How do I calculate the volume of a sphere?

Volume = (4/3) × π × r³. For a sphere with radius 5: V = (4/3) × π × 125 ≈ 523.6 cubic units.

What is the volume of a cone?

Volume = (1/3) × π × r² × h. A cone is exactly 1/3 the volume of a cylinder with the same base and height.

Volume Calculator - Free Online Calculator

Calculate the volume of 3D shapes: cube, sphere, cylinder, cone, and rectangular prism.

How to Use This Calculator

Enter the appropriate dimensions for your 3D shape and click "Calculate" for instant results with step-by-step working. Use the "Length/Radius" field for the primary dimension, "Width" for the second dimension (prisms), and "Height" for the third. For spheres, only the radius (Length field) is needed.

Volume Formulas by Shape

Cube: V = s³ | Sphere: V = 4/3 × π × r³ | Cylinder: V = π × r² × h | Cone: V = 1/3 × π × r² × h

Complete Shape Reference with Examples

Cube: V = s³. All sides equal. Example: s=5 → V = 125 cubic units.
Rectangular Prism (Box): V = l × w × h. Example: 4×3×2 = 24 cubic units.
Sphere: V = 4/3 × π × r³. Example: r=5 → V ≈ 523.6 cubic units.
Cylinder: V = π × r² × h. Example: r=5, h=4 → V ≈ 314.2 cubic units.
Cone: V = 1/3 × π × r² × h. Exactly 1/3 of a cylinder with same base and height.
Pyramid: V = 1/3 × base area × height. A pyramid is 1/3 of a prism with the same base and height.

Practical Applications

Volume calculations appear in everyday and professional contexts: calculating how many gallons a tank holds (aquarium, fuel tank, swimming pool), determining the amount of concrete needed for a cylindrical column or rectangular foundation, figuring out how much material fits in a box for shipping, computing dosage in a cylindrical syringe, and estimating the weight of a metal sphere or cylinder given the density of the material (Weight = Volume × Density).

Units and Conversions

Volume is expressed in cubic units. Common conversions: 1 liter = 1,000 cm³ = 1 dm³ | 1 US gallon = 231 cubic inches ≈ 3.785 liters | 1 cubic foot = 7.481 US gallons | 1 cubic meter = 1,000 liters = 264.2 US gallons. When your dimensions are in different units, convert all to the same unit before calculating. Mixing inches and feet will give incorrect results.

Surface Area vs. Volume

Volume measures the 3D space inside a shape (cubic units). Surface area measures the total area of all outer faces (square units). A sphere has the most volume for a given surface area of any shape — this is why bubbles and water droplets form spheres (minimizing surface tension). Packing problems (how many boxes fit in a truck, how much fruit packs into a container) involve both volume and the efficiency of 3D arrangements.

Volume Calculator