Volume Calculator
Calculate the volume of 11 different 3D shapes including sphere, cylinder, cone, cube, cuboid, triangular prism, pyramid, tetrahedron, ellipsoid, torus, and frustum. Get instant results with detailed step-by-step solutions.
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About Volume Calculator
Welcome to the Volume Calculator, your comprehensive tool for calculating the volume of 11 different 3D geometric shapes. Whether you need to find the volume of a sphere, cylinder, cone, cube, or more complex shapes like torus and frustum, this calculator provides instant results with detailed step-by-step solutions and visual diagrams.
Supported 3D Shapes
| Shape | Volume Formula | Parameters |
|---|---|---|
| Sphere | \( V = \frac{4}{3}\pi r^3 \) | Radius (r) |
| Cylinder | \( V = \pi r^2 h \) | Radius (r), Height (h) |
| Cone | \( V = \frac{1}{3}\pi r^2 h \) | Radius (r), Height (h) |
| Cube | \( V = a^3 \) | Side length (a) |
| Cuboid | \( V = l \times w \times h \) | Length, Width, Height |
| Triangular Prism | \( V = \frac{1}{2}bhl \) | Base, Height, Length |
| Square Pyramid | \( V = \frac{1}{3}a^2 h \) | Base side (a), Height (h) |
| Tetrahedron | \( V = \frac{a^3}{6\sqrt{2}} \) | Edge length (a) |
| Ellipsoid | \( V = \frac{4}{3}\pi abc \) | Semi-axes (a, b, c) |
| Torus | \( V = 2\pi^2 Rr^2 \) | Major radius (R), Minor radius (r) |
| Frustum | \( V = \frac{1}{3}\pi h(r_1^2 + r_1r_2 + r_2^2) \) | Top radius, Bottom radius, Height |
How to Use This Calculator
- Select a shape: Click on one of the shape cards to choose the 3D shape you want to calculate.
- Enter dimensions: Input the required measurements (radius, height, length, etc.).
- Calculate: Click the "Calculate Volume" button to get your result.
- Review: See the volume, surface area (where applicable), and step-by-step solution.
Understanding Volume
Volume is the amount of three-dimensional space enclosed within a closed surface. It tells us how much space an object occupies or how much it can contain. Volume is measured in cubic units such as:
- Cubic meters (m³)
- Cubic centimeters (cm³)
- Liters (L) - 1 L = 1000 cm³
- Cubic feet (ft³)
- Cubic inches (in³)
Volume Formulas Explained
Sphere Volume
A sphere is a perfectly round 3D shape where every point on the surface is equidistant from the center. The volume depends only on the radius.
Cylinder Volume
A cylinder has two parallel circular bases connected by a curved surface. Its volume is the area of the base circle multiplied by the height.
Cone Volume
A cone has a circular base that tapers to a point (apex). Its volume is exactly one-third of a cylinder with the same base and height.
Frequently Asked Questions
What is volume in geometry?
Volume is the amount of three-dimensional space enclosed within a closed surface. It is measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), liters, or cubic feet. Volume tells you how much space an object occupies or how much it can hold.
How do you calculate the volume of a sphere?
The volume of a sphere is calculated using the formula V = (4/3)πr³, where r is the radius. For example, a sphere with radius 5 has volume V = (4/3)π(5)³ = (4/3)π(125) ≈ 523.6 cubic units.
What is the difference between a cube and a cuboid?
A cube is a special case of a cuboid where all six faces are equal squares (length = width = height). A cuboid (rectangular prism) has rectangular faces where dimensions can differ. Cube volume is a³, while cuboid volume is length × width × height.
How do you find the volume of a cone?
The volume of a cone is V = (1/3)πr²h, where r is the radius of the circular base and h is the height. This formula shows that a cone has exactly one-third the volume of a cylinder with the same base and height.
Additional Resources
Reference this content, page, or tool as:
"Volume Calculator" at https://MiniWebtool.com/volume-calculator/ from MiniWebtool, https://MiniWebtool.com/
by miniwebtool team. Updated: Jan 19, 2026
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