How this calculator works
Surface area is the total area of every outer face and curved patch of a solid. Each shape has its own formula, but they share one idea: add the area of each face, counting curved surfaces as if they were flattened out. This calculator compares six common solids and also reports the volume needed to turn the area into a surface to volume ratio, which is useful when heat loss, buoyancy or material thickness depends on how exposed the shape is relative to its contents.
Formula
Sphere: A = 4πr², V = 4/3 πr³. Cube: A = 6a², V = a³. Cylinder: A = 2πr² + 2πrh. Cone: A = πr(r + √(r² + h²)). Rectangular prism: A = 2(lw + lh + wh). Square pyramid: A = a² + 2a√(h² + (a/2)²).
Worked example
A sphere of radius 3 m has a surface area of 36π ≈ 113.097 m² and a volume of about 113.097 m³, a ratio of 1.0 per metre. A cube of side 4 m has a surface area of 96 m² and a volume of 64 m³, a ratio of 1.5 per metre.
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Frequently asked questions
Does surface area include the base?
Yes, the total surface area counts every exposed surface, including flat bases. If you only need the sides, use the lateral area given by the matching single-shape calculator.
Why is the ratio in per metre?
Surface area grows with length squared and volume grows with length cubed, so their ratio has units of one over length. It is expressed per metre because the calculator works in metres internally.
Which shape has the smallest ratio for a given volume?
A sphere. For a fixed volume it has the least surface area of any closed shape, which is why bubbles and droplets become round and why a sphere loses heat more slowly than a long thin shape of the same volume.