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Hemisphere Surface Area Calculator

Find the surface area of a hemisphere — total surface 3πr² or curved surface only 2πr², step by step with the formula, worked examples and FAQ.

Quick answer
How do you find the surface area of a hemisphere?
The curved surface (the dome only) is 2πr². Include the circular base and you get the total surface 2πr² + πr² = 3πr². Example r = 6: dome ≈ 226.19, total ≈ 339.29.
The tool

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Closed hemisphere including the base circle?
Comma or dot as decimal separator, negative values allowed.
Step-by-step
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HowTo

Hemisphere surface area — 3 steps

Using r = 6
  1. 1
    Step 1 of 3

    Find the radius

    Note the radius r of the hemisphere, e.g. r = 6.

  2. 2
    Step 2 of 3

    Choose the formula

    Dome only: A = 2πr². Closed hemisphere including the base: A = 3πr².

  3. 3
    Step 3 of 3

    Substitute and compute

    With r = 6: dome = 2π·36 ≈ 226.19; total = 3π·36 ≈ 339.29.

Examples

Hemisphere surface area — worked examples

Curved surface and total surface
r = 6 (dome)
2π·6²
2π·36
≈ 226.19
r = 6 (total)
3π·6²
3π·36
≈ 339.29
r = 1 (total)
3π·1²
≈ 9.42
r = 10 (dome)
2π·10²
2π·100
≈ 628.32
r = 2.5 (total)
3π·2.5²
3π·6.25
≈ 58.90
Theory

Dome, base and total surface

A hemisphere is what you get when you cut a sphere through its centre. Its surface has two parts: the curved dome and the circular cut base. The dome is exactly half of the sphere’s surface 4πr², so 2πr². The base is a circle with area πr². For a closed hemisphere (a solid whose base also counts) you add the two: A = 2πr² + πr² = 3πr². Whether you need 2πr² or 3πr² depends on the problem: for a bowl or an open dome only the curved surface counts (2πr²); for the whole outer skin of a solid half-body you take 3πr². This distinction is the most common source of error. Hemisphere surface areas belong to the solid geometry of middle and upper secondary school and show up with domes, tanks and lenses.

Pitfalls

Common mistakes

Confusing dome and total

2πr² is the curved surface only. With the base it is 3πr². Read whether the base circle counts.

Not squaring the radius

Both formulas use r². 2πr (no square) is wrong.

Using the full sphere

A sphere has 4πr². The hemisphere’s dome is half of that, 2πr² — not 4πr².

Diameter instead of radius

If the diameter is given, halve it first: r = d/2.
FAQ

Frequently asked questions

Glossary

Glossary — key terms explained simply

Hemisphere
Half of a sphere, cut through the centre.
Curved surface
The dome of the hemisphere, 2πr².
Base circle
The circular cut base, area πr².
Total surface
Dome plus base, 3πr².
Sphere surface
Surface of the full sphere, 4πr².
Radius (r)
Distance from the centre to the surface.