Free volume calculator for 3D shapes: cube, rectangular prism, cylinder, sphere, cone, and pyramid with step-by-step formulas.
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Cube: V = s³ | Cylinder: V = π×r²×h | Sphere: V = (4/3)×π×r³rRadiushHeightsSide length (cube)πPi ≈ 3.14159Volume measures the three-dimensional space occupied by a solid shape. Each shape has a unique formula based on its geometry. Surface area measures the total area of all outer faces of the shape.
Volume calculation is fundamental to science, engineering, cooking, architecture, and everyday life. From calculating how much water fills a swimming pool to determining the capacity of a storage container, understanding 3D geometric volume is an essential mathematical skill.
Select your 3D shape, enter the required dimensions, and the calculator instantly computes the volume and surface area using the appropriate geometric formula with step-by-step working.
| Shape | Formula |
|---|---|
| Cube | V = s³ |
| Rectangular prism | V = l × w × h |
| Cylinder | V = π × r² × h |
| Sphere | V = (4/3) × π × r³ |
| Cone | V = (1/3) × π × r² × h |
| Square pyramid | V = (1/3) × base² × h |
| Triangular prism | V = (1/2 × base × height) × length |
A cylindrical tank 5 units in radius and 10 units tall.
Volume ≈ 785.4 cubic units.
Use the radius, not the diameter — halve the diameter first if that's what you measured.
A ball of radius 6 units.
Volume ≈ 904.8 cubic units.
This calculator covers seven common 3D shapes, providing both volume and surface area — the two most important measurements for any solid figure. The step-by-step breakdown makes it ideal for students learning geometry.
Ensure you enter radius (not diameter) for cylinders, spheres, and cones. The radius is half the diameter. Also, volume is always in cubic units (cm³, m³) while area is in square units (cm², m²) — mixing these up is a common error.
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