The Moon seen from Earth
wide = (arcminutes)
Earth seen from the Moon
wide = (arcminutes)
Earth looks times wider than the Moon.
True scale means both pictures use the exact same camera zoom: each view shows a patch of sky 5 degrees tall. So the Moon and Earth are drawn at their real sizes compared to each other.
Exaggerated: each picture is zoomed in by a different amount so you can see the details. The sizes are not fair to compare in this mode. Switch back to True scale for that.
The formula
angle = 2 × atan(radius ÷ distance)
Moon:
Earth:
How many times wider:
Show the math
- Picture a skinny triangle from your eye to the middle of the other world, then out to its edge. The long side is the distance, km. The short side is the world's radius (half its width).
- Divide: radius ÷ distance. Moon: 1,737.4 ÷ = . Earth: 6,371.0 ÷ same = .
- "atan" (arctangent, a calculator button) turns that into an angle. Doubling it gives the angle across the whole width, edge to edge: Moon , Earth . These are in radians, a math unit for angles.
- One radian is about 57.3 degrees, so multiply: Moon °, Earth °.
- A degree splits into 60 arcminutes (written ′), like an hour splits into 60 minutes. Moon ′, Earth ′.
- Here's a neat trick: both worlds are the same distance apart, whichever one you stand on. So Earth always looks about 6,371 ÷ 1,737.4 ≈ 3.67 times wider than the Moon, near or far. Try the distance slider: both numbers change, the "times wider" barely does.
How we figured this
Where the numbers come from (NASA)
- Moon's radius 1,737.4 km and average distance 384,400 km, and the range "roughly 357,000 km to 407,000 km": NASA Moon Fact Sheet.
- Earth's radius 6,371.0 km: NASA Earth Fact Sheet.
- Both radii are the "volumetric mean": the radius of a perfect ball with the same volume.
Pictures (NASA, public domain)
- Earth: Blue Marble: Next Generation (December), NASA Earth Observatory, Reto Stöckli. Clouds are not shown.
- Moon: CGI Moon Kit color map from the Lunar Reconnaissance Orbiter camera (LROC). Credit: NASA's Scientific Visualization Studio, Ernie Wright.
- 3D drawing: three.js (MIT license), stored on this site.
What we assumed
- "Distance" is from the center of Earth to the center of the Moon. Standing on the ground brings you a little closer (up to about 6,400 km from Earth or 1,700 km from the Moon), which makes the other world look up to about 2% bigger.
- Both worlds are treated as perfect balls. Phases ignore eclipses and the tilt of the Moon's orbit.
- The Moon always shows us the same face, so its picture doesn't spin. Earth spins much faster here (once every 2 minutes) than in real life (once a day).
- The stars are for looks. In real life the sunlit Moon or Earth is so bright that most stars would be hard to see next to it.