Surface Area Calculator
Surface area calculator for common 3D shapes: box, cube, sphere, cylinder, cone, triangular prism. Enter dimensions in mm, cm, m, inches, or feet and get total surface area with formulas and step-by-step explanation.
Full original guide (expanded)
Surface Area Calculator
Multi-shapeCompute 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
Choose the 3D shape that best matches your problem.
All entered dimensions must use this unit. The calculator converts internally to square meters.
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 \(h\):
Cube
A cube is a special case of a rectangular prism where all edges are equal (\(a\)):
Sphere
For a sphere of radius \(r\), the surface area is:
Right circular cylinder
For a cylinder of radius \(r\) and height \(h\) (with two circular bases):
Right circular cone
For a right circular cone of base radius \(r\) and height \(h\), the slant height is:
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.
Frequently asked questions
Formula (LaTeX) + variables + units
A_{\text{box}} = 2(lw + lh + wh)
A_{\text{cube}} = 6a^2
A_{\text{sphere}} = 4\pi r^2
A_{\text{total}} = 2\pi r^2 + 2\pi r h
s = \sqrt{r^2 + h^2}
A_{\text{total}} = \pi r^2 + \pi r s
\[ A_{\text{box}} = 2(lw + lh + wh) \]
\[ A_{\text{cube}} = 6a^2 \]
\[ A_{\text{sphere}} = 4\pi r^2 \]
\[ A_{\text{total}} = 2\pi r^2 + 2\pi r h \] where the lateral area is \(A_{\text{lateral}} = 2\pi r h\) and the two bases contribute \(2\pi r^2\).
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.