Volume Calculator
Calculate the volume of cubes, cylinders, spheres, cones, and rectangular prisms. Enter your dimensions and get instant results with formulas and a visual breakdown. Perfect for students, engineers, and DIY enthusiasts.
What Is Volume?
Volume is the measure of the amount of space occupied by a three-dimensional object. It is measured in cubic units, such as cubic meters (m³), cubic feet (ft³), or cubic centimeters (cm³). Volume is a fundamental concept in geometry with countless real-world applications — from calculating the capacity of containers to determining material quantities for construction and manufacturing.
This calculator supports five common shapes: cubes, cylinders, spheres, cones, and rectangular prisms. Each shape has a specific formula that uses its dimensions to calculate the volume.
How Does the Volume Calculator Work?
The calculator uses standard geometric formulas for each shape:
Cube: Volume = Side³
Cylinder: Volume = π × Radius² × Height
Sphere: Volume = ⁴⁄₃ × π × Radius³
Cone: Volume = ⅓ × π × Radius² × Height
Rectangular Prism: Volume = Length × Width × Height
Simply select a shape, enter the required dimensions, and the calculator will instantly compute the volume. You can switch between metric and imperial units, and choose how many decimal places to display.
Why Use This Volume Calculator?
- Five Shapes: Supports cubes, cylinders, spheres, cones, and rectangular prisms.
- Unit Flexibility: Switch between metric (centimeters, meters) and imperial (inches, feet).
- Formula Display: See the formula used and the step-by-step calculation.
- Multiple Output Units: Display volume in cubic units, liters, or gallons.
- Free & Private: No registration, no data storage.
Real-World Applications of Volume
- Construction: Calculating concrete needed for foundations or columns.
- Manufacturing: Determining material quantities for production.
- Shipping: Calculating cargo capacity of containers and trucks.
- Cooking: Measuring ingredients and container capacities.
- Science: Calculating volumes in chemistry, physics, and biology.
❓ Volume Calculator FAQ
What is volume?
Volume is the amount of three-dimensional space occupied by an object. It is measured in cubic units (e.g., cm³, m³, ft³).
How do I calculate the volume of a cube?
Multiply the side length by itself three times: V = s × s × s = s³. For example, a cube with side 5 cm has a volume of 125 cm³.
How do I calculate the volume of a cylinder?
Multiply π (3.14159) by the radius squared, then by the height: V = πr²h. For example, a cylinder with radius 3 cm and height 10 cm has a volume of π × 9 × 10 ≈ 282.74 cm³.
How do I calculate the volume of a sphere?
Multiply ⁴⁄₃ by π, then by the radius cubed: V = ⁴⁄₃πr³. For example, a sphere with radius 5 cm has a volume of ⁴⁄₃ × π × 125 ≈ 523.60 cm³.
How do I calculate the volume of a cone?
Multiply ⅓ by π, by the radius squared, then by the height: V = ⅓πr²h. For example, a cone with radius 4 cm and height 9 cm has a volume of ⅓ × π × 16 × 9 ≈ 150.80 cm³.
How do I calculate the volume of a rectangular prism?
Multiply the length, width, and height: V = l × w × h. For example, a prism with length 10 cm, width 6 cm, and height 4 cm has a volume of 240 cm³.
What is the difference between volume and capacity?
Volume is the amount of space a solid object occupies. Capacity is the amount of liquid or gas a container can hold. For a container, the volume and capacity are numerically equal when measured in the same units.
How do I convert cubic centimeters to liters?
1 cubic centimeter (cm³) = 0.001 liters. To convert, divide the volume in cm³ by 1000. For example, 1000 cm³ = 1 liter.
How do I convert cubic inches to gallons?
1 US gallon = 231 cubic inches. To convert, divide the volume in in³ by 231. For example, 231 in³ = 1 gallon.
How do I convert cubic meters to liters?
1 cubic meter (m³) = 1000 liters. To convert, multiply the volume in m³ by 1000.
What is the volume of a cylinder with diameter 6 and height 10?
Radius = Diameter/2 = 3. Volume = π × 3² × 10 = π × 9 × 10 ≈ 282.74 cubic units.
What is the volume of a sphere with diameter 10?
Radius = 5. Volume = ⁴⁄₃ × π × 5³ ≈ 523.60 cubic units.
How does the volume change if I double the dimensions?
Volume scales with the cube of the dimensions. Doubling all dimensions increases the volume by a factor of 8 (2³).
What is the difference between a prism and a cylinder?
A prism has polygonal bases (e.g., triangles, rectangles), while a cylinder has circular bases. Both have the same volume formula: base area × height.
What is a right circular cylinder?
A right circular cylinder has circular bases that are perpendicular to the axis (the line connecting the centers of the bases). The sides are straight and perpendicular to the bases.
What is the volume of a cone compared to a cylinder?
A cone with the same base radius and height as a cylinder has exactly one-third the volume of the cylinder. V_cone = ⅓ × V_cylinder.
Can I use this calculator for irregular shapes?
This calculator is designed for regular geometric shapes. For irregular shapes, you may need to use displacement methods or break the shape into regular components.
What units can I use for volume?
Volume can be measured in cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), cubic inches (in³), liters, gallons, and many other units. This calculator supports metric and imperial systems.