Volume Calculator
Calculate the volume of 11 common three-dimensional geometric shapes instantly with detailed step-by-step formulas.
Sphere Volume
Cone Volume
Cube Volume
Cylinder Volume
Rectangular Tank
Capsule Volume
Spherical Cap
Conical Frustum
Ellipsoid Volume
Square Pyramid
Tube / Pipe Volume
Understanding Volume and 3D Measurement Principles
Volume measures the total three-dimensional space enclosed inside a closed boundary or object. The international standard (SI) unit for volume is the cubic meter (m³). In practical scenarios, container volume often denotes storage capacity or liquid displacement rather than external dimensions. While regular shapes rely on direct geometric formulas, irregular geometries can be evaluated using calculus or finite element modeling.
1. Sphere
A sphere is a perfectly symmetrical round spatial body where all surface points maintain an equal distance (r) from the exact center point. Unlike flat circles, spherical structures possess volume governed by radial dimensions.
Example: Filling a spherical water balloon having a radius of 0.15 ft yields a volume of 4/3 × π × 0.15³ = 0.141 ft³.
2. Cone
A cone is a tapered 3D geometric shape that narrows smoothly from a circular base up to a terminal vertex or apex. Only standard right circular cones are addressed here.
Example: Evaluating a waffle cone with a circular base radius of 1.5 in and height of 5 in gives 1/3 × π × 1.5² × 5 = 11.781 in³.
3. Cube
A cube is a regular hexahedron bound by six congruent square faces meeting at perpendicular 90-degree angles.
Example: A cubic container with side edges measuring 2 feet provides a capacity of 2³ = 8 ft³.
4. Cylinder
A cylinder consists of two parallel circular end caps connected by a curved tubular surface of height h.
Example: A cylindrical barrel with radius 3 ft and height 4 ft holds π × 3² × 4 = 113.097 ft³ of material.
5. Rectangular Tank
A rectangular box or cuboid features length, width, and height dimensions that can vary independently across six flat faces.
Example: Packing a travel case with dimensions 2 ft × 3 ft × 4 ft totals 2 × 3 × 4 = 24 ft³.
6. Capsule
A capsule combines a central cylindrical section capped by two hemispherical ends on both sides.
Example: Given radius 1.5 ft and cylinder height 3 ft, the total volume computes to π × 1.5² × 3 + 4/3 × π × 1.5³ = 35.343 ft³.
7. Spherical Cap
A spherical cap represents a rounded segment separated from a full sphere by an intersecting cutting plane.
Related dimension formulas include finding height or base radius: h = R ± √(R² - r²) and R = (h² + r²) / (2h).
8. Conical Frustum
A conical frustum is the lower portion of a cone remaining after the upper tip is sliced off parallel to its base.
Example: Using top radius 0.2 in, bottom radius 1.5 in, and height 4 in yields 10.849 in³.
9. Ellipsoid
An ellipsoid is a deformed spherical geometry stretched across three distinct principal perpendicular semi-axes (a, b, c).
Example: Axis lengths of 1.5 in, 2 in, and 5 in result in 4/3 × π × 1.5 × 2 × 5 = 62.832 in³.
10. Square Pyramid
A square pyramid features a square base foundation and four triangular slopes meeting at a single top vertex.
Example: A pyramid with base edge 5 ft and height 12 ft gives 1/3 × 5² × 12 = 100 ft³.
11. Tube / Pipe
A hollow tubular pipe volume is calculated by finding the difference between outer and inner cylinder capacities over a specific length (l).
Example: Outer diameter 3 ft, inner diameter 2.5 ft, and length 10 ft yields π × ((3² - 2.5²) / 4) × 10 = 21.6 ft³.
Common Volume Units Conversion Reference
| Unit | Cubic Meters (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 |