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Volume Calculator

Choose the desired geometric shape to calculate its volume with this calculator.

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Volume Calculator

Use this volume calculator to calculate the volume of three-dimensional geometric shapes. It provides results in different units and shows the formula for each selected shape.

Volume Definition

"The amount of space enclosed by a 3D object."

Volume is the space inside an object. The SI unit for volume is cubic meters (m³).

How To Calculate the Volume of a Body?

Different shapes have different formulas. To calculate the volume of any object, use the corresponding volume formula for that shape.

Volume Formulas

  • Cube: Volume = (side length)³
  • Rectangular Prism: Volume = length × width × height
  • Sphere: Volume = (4/3) × π × radius³
  • Cylinder: Volume = π × radius² × height
  • Cone: Volume = (1/3) × π × radius² × height
  • Tube (Hollow Cylinder): Volume = π × height × (R² - r²)
  • Hemisphere: Volume = (2/3) × π × radius³
  • Pyramid: Volume = (1/3) × base area × height
  • Truncated Pyramid: Volume = (h/3) × (A₁ + A₂ + √(A₁ × A₂))
  • Conical Frustum: Volume = (1/3) × π × height × (R² + r² + R × r)
  • Ellipsoid: Volume = (4/3) × π × a × b × c
  • Triangular Prism: Volume = (1/4) × height × √[(a+b+c)(b+c-a)(c+a-b)(a+b-c)]

Examples

Example #1: Find the volume of a cube with side length 6 cm.

Solution:

  • Side length = 6 cm
  • Volume = 6³ = 6 × 6 × 6 = 216 cm³

Example #2: Find the volume of a cone with height 6 cm and radius 4 cm.

Solution:

  • Height = 6 cm, Radius = 4 cm
  • Volume = (1/3) × π × 4² × 6 = (1/3) × 3.14 × 16 × 6 ≈ 100.48 cm³

For complex calculations, you can use our free online volume calculator.

Common Volume Units

Unit Cubic Meters Milliliters
Milliliter (cm³) 0.000001 1
Cubic Inch 0.00001639 16.39
Pint 0.000473 473
Quart 0.000946 946
Liter 0.001 1,000
Gallon 0.003785 3,785
Cubic Foot 0.028317 28,317
Cubic Yard 0.764555 764,555
Cubic Meter 1 1,000,000
Cubic Kilometer 1,000,000,000 10&sup5;

Applications of Volume Calculator

  • DIY & Home Improvement: Calculate paint, concrete, or material needed for projects.
  • Construction & Engineering: Estimate the volume of tanks, concrete, or storage containers.
  • Science & Research: Measure volume of cells, organs, or substances to determine density.

FAQ's

What is the difference between surface area and volume?

  • Surface Area: 2D measure of the total area of all external faces.
  • Volume: 3D measure representing space enclosed by an object.

How much liquid can a container hold?

  • Determine the container's shape.
  • Measure its dimensions.
  • Use the corresponding volume formula.
  • Or, use the water displacement method for irregular shapes.

What are the methods used to measure volume?

  • Geometric formulas: For regular shapes like spheres, cubes, cylinders, cones, prisms.
  • Water displacement: Measure water rise when an object is submerged.
  • Mass & Density: Volume = Mass / Density for known density objects.

References: From Wikipedia: Volume

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