Volume Calculator
Calculate the volume of cubes, rectangular prisms, cylinders, spheres, cones, and pyramids.
Volume Formulas Reference
| Shape | Formula | Variables |
|---|---|---|
| Cube | V = s³ | s = side length |
| Rectangular Prism | V = l × w × h | l, w, h = dimensions |
| Cylinder | V = π r² h | r = radius, h = height |
| Sphere | V = (4/3) π r³ | r = radius |
| Cone | V = (1/3) π r² h | r = radius, h = height |
| Square Pyramid | V = (1/3) b² h | b = base side, h = height |
Frequently Asked Questions
What is the formula for the volume of a sphere?
The volume of a sphere is V = (4/3) × π × r³, where r is the radius. For example, a sphere with radius 3 cm has volume (4/3) × π × 27 ≈ 113.1 cm³. Notice volume grows with the cube of the radius — doubling the radius increases volume by a factor of 8.
How is the volume of a cone calculated?
A cone's volume is exactly one-third of the volume of a cylinder with the same base radius and height: V = (1/3) × π × r² × h. This is easy to verify experimentally — a cone-shaped container holds exactly one-third the water of a same-sized cylinder.
What is the difference between volume and surface area?
Volume measures the three-dimensional space inside a shape (in cubic units), while surface area measures the total area of the outer faces (in square units). A cube with side length 3 has volume 27 cubic units and surface area 54 square units. This calculator computes volume only.
How do I find the volume of an irregular shape?
For irregular shapes, water displacement is a practical method: submerge the object in water and measure the volume of water displaced. In math, irregular volumes can often be calculated by breaking the shape into simpler components and summing their volumes.
What units should I use for volume calculations?
This calculator is unit-agnostic — enter dimensions in any consistent unit and the result is in that unit cubed. For example, entering metres gives cubic metres (m³). To convert: 1 m³ = 1,000 litres = 264.2 US gallons. 1 cubic foot = 7.48 US gallons = 28.32 litres.