Volume Calculator

Calculate Volume by Shape

Choose the 3D shape first so the calculator only asks for the dimensions that shape needs.

Choose a 3D shape

Supported shapes in this tool: cube, cylinder, and sphere.

Volume result

Volume Choose a shape The formula and required dimensions update after calculation.

What is Volume?

Volume is the amount of three-dimensional space enclosed within a boundary. It measures how much space a 3D object occupies and is expressed in cubic units such as cubic meters (m³), cubic feet (ft³), or liters (L).

Understanding volume is essential in many fields including engineering, construction, cooking, and science. Whether you're calculating how much liquid a container can hold or determining the capacity of a storage space, volume calculations are fundamental.

How Volume Is Calculated

Follow these detailed steps:

  1. Step 1: Identify the 3D Shape
    Determine if your object matches one of the supported shapes in this tool: cube, cylinder, or sphere.
  2. Step 2: Measure Required Dimensions
    Cube: side length. Cylinder: radius and height. Sphere: radius. Measure carefully for accuracy.
  3. Step 3: Apply Volume Formula
    Cube: V = s³. Cylinder: V = πr²h. Sphere: V = (4/3)πr³.

Volume Formulas

Cube Volume: V = s³ (where s is the side length)

Cylinder Volume: V = π × r² × h (where r is radius, h is height)

Sphere Volume: V = (4/3) × π × r³ (where r is radius)

Examples

Cube Example

Problem: Calculate the volume of a cube with side length 5 cm.

Solution: V = 5³ = 5 × 5 × 5 = 125 cm³

Cylinder Example

Problem: Calculate the volume of a cylinder with radius 3 m and height 10 m.

Solution: V = π × 3² × 10 = π × 9 × 10 = 90π ≈ 282.74 m³

Sphere Example

Problem: Calculate the volume of a sphere with radius 4 inches.

Solution: V = (4/3) × π × 4³ = (4/3) × π × 64 ≈ 268.08 in³

Quick Calculation Tips

  • 1 cubic foot = 7.48 gallons; 1 cubic yard = 27 cubic feet
  • For irregular containers, fill with water and measure the water
  • 6 inches = 0.5 feet; convert all measurements to same unit first
  • Always round up for ordering materials like concrete

Common Mistakes to Avoid

  • Forgetting to convert units
    If dimensions are in inches and you need cubic feet, divide by 1728 (12³) to convert.
  • Using diameter in cylinder formula
    Use radius, not diameter. For diameter 10", use r = 5" in πr²h.

Frequently Asked Questions

What is the difference between volume and capacity?

Volume refers to the amount of space an object occupies, while capacity refers to the amount a container can hold. They use different units - volume uses cubic units (m³, ft³), while capacity often uses liters or gallons.

Why is the sphere formula 4/3 times π?

The 4/3 factor comes from calculus and the geometric relationship between a sphere's surface area and volume. The sphere's volume is exactly 2/3 of the volume of the smallest cylinder that contains it.

How do I convert between volume units?

To convert between units, use conversion factors. For example, 1 cubic meter = 1000 liters, 1 cubic foot ≈ 28.317 liters, and 1 gallon ≈ 3.785 liters.

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