🌞 How Many Earths Fit in the Sun? (…and other worlds!)

How we figure it out (friendly space math)

We compare the volumes of two spheres. If the big world has radius R and the small world has radius r, their volumes are V = 4/3 · π · R³ and v = 4/3 · π · r³. The ideal count is simply the ratio V ÷ v = (R/r)³ (rounded down in the real world, but we present the integer count for clarity).

However, if you try to fill a big sphere with lots of smaller spheres, there will be empty space between them. The densest sphere-packing fills about 74% of the volume, so a more realistic packed count is roughly 0.74048 × (R/r)³. Real planets aren’t perfect spheres (they bulge a little at the equator), but the sphere model gives a great first estimate.

Big vs Small in Space: Why the Numbers Get Huge

When we ask “How many Earths fit in the Sun?”, we’re comparing volumes, not just diameters. A sphere’s volume grows with the cube of its radius: V = (4/3) × π × r3. That little “³” is the secret: if one world is 10 times wider than another, it can be about 1,000 times bigger by volume! That’s why the Sun is so unbelievably roomy compared to Earth.

From diameter to “how many fit”

Our calculator uses mean (average) radii for each body and takes a clean, spherical model. If the big world has radius R and the small world has radius r, the ideal count is (R / r)3. This is a perfect-packing dream: no gaps, perfectly rigid spheres, everything exactly full. It’s great for learning the scale of space.

But spheres don’t pack perfectly

Try filling a jar with marbles — you’ll see little air pockets between them. In 3D, the best possible sphere arrangement fills about 74% of the space. We call this the “sphere-packing” limit. That’s why the tool also shows a packed estimate: we multiply the ideal count by ~0.74048 to model real-world gaps. The packed value is more realistic if you imagine stacking many small worlds inside a larger one.

Quick example: Earth vs the Sun

The Sun’s mean radius is about 695,700 km; Earth’s is about 6,371 km. The radius ratio is roughly 695,700 / 6,371 ≈ 109. Cube that and you get 1093 ≈ 1.29 million. That’s the ideal number of Earth-sized volumes in a Sun-sized volume. Apply sphere-packing and the estimate drops to roughly 0.74 × 1.29 million ≈ 950,000. Either way, the Sun is vast.

Planets aren’t perfect spheres

Real worlds bulge a little at the equator (they’re “oblate”) and have mountains, oceans, and layered interiors. Using a mean radius smooths out those details so we can make clean, consistent comparisons. For quick estimates and classrooms, this is a helpful simplification.

Fun comparisons to try

• Jupiter vs Moon: Choose Jupiter as the big world and the Moon as the small one. You’ll see how gas giants dwarf rocky moons.
• Neptune vs Pluto: A nice way to explore why “dwarf planet” is still very large!
• Earth vs Ceres: Compare our home planet to the largest object in the asteroid belt.

Why this helps intuition

Our eyes notice width, but the universe cares about volume and mass. By playing with diameter ratios and seeing the cube rule in action, kids (and grown-ups!) build a stronger sense of scale. Once you feel how sizes explode with that tiny ³, space starts to make a lot more sense.