A first quarter moon shows half of its lighted hemisphere – half of its day side – to Earth.
But we officially call this moon a quarter and not a half because it is one quarter of the way around in its orbit of Earth, as measured from one new moon to the next.
This moon appears half-lit to us, and half moon is a beloved name (although not an official one). Still, it’s good to recall that the illuminated portion of a first quarter moon truly is just a quarter. On the night of first quarter moon, we see half the moon’s day side, or a true quarter of the moon. Another lighted quarter of the moon shines just as brightly in the direction opposite Earth!
A first quarter moon rises at noon and is high overhead at sunset. It sets around midnight.
First quarter moon comes a week after new moon. Now, as seen from above, the moon in its orbit around Earth is at right angles to a line between the Earth and sun.
As the moon orbits Earth, it changes phase in an orderly way. Follow these links to understand the various phases of the moon.