Hemisphere Surface Area Calculator — CSA and TSA
Find the curved surface area (CSA) and total surface area (TSA) of a hemisphere. Enter the radius and get both results instantly — CSA is the dome only; TSA adds the flat circular base.
units
Curved dome (2πr²) plus flat circular base (πr²)
- 1
Square the radius
5 × 5 = 25 - 2
Curved surface area (dome)
2 × π × 25 = 157.0796 - 3
Base circle area
π × 25 = 78.5398 - 4
Total surface area
157.0796 + 78.5398 = 235.6194TSA = curved dome (2πr²) + flat base (πr²) = 3πr².
How does this calculator work?
A hemisphere has two surfaces: dome (CSA = 2πr²) and flat base (πr²). Total surface area = 3πr². For r = 5: CSA ≈ 157.08, TSA ≈ 235.62 square units. The dome equals half the full sphere surface (4πr²); TSA equals 75% of a full sphere.
Formula
How this is calculated
A hemisphere is exactly half a sphere cut through its centre. It has two distinct surfaces: the curved dome and the flat circular base. The dome is exactly half the full sphere skin (which is 4πr²), giving a curved surface area of 2πr². The base is a circle of radius r with area πr². Summing both gives the total surface area of 3πr².
Enter the radius in any consistent length unit — metres, centimetres, feet or any other — and both areas are returned in that unit squared. No additional measurements are needed because every hemisphere property follows from the radius alone. If you have the diameter instead, divide by two before entering.
The formulas assume a perfect mathematical hemisphere with zero wall thickness. For real-world objects such as bowls, domes, or caps, the outer and inner radii differ; in those cases compute with the outer radius for the external CSA and the inner radius for any interior surface. The formula also assumes a solid closed base — if the base is open (like a bowl with no bottom), use only CSA = 2πr².
Frequently asked questions
The curved surface area (CSA = 2πr²) covers only the dome-shaped outer surface. The total surface area (TSA = 3πr²) also includes the flat circular base (πr²) that closes the solid. Use CSA for an open hemisphere (no base), TSA for a closed solid.
A sphere has surface area 4πr². A hemisphere's dome is exactly half of that: 2πr². Adding the base πr² gives TSA = 3πr², which is 75% of the full sphere's surface area.
Divide the diameter by two to get the radius, then use the formulas. For example, a diameter of 10 units gives r = 5, CSA = 2π×25 ≈ 157.08 square units, TSA = 3π×25 ≈ 235.62 square units.
Also known as
TG we-Calculate Editorial Team. (2026). Hemisphere Surface Area Calculator — CSA and TSA [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/area-of-hemisphere-calculator
TG we-Calculate Editorial Team. "Hemisphere Surface Area Calculator — CSA and TSA." TG we-Calculate. 2026. https://we-calculate.com/calculator/area-of-hemisphere-calculator.
TG we-Calculate Editorial Team, "Hemisphere Surface Area Calculator — CSA and TSA," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/area-of-hemisphere-calculator
@misc{wecalculate_area_of_hemisphere_calculator, title = {Hemisphere Surface Area Calculator — CSA and TSA}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/area-of-hemisphere-calculator}}, year = {2026}, note = {TG we-Calculate} }
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