Free Surface Area Calculator

Add the surfaces that belong to your solid

The result covers the complete boundary of a closed solid. A rectangular prism has three pairs of matching rectangles. A cylinder combines a curved side with two circular ends. The table separates these contributions so you can see what the total includes.

• Cube: S = 6a², where a is the edge length.
• Rectangular prism: S = 2(lw + lh + wh).
• Sphere: S = 4πr², using radius r.
• Right cylinder: S = 2πrh + 2πr².
• Right cone: S = πrℓ + πr², with slant height ℓ = √(r² + h²).
• Right square pyramid: S = a² + 2aℓ, where ℓ = √[h² + (a/2)²].
• Right triangular prism: S = 2B + (a + b + c)L, where B is one triangular end’s area and L is prism length.

Worked example: a cylinder with two ends

For radius 3 cm and height 4 cm, the curved side has area 2 × π × 3 × 4 = 24π cm². Its two circular ends contribute 2 × π × 3² = 18π cm². Adding them gives 42π, approximately 131.946891 cm².

An open tube with no ends uses only the curved side. A container with one open end includes the curved side plus one base. The calculator shows the closed total; use its breakdown to select the surfaces required by your problem.

Use perpendicular height for cones and pyramids

Both forms ask for the straight height to the base. The tool finds the slant height using a right triangle before calculating the sloping surface. A square pyramid with side 8 cm and perpendicular height 3 cm has face slant height 5 cm. Its four triangles total 80 cm²; the 64 cm² base brings the total to 144 cm².

The pyramid assumes its apex sits above the center of the base. Its face slant height ends at the midpoint of a base edge. A corner-to-apex edge is a different measurement and cannot be substituted.

Convert square units after matching the input lengths

Enter all dimensions in the same length unit. Choosing a different input unit changes the meaning of the numbers; it does not convert them. The separate result-unit selector converts the calculated area.

For example, a cube with 10 cm edges has surface area 600 cm². Since 1 cm = 0.01 m, its area in square metres is 600 × 0.01² = 0.06 m². Squaring the conversion factor is essential.

Check the model before using the answer

• Use radius, not diameter, for round solids.
• Triangular ends need three sides that form a real triangle; the two shorter sides must add to more than the longest.
• These formulas describe ideal right solids. They exclude wall thickness, joints, holes and overlapping or hidden faces in composite objects.
• Doubling every dimension multiplies surface area by four. Volume scales differently and is available in the related volume tool.