Area of a Hemisphere Calculator
Find the total surface area of a hemisphere from its radius. A solid hemisphere has a curved surface of 2πr² plus a flat circular base of πr², so the total surface area is 3πr². Enter the radius and you get both the curved and total areas in the same square units.
Formula
Total surface area = 3πr² (curved 2πr² + base πr²)
- The total surface area of a solid hemisphere is 3πr²: the curved dome (2πr²) plus the flat circular base (πr²).
- If you only need the curved (dome) surface and not the flat base, use 2πr² — shown separately as the curved surface area.
- All three outputs share the same square unit as the square of the radius you enter (enter the radius in cm and areas come out in cm²).
- A full sphere has surface area 4πr², exactly twice the curved surface of a hemisphere.
Example: hemisphere of radius 5
Inputs
- Radius (r): 5
With r = 5, the curved surface is 2π × 5² ≈ 157.08 and the base is π × 5² ≈ 78.54, so the total surface area is 3π × 25 ≈ 235.62 square units.
Frequently asked questions
What is the surface area of a hemisphere?
For a solid hemisphere, the total surface area is 3πr² — the curved dome (2πr²) plus the flat circular base (πr²).
What if I only want the curved part?
The curved (dome) surface alone is 2πr². This calculator shows it separately as the curved surface area, so you can use whichever value fits your problem.
Why is a hemisphere not just half a sphere's surface?
Half of a sphere's surface (4πr²) is 2πr², which is only the curved dome. Cutting a sphere in half also exposes a flat circular face of πr², which adds to the total.
What units does the answer use?
The areas are in the square of whatever length unit you use for the radius. A radius in metres gives areas in square metres.
How do I find the radius from the area?
For total surface area A, rearrange A = 3πr² to r = √(A ÷ (3π)). For curved area only, use r = √(A ÷ (2π)).