How much water does a cylindrical tank hold? How much concrete is needed for a conical foundation pad? What is the capacity of an aquarium? For all these everyday questions, the volume calculator provides instant answers – for six different solid shapes, each with the appropriate formula.
Step by Step: How to Use the Volume Calculator
- Select the shape: Choose from cube, cuboid, cylinder, sphere, cone or pyramid.
- Enter the dimensions: Input the required measurements – for a cuboid enter length, width and height; for a cylinder enter radius and height; for a sphere just the radius.
- Choose the unit: Work in mm (for small components), cm (for household applications) or m (for construction and architecture).
- Enter a fill level: For tanks and containers, you can enter a fill percentage to find the actual volume of liquid currently inside.
- Read the result in multiple units: Volume is displayed in cm³, litres and m³ – whichever suits your purpose.
Practical Examples
Example 1 – Heating oil tank (horizontal cylinder): Diameter 1.2 m (radius 0.6 m), length 2.8 m. Volume: π × 0.6² × 2.8 = π × 0.36 × 2.8 = 3.166 m³ = 3,166 litres. At 70% fill: 2,216 litres of heating oil in the tank.
Example 2 – Garden pond (simplified as a cuboid): 3 × 2 × 0.8 m = 4.8 m³ = 4,800 litres. For pump sizing (complete water circulation every 2 hours), a pump with at least 2,400 L/h is needed.
Example 3 – Concrete pillars (cylinders): Foundations for a garden pergola: 6 cylindrical pillars, diameter 30 cm (radius 15 cm), depth 80 cm. Volume per pillar: π × 0.15² × 0.8 = 0.05655 m³. 6 pillars: 0.3393 m³ ≈ 340 litres of concrete, equivalent to around 8 bags of dry concrete at 40 kg each.
Volume Formulas for All Shapes
Cube: V = a³. Cuboid: V = l × w × h. Cylinder: V = π × r² × h. Sphere: V = (4/3) × π × r³. Cone: V = (1/3) × π × r² × h. Pyramid: V = (1/3) × A × h.
Frequently Asked Questions (FAQ)
How do I convert cm³ to litres?
1 litre = 1,000 cm³. So 4,800 cm³ = 4.8 litres. And 1 m³ = 1,000 litres = 1,000,000 cm³. These conversions are handled automatically by the calculator.
Why is the cone only 1/3 of the cylinder's volume?
This can be proven geometrically: three cones with the same base area and height fill exactly one cylinder. The same ratio applies to a pyramid and a rectangular prism. To visualise it: fill a cone with sand and pour it three times into the matching cylinder – it will be exactly full.
How do I calculate the volume of an L-shaped swimming pool?
Split the shape into two cuboids, calculate each volume separately and add them together. Alternatively, calculate the total enclosing cuboid and subtract the missing section. For irregular pools, breaking the shape into the smallest possible rectangular sections is recommended.
