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Surface Area Calculator: CSA and TSA of 8 Solids

Choose a solid and enter its measurements. You get the total surface area (TSA), the curved or lateral surface area and the base area, with steps.

Total surface area (TSA)

747.6991cm²

Curved surface area (CSA)
439.823 cm²
Base area
153.938 cm²
Show working
  1. CSA = 2πrh
  2. CSA = 2 × π × 7 × 10 = 439.823 cm²
  3. TSA = 2πr(r + h) = 747.6991 cm²

How to use

  1. Choose the solid.
  2. Enter the measurements and a length unit.
  3. Read TSA and CSA/LSA; open "Show working" to follow the steps.

Good to know

NCERT uses curved surface area (CSA) for round solids and lateral surface area (LSA) for flat-sided ones. Cylinder: CSA 2πrh, TSA 2πr(r + h). Cone: CSA πrl, TSA πr(l + r) with l = √(r² + h²). Sphere 4πr², hemisphere CSA 2πr² and TSA 3πr².

Cuboid TSA = 2(lb + bh + hl) and LSA (the four walls) = 2h(l + b). A square pyramid uses the slant height of a face, s = √(h² + (a/2)²), and a triangular prism uses Heron's formula for its triangular ends.

Real uses: paint for walls (LSA of a room), sheet metal for a tank, cloth for a tent (CSA of a cone). Remove the area of doors, windows or open ends that will not be covered.

Questions

What is the difference between CSA and TSA?

CSA (or LSA) is only the side surface. TSA adds the top and bottom faces as well.

How do I find the area of four walls of a room?

Choose cuboid and read the lateral surface area, 2h(l + b). Subtract doors and windows.

What is the TSA of a hemisphere?

3πr²: the curved part 2πr² plus the flat circle πr².

Do I need the slant height for a cone?

No. Enter the vertical height and the calculator finds the slant height l = √(r² + h²). The cone calculator also accepts slant height directly.

Is anything I enter stored?

No. The calculation runs in your browser and nothing is sent to a server.

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