The mass of the Moon is 7.347 x 1022 kg.
That sounds like a large number, and I suppose it is compared to the mass of a single person, a car or even a building. But you’ve got to keep it in context. The mass of the Moon is only 1.2% the mass of the Earth. In other words, you would need 81 objects with the mass of the Moon to match the mass of the Earth.
The diameter of the Moon is only about 1/4 the diameter of the Earth, so it might seem like the mass of the Moon is strangely low. And you would be right. The key is the Moon’s low density. It has a density of only 3.3 g/cm3. This is almost half the density of Earth.
Astronomers think that a Mars-sized object crashed into the Earth about 100 million years after the Earth formed. The huge cloud of ejected debris coalesced into the Moon, which still orbits us today. The Moon has a lower density because the impact gouged out the outer crust and mantle, and didn’t eject so much of the Earth’s iron core.
The Physics Factbook has more information about the mass of the Moon. And here’s an article that explains how you would go about weighing the Moon.
You can listen to a very interesting podcast about the formation of the Moon from Astronomy Cast, Episode 17: Where Did the Moon Come From?
NASA Moon Facts