Which shapes does this surface area calculator support?

This calculator supports rectangular prisms (including cubes), spheres, right circular cylinders, right circular cones, and right triangular prisms. Each shape uses its standard analytic formula, with clear assumptions documented on the page.

How accurate are the surface area results?

All formulas are exact for the ideal geometric shapes they describe. The numerical results are computed using double-precision floating-point arithmetic and rounded for display. In practice, the main uncertainty usually comes from measurement errors in the input dimensions.

What is the difference between lateral surface area and total surface area?

Lateral surface area includes only the side surfaces of a 3D shape, excluding its base and top. Total surface area includes all exposed faces, such as the circular ends of a cylinder or the base of a cone. This calculator reports total surface area and also shows the lateral contribution for shapes where it matters.

Surface Area Calculator

Multi-shape

Compute the total surface area of common 3D solids: rectangular prism (box or cube), sphere, right circular cylinder, right circular cone, and right triangular prism. Enter dimensions once and get results in multiple square units.

Designed for students, engineers, architects, and teachers who need fast, traceable calculations with clear formulas.

Interactive surface area calculator

Shape

Choose the 3D shape that best matches your problem.

Length unit

All entered dimensions must use this unit. The calculator converts internally to square meters.

Results

Quantity	Value	Unit

What is surface area?

The surface area of a solid is the total area of its outer “skin” — all faces and curved surfaces that separate the object from the surrounding space. It is measured in square units, such as cm², m², in², or ft².

For polyhedra (solids with flat faces), surface area is the sum of the areas of all faces. For curved solids such as cylinders, cones, and spheres, the surface area is given by analytic formulas derived from calculus and geometric arguments.

Surface area formulas for common 3D shapes

Rectangular prism / box

For a box with length \(l\), width \(w\), and height \(h\):

\[ A_{\text{box}} = 2(lw + lh + wh) \]

Cube

A cube is a special case of a rectangular prism where all edges are equal (\(a\)):

\[ A_{\text{cube}} = 6a^2 \]

Sphere

For a sphere of radius \(r\), the surface area is:

\[ A_{\text{sphere}} = 4\pi r^2 \]

Right circular cylinder

For a cylinder of radius \(r\) and height \(h\) (with two circular bases):

\[ A_{\text{total}} = 2\pi r^2 + 2\pi r h \] where the lateral area is \(A_{\text{lateral}} = 2\pi r h\) and the two bases contribute \(2\pi r^2\).

Right circular cone

For a right circular cone of base radius \(r\) and height \(h\), the slant height is:

\[ s = \sqrt{r^2 + h^2} \] \[ A_{\text{total}} = \pi r^2 + \pi r s \] where \(A_{\text{lateral}} = \pi r s\) and \(\pi r^2\) is the area of the base.

Right triangular prism

For a right prism with triangular base of side lengths \(a\), \(b\), \(c\) and prism length \(L\):

Use Heron's formula for the base area:

\[ s = \frac{a + b + c}{2}, \quad A_{\triangle} = \sqrt{s(s-a)(s-b)(s-c)} \]

Perimeter of the base:

\[ p = a + b + c \]

Total surface area:

\[ A_{\text{prism}} = 2 A_{\triangle} + p L \]

Common pitfalls and checks

Always use consistent units for all dimensions before applying a formula.
For triangular prisms, check the triangle inequality (\(a + b > c\), etc.).
Clarify whether you need total surface area or only lateral surface area.
For real objects with rounded edges or holes, analytic formulas are approximations.