How many square centimeters in the world?

Answer 1

The short answer is that the number of square centimeters in the world cannot be calculated precisely, because the number fluctuates. The long answer follows:

If by "the world" you mean planet Earth, you can use the formula for the surface area of a sphere (ignoring the fact that Earth is slightly oblate). Use the earth's radius of 4000 miles to calculate total square miles.

Then convert to square centimeters. If 1 inch = 2.54 cm, then 1 sq in = (2.54)2 sq cm. If 1 mile = 5280 feet, then 1 sq mi = (5280)2 sq ft. And 1 square foot contains 12 x 12 = 144 square inches. You just grind through a bunch of numbers with a calculator and use scientific notation to express large numbers.

Or just Google it. You'll get a published value for area of Earth, assuming it's a perfectly smooth sphere.

But wait!...

The presence of topography greatly increases area because now the 3rd dimension, altitude, comes into play. It takes more square centimeters to cover the peaks and valleys of a rough terrain than a smooth one. Oceans aren't flat, either, having waves & wavelets that greatly increase its surface area compared to flat water.

The difficulty with natural features like mountains, clouds, or Coastlines is that they exhibit fractal geometry, meaning that parts of an object resemble the whole object - aka self-similarity. Strange properties emerge. See a famous article by Mandelbrot called "How Long Is the Coast of Britain?"

Mathematically, such 3-dimensional objects have infinite surface area contained within a finite volume.

To answer your question, if we specify that features smaller than one centimeter in size be ignored, then the total surface area is finite. It could in principle be measured but it will be way bigger than the above calculation for a sphere.

You can't actually find the answer without an unrealistically detailed knowledge -- down to 1 cm! -- of the entire earth's surface, which in the case of oceans constantly fluctuates according to weather. And there are millions of niggling other details.