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Geometry

Surface Area Calculator

Calculate the total outside area of common three-dimensional shapes from their dimensions.

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Pick the solid, enter its dimensions, and the calculator will return the total exterior area for that shape.
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Outside area measurement notes

Calculating surface area by choosing which faces are actually exposed

Surface area measures the outside

Surface area describes how much outside covering a solid has. It is different from volume, which measures space inside. Paint, wrapping, coating, and exposed material questions usually point to surface area.

Total and lateral surface area are not the same

Total surface area includes all outside faces. Lateral surface area often excludes bases and counts only side faces or curved side surfaces. The correct choice depends on what is being covered. A label on a can may use lateral area, while painting the whole can uses more surfaces.

Cubes are the simplest solid

A cube has six equal square faces. If the side length is known, total surface area is six times the area of one face. If only some faces are exposed, the number of counted faces changes.

Cuboids need three dimensions

A rectangular prism or cuboid has length, width, and height. Opposite faces match, so the surface area comes from pairs of rectangles. Swapping dimensions usually does not change the total, but missing one dimension makes the solid incomplete.

Cylinders combine circles and a rectangle

A cylinder has two circular bases and one curved side. The curved side unwraps into a rectangle whose width is the circumference. If a problem mentions only the side label or curved covering, lateral area may be the intended measure. The Circle Calculator can help review radius, diameter, and circumference before the cylinder is handled.

Cones need slant height for the side

Cone surface area uses slant height for the curved side. Vertical height is not the same measurement unless the cone has collapsed, which would not be a cone. If vertical height and radius are given, slant height may need to be found first.

Pyramids depend on the base and triangular faces

A pyramid combines a base with triangular side faces. The base may be square, rectangular, or another polygon depending on the problem. Slant height describes the height of a triangular face, not the vertical height through the center.

Spheres have no flat faces

A sphere uses a curved surface only. Its surface area depends on radius squared. If the given measurement is diameter, divide by 2 before using the radius-based formula.

Hemispheres can include or exclude the base

A hemisphere is half a sphere, but surface area questions may or may not include the circular base. A dome exterior might exclude the base. A closed half-sphere object might include it. Read the wording before selecting the surface type.

Prisms repeat one cross-section

A prism carries the same cross-section along a length. A triangular prism has two triangular ends and rectangular side faces. If the problem gives side lengths of the triangle, those lengths help form the rectangles along the prism length.

Frustums and torus shapes need specialized fields

A frustum is a solid with the top cut off, so it needs upper and lower measurements. A torus uses major and minor radii. These shapes should not be forced into cylinder, cone, or sphere modes just because they look partly similar.

Use area and volume pages for neighboring questions

If the problem is flat, use the Area Calculator. If it asks how much space the solid holds, use the Volume Calculator. Surface area sits between those ideas: it is square-unit measurement applied to a three-dimensional object.