Surface Area Calculator

Inputs

Select a shape and dimensions to find the total surface area.

Understanding Surface Area

Surface Area is the total area of all the faces and curved surfaces of a 3-dimensional solid object. It is measured in square units (e.g., m², ft²).

Calculating surface area is crucial for tasks like painting a house, wrapping a gift, or determining heat transfer in engineering.

Common Formulas

Cylinder

2 circular bases + rectangular side.

SA = 2πrh + 2πr²

Sphere

4 times the area of its great circle.

SA = 4πr²

Cube

6 identical square faces.

SA = 6s²

Rectangular Prism

Sum of areas of all 6 rectangles.

SA = 2(lw + lh + wh)

Total vs. Lateral Surface Area

Total Surface Area (TSA)

Includes the area of ALL surfaces, including the top and bottom bases.

Lateral Surface Area (LSA)

Includes ONLY the side surfaces, excluding the top and bottom bases. Useful for things like labels on cans.

Frequently Asked Questions

Do units matter?

Yes. Ensure all input dimensions are in the same unit (e.g., all in cm). The result will be in that unit squared (cm²).

How does a sphere have area?

Even though a sphere is round, its surface can be "unwrapped" (mathematically) to cover an area equal to 4 circles of the same radius.

What is the formula for a hemisphere?

For a solid hemisphere, include the flat circular base: SA = 3πr². For a hollow hemisphere (bowl), it's just 2πr².

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