Surface Area of a Hemisphere Calculator

Free Surface Area of a Hemisphere Calculator

Find the curved surface area and total surface area of a hemisphere from its radius.

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Last updated October 13, 2026 · Report an error

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A hemisphere is exactly half a sphere, cut through its center. Its curved surface area (just the dome) and total surface area (dome plus the flat circular base that closes it off) are both simple multiples of πr², and the distinction between the two matters in practical applications like calculating the material needed for a dome roof (curved area only) versus the material for a storage tank's rounded end cap (which may need the flat closing face accounted for separately, or not at all, depending on how it attaches).

How it works

Enter the radius r. A full sphere's surface area is 4πr²; since a hemisphere's dome is exactly half of that sphere's surface, the curved area is A_curved = 2πr². The total surface area adds the flat circular base, which has its own area πr² (a plain circle), giving A_total = 2πr² + πr² = 3πr².

Enter radius.
Click Calculate to see your results.

Examples

Radius = 5

Curved surface area = 2π(25) ≈ 157.08. Total surface area = 3π(25) ≈ 235.62.

Radius = 2

Curved surface area = 2π(4) ≈ 25.13. Total surface area = 3π(4) ≈ 37.70.

Common mistakes to avoid

Reporting the curved surface area when the total (including the base) was actually needed, or vice versa.
Using the full sphere's surface area formula (4πr²) instead of halving it for the dome.
Forgetting to add the base's circular area (πr²) when total surface area is required.

Frequently asked questions

The curved area covers only the dome (the part that was originally part of the sphere's surface); the total area also includes the flat circular base created by slicing the sphere in half.

A hemisphere is literally one half of a sphere, and the dome portion of its surface is precisely half of the full sphere's 4πr² surface area, giving 2πr².

The flat circular base (πr²) is always exactly half the curved dome area (2πr²) — a ratio of 1:2 that holds for any hemisphere regardless of its size.

For materials covering just the visible dome (like roofing shingles or a tarp), use the curved surface area; only include the flat base area if that surface is also being covered or finished.

It increases fourfold (2²=4), since both the curved and total surface area formulas scale with r², not r directly.

No — it's exactly half of it. A full sphere's surface area is 4πr², while a hemisphere's dome alone is 2πr², since the dome represents only half of the original sphere's surface.

You'd compute the curved area for both the outer and inner radius separately, plus the flat ring-shaped rim connecting them, rather than using the solid-hemisphere formulas directly.