How far away is the Moon, in miles?

How to get close to this number

The cleanest route to this number does not involve the Moon at all. Start from the size of the Earth, which most people can recall to within a factor of two, and then remember the standard fact that the gap holds roughly thirty Earths side by side. Multiply and you are close. Chaining a known quantity to a known ratio is almost always more accurate than reaching for the target figure directly.

The reason people guess low is that every diagram they have ever seen is wrong. A textbook illustration of the Earth–Moon system has to fit on a page, so it shrinks the distance and enlarges both bodies, and that image is what the mind retrieves. Drawn to scale, the Moon is a small dot a long way off, and the emptiness of the gap is the whole point — it is why the Apollo transit took days rather than hours.

It is also an average rather than a fixed distance. The orbit is an ellipse, so the Moon is meaningfully nearer at one end than the other, which is what produces the occasional "supermoon". And the figure is slowly growing: tidal interaction is pushing the Moon outward by a few centimetres a year, measured by bouncing lasers off reflectors left on the surface. On human timescales that changes nothing, which is exactly why the number is stable enough to ask about.