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Free Online Volume and Surface Area Calculator

Work out the volume and the surface area of ten solids at once, from a cube, box, cylinder and cone to a sphere, pyramid, prism, torus and capsule. Each shape also gives the extras that go with it, such as the slant height of a cone or the curved surface of a cylinder on its own, with every formula shown.

Free Forever Nothing Uploaded Ten Solids Both At Once
Free Online Volume and Surface Area Calculator
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🧊 Volume and Surface Area Ten solids · volume and surface together · every formula shown

The sum runs in your browser. Nothing you type is sent anywhere.

The solid

🧊 The measurements

Only the boxes this solid needs are shown. Every length must be in the same unit; the volume then comes out in that unit cubed and the surface area in it squared.

Try one of these
A torus needs its ring radius to be larger than its tube radius, or the ring passes through itself.
The volume
—
Surface area—
Surface to volume—

The formulas for this solid, with your own numbers in them.

What Formula With your numbers
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How to Find Volume and Surface Area

Three steps, and the third is the one worth reading.

1
Choose the solid Cube, box, cylinder, cone, sphere, hemisphere, square pyramid, triangular prism, torus or capsule. The boxes change to the measurements that shape needs.
2
Enter the measurements in one unit Every length has to be in the same unit. The volume then comes out in that unit cubed and the surface area in it squared, which is the part people most often get wrong when mixing centimetres and metres.
3
Read the extras as well The slant height of a cone, the curved surface of a cylinder on its own, the space diagonal of a box: those are the numbers people go looking for separately, so they come with the shape.

What to Know About Solids

Why the two go together, and where the formulas trip people up.

Volume and surface area belong together. Both come from the same measurements, so splitting them across two pages means typing the same numbers twice and gives two chances to make a typing error. They are given together here, along with the ratio between them, which is the number that matters whenever heating, cooling, coating or dissolving is involved.
The curved surface is given on its own. Making a label for a tin needs the curved part of a cylinder, not the whole surface including both ends. Painting an open topped tank needs the sides and the base but not the lid. Those partial surfaces are the ones people actually need, so they appear as extras rather than being left as an arithmetic exercise.
A cone has two different heights. The perpendicular height runs from the apex straight down to the centre of the base, and it is what the volume uses. The slant height runs down the sloping side to the rim, and it is what the curved surface uses. They are different numbers and using one in place of the other is the usual mistake, so the slant height is computed and shown rather than being asked for.
A torus needs its ring radius to be the larger one. If the tube is fatter than the ring is wide, the shape passes through itself and is not a torus at all. The formula still returns a number, which is why the check is made before it runs rather than being left to the result to reveal.
Doubling a length multiplies the volume by eight. Surface area grows with the square of a length and volume with the cube, so a shape twice as long has four times the surface and eight times the volume. That is why small animals lose heat faster than large ones and why a large tank keeps its temperature better than a small one. The surface to volume ratio on the page is that relationship as a single number.
It runs in your browser with nothing uploaded. The arithmetic is in the page, so it works offline once loaded and nothing you type is sent anywhere.

Key Features & Capabilities

What it does, and what it deliberately does not.

Ten solids Cube, box, cylinder, cone, sphere, hemisphere, pyramid, prism, torus and capsule.
Volume and surface together From the same measurements, with the ratio between them, so nothing is typed twice.
Partial surfaces given The curved part of a cylinder, the sloping sides of a pyramid, one end of a tube.
Slant heights worked out Computed from the perpendicular height rather than asked for, since confusing the two is the usual error.
Every formula shown With your own numbers in it, so the answer can be checked rather than trusted.
Nothing is uploaded It runs in this tab and keeps working offline.

About Volume and Surface Area

Volume is how much a solid holds and surface area is how much skin it has. Both are determined by the same handful of measurements, which is why this page gives them together: asking for the radius and height of a cylinder on one page for its volume and again on another for its surface is wasted effort and an extra chance to mistype.

The relationship between the two is more interesting than either on its own. Surface area grows with the square of a length while volume grows with the cube, so a shape scaled up by a factor of two has four times the surface and eight times the volume. Everything that happens through a surface, heating, cooling, evaporating, dissolving, coating, therefore gets relatively slower as a shape gets larger. That is why a small animal eats constantly and a large one does not, and why ice cubes melt faster than an iceberg. The surface to volume ratio shown on the page is that comparison in one number.

The formulas themselves hold two traps. The first is the cone, which has two different heights: the perpendicular height from apex to base centre, used for the volume, and the slant height down the sloping side, used for the curved surface. They are different numbers and swapping them is the standard mistake, so the slant height is computed from the perpendicular one and displayed rather than being requested.

The second is partial surfaces. Real questions rarely ask for the total. A label for a tin needs the curved part of the cylinder without the ends. An open tank needs the sides and the base without the lid. A cone’s net needs the curved part separately from the circular base. Those pieces are given as extras here, because working them out from a total is exactly the step people come to a calculator to avoid.

One practical note. Every length entered has to be in the same unit. The volume then comes out in that unit cubed and the surface area in it squared. Mixing centimetres and metres in the same shape is the most common source of an answer that is wrong by a factor of a thousand, and no calculator can detect it, because the numbers themselves look perfectly reasonable.

Frequently Asked Questions

Shapes, units, slant heights and curved surfaces.

Whichever you use, as long as all the lengths are the same one. The volume comes out in that unit cubed and the surface area in it squared. Mixing units within one shape is the usual cause of an answer that is wrong by a factor of a thousand.

The height is straight down from the apex to the centre of the base and gives the volume. The slant height is down the sloping side to the rim and gives the curved surface. The page asks for the height and works out the slant height itself.

Yes, it is given as an extra. That is the figure for a label or a wrap, where the two circular ends are not part of what you are covering.

Because the tube radius is larger than the ring radius, which would make the ring pass through itself. The result would not be a torus, and the formula would give a number for a shape that cannot exist.

How much skin there is for each unit of content. A high ratio means the shape exchanges heat, moisture or anything else through its surface quickly relative to its size. It falls as a shape gets bigger, which is why scale matters so much in engineering and biology.

Yes. It is a cylinder with a hemisphere on each end, which is the usual shape for a pressure vessel or a pill, and the straight length asked for is the cylindrical part only.

No. The arithmetic runs in your browser, so nothing you type leaves the page and it works offline.

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