Surface Area CalculatorFree online math calculator — instant results, no sign-up
Surface area of 3D shapes.
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About the Surface Area Calculator
This calculator determines the total surface area for five common three-dimensional geometric shapes: cubes, rectangular boxes, spheres, cylinders, and cones. It provides students, woodworkers, and designers with the external boundary area needed for materials estimation or mathematical analysis.
- Shape
- Select from Cube, Box, Sphere, Cylinder, or Cone to set the corresponding geometric calculation.
- a (side/length/radius)
- Represents edge length for a cube, base length for a box, or radius for a sphere, cylinder, and cone; positive real number.
- b (width)
- Base width for a rectangular box; not used for other shapes; positive real number.
- Height
- Vertical height for a rectangular box, cylinder, or cone; not used for cubes or spheres; positive real number.
Formula and method
Cube: A = 6 × a²; Box: A = 2 × (a × b + a × h + b × h); Sphere: A = 4 × π × a²; Cylinder: A = 2 × π × a × (a + h); Cone: A = π × a × (a + √(a² + h²))
- ATotal surface area
- aSide length (Cube), base length (Box), or radius (Sphere, Cylinder, Cone)
- bWidth (Box)
- hVertical height (Box, Cylinder, Cone)
- πMathematical constant pi (~3.14159265)
The tool selects the mathematical model corresponding to the chosen shape, maps the inputs to their geometric roles, and evaluates the expression using standard floating-point arithmetic. The final surface area is formatted to up to six decimal places, stripping unnecessary trailing zeros.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- ShapeCube
- a (side/length/radius)3
- b (width)4
- Height5
Results
- Surface area54
How to use the Surface Area Calculator
- 1Select the 3D shape from the dropdown menu.
- 2Enter the primary dimension 'a' (side length, length, or radius) in consistent linear units.
- 3Enter the width 'b' and vertical height 'h' if required by the chosen shape.
- 4Read the computed total surface area displayed in square units corresponding to the input dimension.
Reading your result
The result represents the entire exterior surface area of the solid shape in square units (such as square meters or square inches). For closed solids like the cylinder and cone, this includes both the lateral sides and the flat circular bases.
Limitations
The formulas assume idealized geometric solids with flat bases and zero wall thickness. Calculations do not account for open-ended shapes (e.g., hollow pipes without caps), truncation (frustums), or non-right geometries (oblique cylinders or cones).
Common questions
Does the cylinder surface area include the circular top and bottom?+
Yes. The formula 2πa(a + h) expands to 2πa² + 2πah, which accounts for both circular end caps as well as the curved lateral side.
How is the slant height handled for the cone?+
The slant height is derived automatically from the radius 'a' and vertical height 'h' using the Pythagorean theorem, √(a² + h²).
What happens to unused inputs, like 'b' when calculating a sphere?+
Unused fields are ignored by the calculation for that specific shape. Only the relevant dimensions (such as 'a' for radius on a sphere) are factored into the formula.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.