Volume & Surface Area Calculator
Calculate volume and surface area of spheres, cubes, rectangular prisms, cylinders, cones, and pyramids. Includes shape net visualizations that show each 3D shape unfolded.
Volume & Surface Area
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The Formula
The sphere is the most geometrically efficient shape — it contains the maximum volume for a given surface area. Volume grows with the cube of the radius (double the radius, multiply volume by 8). Surface area grows with the square (double the radius, multiply area by 4).
Variable Definitions
Radius
Distance from the center to the outer surface. All points on the surface are exactly radius r from center.
Volume
Total 3D space enclosed by the sphere. A sphere with radius 5 has volume 523.6 cubic units.
Surface Area
Total area of the outer surface. A sphere with radius 5 has surface area 314.16 square units.
How to Use This Calculator
- 1
Select "Sphere" from the shape tabs above.
- 2
Enter the radius of the sphere.
- 3
View the volume, surface area, and diameter.
A sphere with radius r — the most efficient 3D shape
Understanding the Concept
Spheres appear everywhere: planets, bubbles, droplets, ball bearings. The sphere is the most efficient shape for containing volume with minimal material — which is why soap bubbles form spheres. The formulas were discovered by ancient Greek mathematicians. Archimedes was so proud of proving that a sphere has 2/3 the volume of its circumscribed cylinder that he requested it be carved on his tombstone.
Frequently Asked Questions
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