Volume Calculator
Calculate volumes for various geometric shapes with precision and ease
Calculation Result:
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
| Unit | m³ | milliliters (mL) |
|---|---|---|
| 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 | 1015 |
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