Surface Area Calculator — Common 3D Shapes
Inputs
Use one consistent unit for every length. Areas are reported in the squared version of that unit.
Results
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How the Surface Area Calculator Works
Surface area is the total area covering the outside of a three-dimensional object. This calculator focuses on common classroom and project shapes: cubes, rectangular prisms, spheres, cylinders, cones, square pyramids, and triangular prisms. Where a solid has bases, the result separates lateral area from base area so you can see what is being counted.
The calculator assumes ideal geometric solids: cylinders and cones are right circular, pyramids have a square base with the apex centered above the base, and triangular prisms use a valid triangle for the end faces. Enter all dimensions in the same unit. If you enter centimeters, the answer is in square centimeters; if you enter feet, the answer is in square feet.
How to use it:
- Choose the shape that matches your object.
- Enter the requested dimensions using one consistent unit.
- Choose decimal places and a pi approximation if needed for classwork.
- Click Calculate to see total surface area and the formula used.
- Use Copy or Download CSV when you need to move the result into notes or a spreadsheet.
Surface Area Formulas
| Shape | Formula | Notes |
|---|---|---|
| Cube | S = 6a² | a is edge length. |
| Rectangular prism | S = 2(lw + lh + wh) | l, w, and h are length, width, and height. |
| Sphere | S = 4πr² | r is radius. |
| Cylinder | S = 2πr(r + h) | Lateral area is 2πrh; bases add 2πr². |
| Cone | S = πr(r + l) | l = √(r² + h²) when height is entered instead of slant height. |
| Square pyramid | S = a² + 2al | l = √(h² + (a/2)²) when vertical height is entered. |
| Triangular prism | S = pL + 2B | p is triangle perimeter, L is prism length, and B is triangle area by Heron's formula. |
Limits: This educational calculator handles idealized shapes. Real objects may need allowances for seams, overlap, waste, curvature tolerances, or manufacturing details.
Surface Area Calculator: FAQs
What shapes does this surface area calculator support?
It supports cubes, rectangular prisms, spheres, right circular cylinders, right circular cones, square pyramids, and triangular prisms.
What is the difference between total surface area and lateral surface area?
Total surface area includes every exposed face or curved surface. Lateral surface area excludes bases when a shape has clear bases.
What units should I enter?
Enter all lengths in the same length unit. The calculator labels the answer with the corresponding squared unit, such as cm², ft², or m².
Does the calculator upload my measurements?
No. Computation is entirely client-side; nothing is uploaded.