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Surface area tells you how much material covers the outside of a solid — useful for anything from painting a surface to sizing packaging material.
This calculator finds the surface area of a cube, rectangular prism (box), sphere, cylinder, or cone from its dimensions.
How it works
Choose a shape, then enter the required dimensions (a single side or radius for a cube or sphere; length, width, and height for a box; radius and height for a cylinder or cone). For a cone, the calculator first finds the slant height using the Pythagorean theorem, then applies the surface area formula.
- Enter shape.
- Enter side / length / radius.
- Enter width / height (not used for cube or sphere).
- Enter height (box only).
- Click Calculate to see your results.
Examples
Cone, radius 3, height 4
A cone with a radius of 3 and a height of 4 has a slant height of 5 (from the Pythagorean theorem) and a total surface area of about 75.40 square units.
Who should use it
- Solving geometry homework problems involving 3D shapes.
- Estimating material needed to cover, paint, or wrap a solid object.
Industry applications
- Mathematics education
- Manufacturing, packaging, and construction
Advantages
- Covers five common shapes in a single calculator.
- Shows the specific formula and any intermediate steps (like slant height) used for the selected shape.
Limitations
- Doesn't cover irregular or composite shapes made of multiple combined solids.
Common mistakes to avoid
- Entering a diameter instead of a radius for spheres, cylinders, or cones.
- Forgetting that total surface area includes the base(s), not just the curved lateral surface, for cylinders and cones.
Best practices
- Double-check whether a measurement you're given is a radius or a diameter before entering it — this is the most common source of surface area calculation errors.
Tips
- For a sphere, surface area and volume are related by a simple factor — if you know the volume, you can back into the radius first, then compute surface area from that.