The Square–Cube Law

Why giants can’t exist

An interactive lesson with 8 steps, about 7 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Scale lengths by $k$: areas scale by $k^2$, volumes and masses by $k^3$.
• Stress (weight per area) grows like $k$, so big things are relatively weaker.
• Surface-to-volume ratio scales like $1/k$, so small animals lose heat fast.

Steps

1. Double the cube
2. Areas lag behind volumes
3. A real giant
4. Galileo’s bones
5. Small and cold
6. Surface per volume
7. Falling mice
8. Model ship