Volume and Surface Area Calculator

How are volume and surface area calculated?

Volume is the space a solid takes up or holds, and surface area is the total area of its outside. Tank capacity, cut and fill quantities and material needs depend on volume, while paint, insulation and sheet metal depend on surface area. Choose the solid from the tabs above and enter its dimensions.

Formulas

• Box: V = a × b × c.
• Cylinder: V = π × r² × h, lateral area 2 × π × r × h.
• Sphere: V = 4 / 3 × π × r³, surface 4 × π × r².
• Cone: V = π × r² × h / 3, one third of the cylinder with the same base and height.
• Truncated cone: V = π × h × (R² + R × r + r²) / 3. Buckets, funnels and hopper bottoms have this shape.
• Pyramid: V = base area × height / 3.

For prisms and pyramids with other base shapes, work out the base area first and use the "From base area" tab.

Example

A cylindrical tank of 1 m radius and 2 m height holds π × 1² × 2 = 6.283 m³, or 6283 litres. Its lateral surface is 2 × π × 1 × 2 = 12.57 m². A conical stockpile with a 3 m base radius and 4 m height contains π × 9 × 4 / 3 = 37.70 m³.

Limits

The cone and pyramid are assumed to be right solids. Use inside dimensions for tanks, since wall thickness reduces the volume. Dished tank ends, partial filling of horizontal tanks and irregular stockpiles are outside the scope of this calculator.