the motor is still at low speed) and you'll see the apacitor has to handle unusually high power.

Smaller value ones (10s of uF) are used as run capacitors in smaller (less than 1hp) motors. These phase shift the current to the start winding, but remain connected during operation, so must be rated for continuous operation. These are usually film capacitors (or, if old enough, paper in oil) which are much larger per microfarad than an electrolytic.

In my experience the physical size of a capacitor is proportional to the capacitance times its voltage. Double the voltage, double the size.

In practical terms, voltage is higher still.

• AC voltage is RMS (sinewave peaks are somewhat higher than the stated voltage).
• When a motor is disconnected from load, its windings will see an inductive "kick" of potentially even higher voltage. That means a motor capacitor has to put up with a great deal more than 220V for instance.
• Some motors can be cross-wired to be 120V or 240V, so the capacitor has to be rated for 240 even if you are using it 120.

There are several reasons, not all of them strictly technical.

1. Voltage rating is very important. Since motor returns current (regenerates) they (i) take margins on voltage.
2. Current pumped from bulk caps is in pulses, with high frequency. If you will look at cap datasheet, you will see it is rated for certain ripple current- not enough for a serious motor.
3. Heat is generated on capacitor due to ESR, so in bigger capacitor ESR may be lower. Or in several smaller caps...
4. Not least important: you always have to take spare for bigger motors and prepare space for even bigger capacitors in case you miscalculated.