Cell size & surface-area-to-volume ratio
Enter a cell’s side length or radius to get its surface area, volume, and SA:V ratio with worked steps, and see why doubling the size halves the ratio.
Your cell
Lengths are in micrometers (µm): 1 µm = 0.001 mm. The presets give each cell’s diameter “across”, so the sphere radius is half of it. Real cells are rarely perfect cubes or spheres, but the trend is the same for any shape: SA : V falls as size grows.
Why it works
Cell size & surface-area-to-volume ratio: common questions
Wondering about the why? Start here.
Why are cells so small?
Everything a cell needs enters through its surface, but everything it has to feed grows with its volume. A cube-shaped cell 10 µm across has a surface area of 600 µm² and a volume of 1,000 µm³, a ratio of 0.6 per µm; doubling the side to 20 µm halves the ratio to 0.3 per µm. Past a certain size, diffusion can no longer deliver oxygen and remove waste fast enough, so cells divide instead of growing further.
Read: surface area to volume ratioHow do you calculate the surface area to volume ratio?
Divide the surface area by the volume. For a cube of side s, SA : V = 6s² / s³ = 6 / s; for a sphere of radius r, SA : V = 4πr² / (4⁄3 πr³) = 3 / r. A spherical bacterium 1 µm across (r = 0.5 µm) has a ratio of 6 per µm, ten times that of the 10 µm cube, which is one reason bacteria can grow and divide so fast.
Practice with cell questionsHow do large cells get around the SA:V problem?
They change shape or stay quiet. Intestinal cells fold their surface into microvilli, mitochondria fold their inner membrane into cristae, neurons stretch into long thin fibers, and a plant cell’s central vacuole pushes its cytoplasm into a thin layer just inside the wall. A frog egg 1,000 µm across can be huge because it stores yolk and has a very low metabolic rate until it starts dividing.
See folding at work in a mitochondrion