How big are red giants? How is their size determined?

If you are referring to mass, it can range from 0.3 to 8 solar masses, with 1 solar mass equal to roughly 2×10^30 kg.

Since measuring binary star systems stars is easy, they measure the mass of the stars based on their orbital speed and each other's orbit. This method is not entirely accurate because the stars are too far away to be measured precisely. Instead, they look at similar non-binary system stars and measure them using the approximate method.

That is one method of measuring them; other methods include the Hertzprung-Russel Diagram (look it up if you need to) which uses parameters like age, luminosity, and radius/diameter.

The other thing your quest might imply by size is radius/diameter; a red giant's radius can range from 100 million to 1 billion kilometers and is always expanding.

Since diameter is difficult to measure due to diffraction, methods like measuring with a telescope rather than multiplying or using lunar occultations—which are also uncommon—to obtain precise measurements are more difficult.

Observations of a red giant's luminosity, temperature, and distance from Earth allow astronomers to calculate its radius using techniques like stellar interferometry or atmosphere modeling. Red giants can vary greatly in size, but on average, their diameters range from tens to hundreds of times larger than the Sun.