Volume & Surface Area Calculator — Free Online Calculator & Guide
Calculate volume and surface area of spheres, cubes, rectangular prisms, cylinders, cones, and pyramids. Free, instant, and accurate.
Volume & Surface Area
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Surface Area
314.159265
Diameter
10
Scenario Comparison
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Volume
523.598776 cu units
Surface Area
314.159265 sq units
3D View
Drag to rotate • Scroll while dragging
The Net (Unfolded)
How the Net Works
A sphere is unique among 3D shapes — it has NO flat net because its surface is continuously curved. Unlike polyhedra, a sphere cannot be unfolded into flat polygons without distortion (similar to how you cannot flatten an orange peel without tearing). Use formulas directly: SA = 4πr².
Formula Applied
Interesting Fact
The sphere is the most efficient 3D shape — it has the largest volume for the smallest surface area. A sphere's surface area (4πr²) is exactly 4 times the area of its great circle (πr²).
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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