Why does a full moon look full?

Remember that half the moon is always illuminated by the sun. That lighted half is the moon’s day side.

Technically speaking, the moon is full at the instant it’s 180 degrees from the sun in ecliptic longitude. So why does a full moon look full? Remember that half the moon is always illuminated by the sun. That lighted half is the moon’s day side.

In order to appear full to us on Earth, we have to see the entire day side of the moon. That happens only when the moon is opposite the sun in our sky. So a full moon looks full because it’s opposite the sun.

That’s also why every full moon rises in the east around sunset – climbs highest up for the night midway between sunset and sunrise (around midnight) – and sets around sunrise. Stand outside tonight around sunset and look for the moon. Sun going down while the moon is coming up? That’s a full moon, or close to one.

Just be aware that the moon will look full for at least a couple of night around the instant of full moon.

A full moon is opposite the sun. We see all of its dayside.

If a full moon is opposite the sun, why doesn’t Earth’s shadow fall on the moon at every full moon? The reason is that the moon’s orbit is titled by 5.1 degrees with respect to Earth’s orbit around the sun. At every full moon, Earth’s shadow sweeps near the moon. But, in most months, there’s no eclipse.

A full moon normally passes above or below Earth’s shadow, with no eclipse.

Source - EarthSky.org