Volume Calculator

1. Choose the shape: sphere, cube, box, cylinder or cone.
2. Enter the dimensions that shape needs.
3. Read the volume, the space it holds.
4. See the surface area as well.

Here is what each result means:

Volume is the amount of three-dimensional space a solid takes up, measured in cubic units. A box a certain length, width and height holds length times width times height of space. Each common shape has its own formula, but all of them measure the same thing: how much fits inside.

Volume comes up constantly, from filling a tank or a pool to shipping a parcel or baking in a tin. Surface area, the total area of the outside, is a companion measurement that matters for wrapping, painting or coating a solid. This calculator gives both for the most common shapes.

Volume always grows faster than length, because it stretches in three directions at once. Doubling the size of a solid multiplies its volume by eight, not two, since each of the three dimensions doubles. That is why a slightly larger radius or side can make a surprisingly large difference to how much a shape holds.

It applies the standard volume and surface-area formula for the shape you pick.

1. Read the dimensions your shape needs.
2. Apply the matching volume formula.
3. Compute the surface area from the same dimensions.

For flat shapes rather than solids, the circle calculator and triangle area calculator handle two-dimensional area.

Find the volume of a cylinder with radius 2 and height 5.

Calculation: V = pi r^2 h = pi (2)^2 (5) = 20 pi = 62.83. A sphere of radius 3, by comparison, holds (4/3) pi (3)^3 = 113, showing how the shape changes the result even at similar sizes.

Each solid has its own formula, all in cubic units.

A cone holds exactly one third of the cylinder with the same base and height, a handy fact to remember.

The two measure different things about the same solid.

Volume tells you how much a solid holds; surface area tells you how much material covers it. This tool reports both.

The Radius or Side

Volume grows fast with these, often with the cube or square, so a small increase makes a big difference.

The Height

For a cylinder or cone, volume scales directly with height. Doubling the height doubles the volume.

The Shape Itself

The same base and height give very different volumes for a cylinder, a cone and a box.

Filling and Capacity

Work out how much a tank, pool or container holds.

Shipping and Packing

Find the volume of a box or cylinder for freight or storage.

DIY and Cooking

Size a tin, planter or mold from its dimensions.

1. Using Diameter as Radius

Sphere, cylinder and cone formulas use the radius. Halve a diameter first.

2. Forgetting to Cube or Square

Volume raises a length to a power. Missing the cube or square gives a far smaller answer.

3. Wrong Shape Formula

A cone is a third of a cylinder. Using the cylinder formula for a cone triples the volume.

4. Mixed Units

Keep all dimensions in the same unit; the volume is then in that unit cubed.

5. Confusing Volume with Surface Area

Volume is the space inside; surface area is the outside. They use different units.

The formulas are exact; only the displayed decimals are rounded.

Use the formula for the shape. A box is length times width times height, a cylinder is pi times radius squared times height, and a sphere is four-thirds pi times radius cubed. This tool applies the right one.

It is four-thirds pi times the radius cubed. A sphere of radius 3 has a volume of four-thirds pi times 27, about 113 cubic units.

It is pi times the radius squared times the height. A cylinder of radius 2 and height 5 holds pi times 4 times 5, about 62.83 cubic units.

A cone holds exactly one third of the cylinder with the same base and height. So its volume is one-third pi times radius squared times height.

Volume is in cubic units of whatever length unit you use. If dimensions are in centimeters, the volume is in cubic centimeters.

The sphere, cylinder and cone formulas use the radius, which is half the diameter. If you have the diameter, divide it by two first.

Surface area is the total area of the outside of a solid, in square units. It matters for painting, wrapping or coating, and this tool reports it alongside the volume.

No. This tool covers five regular solids. An irregular or composite shape must be split into these simpler pieces, whose volumes you then add.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Volume (Wikipedia).
• Volume formulas (Maths Is Fun).
• Surface area (Wikipedia).