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The radius of the Moon is, on average, 1,737.1 km.
We say “on average”, because the Moon’s rotation causes it to flatten out. The equatorial radius (from the center of the Moon to its equator) is 1,738.14 km, while its polar radius is 1,735.97 km. In other words, a point on the equator of the Moon is 2.17 km further from the center of the Moon than a point on its poles. This flattening isn’t much because the Moon takes more than 27 days to turn once on its axis.
Need a comparison? The average radius of the Earth is 6,371.0 km. In other words, the Earth is about 4 times larger than 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