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