Volume Calculator
MiniWebtool’s Volume Calculator calculates the volume of 11 different 3D shapes: 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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Choose one of the 11 shapes below and enter its measurements to get the volume with step-by-step working.
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.
At a Glance
Volume Calculator finds the volume of 11 three-dimensional shapes: sphere, cylinder, cone, cube, cuboid, triangular prism, pyramid, tetrahedron, ellipsoid, torus and frustum. It shows each formula step.
| Feature | What you get | Good for |
|---|---|---|
| 11 shapes | Select a shape card: sphere, cylinder, cone, cube, cuboid, triangular prism, square pyramid, tetrahedron, ellipsoid, torus or frustum. | Switching between common solids in one place |
| Shape inputs | Each shape asks only for its own measurements, such as radius, height, edge length, semi-axes or major and minor radius. | Entering exactly what a textbook problem gives |
| Formulas used | Examples: sphere V = 4/3 πr³, cone V = 1/3 πr²h, cuboid V = l × w × h, torus V = 2π²Rr². | Checking which formula applies to a shape |
| Step-by-step solution | The result includes a worked breakdown of the formula with your numbers. | Homework and showing work in geometry |
| Surface area | Surface area is also given for shapes where it applies. | Comparing volume and surface for one solid |
| Shape diagrams | Interactive SVG diagrams show the selected shape. | Seeing which dimension each input refers to |
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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