📦 Volume Calculator (3D Shapes)
By ToolNimba Math Team · Updated 2026-06-19
Pick a shape and enter the dimensions to compute the volume.
This volume calculator finds how much space a 3D shape takes up. Pick a solid (cube, box, sphere, cylinder, cone, or pyramid), enter its dimensions, and the volume appears instantly along with the exact formula used. Just keep every measurement in the same unit and the result comes out in that unit cubed.
What is the Volume Calculator?
Volume measures the amount of three-dimensional space inside a closed shape. It is always expressed in cubic units (for example cubic centimetres, cm³, or cubic feet, ft³) because you are multiplying three lengths together. A cube one centimetre on each side holds exactly one cubic centimetre, so volume tells you how many of those unit cubes would fit inside the shape.
Each common solid has its own formula, but they fall into clear families. Box-like shapes (the cube and the rectangular prism) are just length times width times height. Round shapes built on a circle (the cylinder, the cone, and the sphere) all involve pi, because their cross-section is a circle of area pi x r². A cylinder is a circle dragged straight up, so its volume is the circle area times the height. A cone or a pyramid tapers to a point, and a neat result of calculus is that any such tapering solid holds exactly one third of the prism or cylinder that shares its base and height.
The single most important habit is consistent units. Because volume multiplies three lengths, mixing units (say, a radius in centimetres with a height in metres) produces a meaningless answer. Convert everything to one unit first. It also helps to remember that scaling matters cubically: double every dimension of a shape and its volume grows eight times, not two, because 2³ = 8. That is why a slightly bigger container can hold far more than it looks.
When to use it
- Working out how much water, soil, or liquid a tank, pool, or container will hold.
- Estimating shipping or storage space needed for boxes and packages.
- Checking homework or exam answers for geometry volume problems.
- Sizing materials such as concrete for a cylindrical post or sand for a conical pile.
How to use the Volume Calculator
- Choose the shape you want from the dropdown (cube, box, sphere, cylinder, cone, or pyramid).
- Enter the required dimensions for that shape in the same unit.
- Optionally pick a length unit so the answer is labelled in cubic units.
- Read off the volume and the formula that was applied.
Formula & method
Worked examples
Find the volume of a cylinder with radius 3 and height 10.
- Use V = π × r² × h
- r² = 3 × 3 = 9
- π × 9 = 28.27433
- V = 28.27433 × 10 = 282.7433
Result: V ≈ 282.74 cubic units
Find the volume of a cone with radius 3 and height 10.
- Use V = 1/3 × π × r² × h
- π × r² × h = 3.14159 × 9 × 10 = 282.7433
- V = 282.7433 ÷ 3 = 94.2478
- Note this is exactly one third of the matching cylinder above
Result: V ≈ 94.25 cubic units
Find the volume of a sphere with radius 5.
- Use V = 4/3 × π × r³
- r³ = 5 × 5 × 5 = 125
- π × 125 = 392.699
- V = 4/3 × 392.699 = 523.5988
Result: V ≈ 523.60 cubic units
Volume formulas for common 3D solids
| Shape | Dimensions needed | Volume formula |
|---|---|---|
| Cube | side s | V = s³ |
| Box (rectangular prism) | length, width, height | V = l × w × h |
| Sphere | radius r | V = 4/3 × π × r³ |
| Cylinder | radius r, height h | V = π × r² × h |
| Cone | radius r, height h | V = 1/3 × π × r² × h |
| Pyramid | base area B, height h | V = 1/3 × B × h |
Volume of a cube and a sphere as the size grows
| Measurement | Cube (V = s³) | Sphere (V = 4/3 π r³) |
|---|---|---|
| 1 | 1 | 4.19 |
| 2 | 8 | 33.51 |
| 3 | 27 | 113.10 |
| 5 | 125 | 523.60 |
| 10 | 1000 | 4188.79 |
Common mistakes to avoid
- Mixing units. Volume multiplies three lengths, so a radius in centimetres and a height in metres give a nonsense answer. Convert every dimension to the same unit before you calculate.
- Confusing radius with diameter. Sphere, cylinder, and cone formulas all use the radius, which is half the diameter. If you measured across the full width, divide by two first or the volume will be far too large.
- Forgetting the one-third on a cone or pyramid. A cone or pyramid holds exactly one third of the cylinder or prism with the same base and height. Dropping the 1/3 triples the answer.
- Reporting volume in square units. Volume is a cubic measure (cm³, m³, ft³), not square (cm², m²). Area uses two dimensions, volume uses three.
Glossary
- Volume
- The amount of three-dimensional space a shape encloses, measured in cubic units.
- Radius (r)
- The distance from the centre of a circle or sphere to its edge, equal to half the diameter.
- Rectangular prism
- A box shape with six rectangular faces, also called a cuboid.
- Base area (B)
- The area of the flat bottom face of a pyramid or prism, used in volume formulas.
- Pi (π)
- The constant ratio of a circle’s circumference to its diameter, approximately 3.14159.
Frequently asked questions
How do I calculate the volume of a cylinder?
Use V = π × r² × h. Square the radius, multiply by pi (about 3.14159), then multiply by the height. For a cylinder with radius 3 and height 10, V = 3.14159 × 9 × 10 ≈ 282.74 cubic units.
What is the formula for the volume of a sphere?
The volume of a sphere is V = 4/3 × π × r³, where r is the radius. Cube the radius, multiply by pi, then multiply by four thirds. A sphere of radius 5 has a volume of about 523.60 cubic units.
How do I find the volume of a box?
A box (rectangular prism) is simply length × width × height. For example, a box 2 by 3 by 4 has a volume of 2 × 3 × 4 = 24 cubic units. A cube is the special case where all three are equal, so V = s³.
Why do cones and pyramids have a one-third in the formula?
A cone or pyramid that tapers to a point holds exactly one third of the cylinder or prism with the same base and height. Calculus proves this exactly, which is why both formulas multiply the base times height by 1/3.
What units does the volume come out in?
Volume is in cubic units of whatever length unit you used. If you entered centimetres the result is cubic centimetres (cm³); if you used feet it is cubic feet (ft³). Keep every dimension in one unit for a correct answer.
What happens to volume if I double the size of a shape?
Volume scales by the cube of the change. Doubling every dimension multiplies the volume by 2³ = 8, and tripling multiplies it by 3³ = 27. That is why small increases in size hold much more than you might expect.