Volume Calculator

What Volume Means

Volume is how much space a solid takes up - picture how many unit cubes it would take to fill it. For a box you stack cubes in rows, in layers, so the volume is simply $\text{length} \times \text{width} \times \text{height}$.

The round shapes follow the same “base times height” idea:

• A cylinder is a circle pushed straight up, so its volume is the circle’s area times the height ($\pi r^2 \times h$).
• A cone with the same base and height holds exactly one third as much as that cylinder - a handy fact to remember.
• A sphere works out to $\tfrac{4}{3}\pi r^3$.

Pick a shape above and the diagram redraws to your measurements. For the round shapes you can also choose which value of π to use.

Volume Formulas

$$\begin{aligned} \text{box} &= \text{length} \times \text{width} \times \text{height} \\ \text{cube} &= \text{side}^3 \\ \text{sphere} &= \tfrac{4}{3}\pi r^3 \\ \text{cylinder} &= \pi r^2 \times \text{height} \\ \text{cone} &= \tfrac{1}{3}\pi r^2 \times \text{height} \end{aligned}$$

A cone holds exactly one third of the cylinder with the same base and height.

How to Use It

1. Choose the shape.
2. Enter the measurements it asks for.
3. Read the volume and the steps.

Worked Examples

Shape	Measurements	Volume
Box	4 × 3 × 2	24
Cube	side 4	64
Sphere	radius 3	≈ 113.1
Cylinder	radius 3, height 4	≈ 113.1
Cone	radius 3, height 4	≈ 37.7

FAQ

How do you find the volume of a box?

Multiply length by width by height. For 4 × 3 × 2: $24$.

What is the volume of a sphere?

Use $\frac{4}{3} \times \pi \times r^3$. For a radius of 3: $\frac{4}{3} \times \pi \times 27 \approx 113.1$.

How do you find the volume of a cylinder?

Multiply the base area by the height: $\pi \times r^2 \times \text{height}$.

Why is a cone’s volume a third of a cylinder’s?

A cone with the same base and height holds exactly one third as much, so its formula is $\frac{1}{3} \times \pi \times r^2 \times \text{height}$.