Volume Calculator

What is Volume?

Volume measures the amount of three-dimensional space an object occupies. Its SI unit is the cubic meter (m³). Typically, volume is used to represent how much a container can hold, not the space it displaces.

Most basic shapes have standard formulas for volume calculation. For complex objects, volume can be found by breaking them into simpler shapes or by using advanced mathematical techniques like integral calculus or finite element analysis. If an object’s density is known and uniform, volume can also be determined through its weight.

Volume Formulas for Common Shapes

1. Sphere

Formula: Volume = 4/3 × πr³

Example: A spherical balloon with a radius of 0.15 ft holds approx 0.141 ft³ of liquid.

2. Cone

Formula: Volume = 1/3 × πr²h

Example: A cone with a radius of 1.5 in and height 5 in holds approx 11.78 in³.

3. Cube

Formula: Volume = a³

Example: A cube with 2 ft edges holds 8 ft³ of volume.

4. Cylinder

Formula: Volume = πr²h

Example: A cylinder with radius 3 ft and height 4 ft holds approx 113.1 ft³.

5. Rectangular Tank

Formula: Volume = length × width × height

Example: A box 4 ft × 3 ft × 2 ft holds 24 ft³.

6. Capsule

Formula: Volume = πr²h + 4/3 × πr³ = πr²(h + 4r/3)

Example: A capsule with radius 1.5 ft and height 3 ft holds approx 35.34 ft³.

7. Spherical Cap

Formula: Volume = 1/3 × πh²(3R – h)

Example: A cap from a sphere of radius 1.68 in and height 0.3 in holds approx 0.447 in³.

8. Conical Frustum

Formula: Volume = 1/3 × πh(r² + rR + R²)

Example: A frustum with radii 1.5 in and 0.2 in, and height 4 in holds approx 10.85 in³.

9. Ellipsoid

Formula: Volume = 4/3 × πabc

Example: An ellipsoid with axes 1.5 in, 2 in, and 5 in holds approx 62.83 in³.

10. Square Pyramid

Formula: Volume = 1/3 × a²h

Example: A pyramid with a 5 ft square base and height 12 ft holds 100 ft³.

11. Tube

Formula: Volume = π/4 × (d1² – d2²) × l

Example: A tube with outer diameter 3 ft, inner diameter 2.5 ft, and length 10 ft holds approx 21.6 ft³.

Common Volume Units Conversion

Related Calculator:
Triangle Calculator, Percent Error Calculator, Standard Deviation Calculator

External Resources:
Volume Calculator on Calculator.net