Quick answer
A hemisphere of radius r has a curved surface area of 2πr² and a total surface area of 3πr² (including the flat base). For r = 1 these are 6.2832 and 9.4248.
Enter the radius. The calculator returns the curved and total surface areas.
Related tools: Surface Area Calculator: Surface area of a sphere, cube, cylinder, cone or box. Surface Area of a Cylinder Calculator: Surface area and volume of a cylinder. Cuboid Surface Area Calculator: Surface area of a cuboid.
How to use the Hemisphere Surface Area Calculator
- Enter radius (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Radius | A number | > 0 |
Formula and method
Formula
curved = 2πr²; total = 3πr²
IEEE-754 double precision; shown to at most 6 decimal places.
Half a sphere's surface plus the circular base for the total.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Radius = 1.
| Result | Value |
|---|---|
| Curved surface area | 6.283185 |
| Total surface area | 9.424778 |
Example 2
Inputs: Radius = 3.
| Result | Value |
|---|---|
| Curved surface area | 56.548668 |
| Total surface area | 84.823002 |
The first line is the headline result (curved surface area). Below it the hemisphere Surface Area Calculator lists total surface area, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
From the sphere
A sphere has area 4πr², so half is 2πr². Adding the circular base πr² gives 3πr². For r = 5, the curved area is 157.08 and the total 235.62.
Uses
Domes, bowls and tank ends are hemispherical. Paint a dome using the curved area only. Volume of a hemisphere is (2/3)πr³, a separate calculation.
Curved versus total surface
The curved surface of a hemisphere is 2πr², half of a sphere's 4πr². The total adds the flat circular base, πr², giving 3πr². For r = 1 the values are 6.283185 and 9.424778.
A dome roof needs only the curved part. A solid bowl or paint on a closed half-ball needs the total. A diameter of 10 means r = 5, so curved ≈ 157.08 and total ≈ 235.62.
How the result changes with radius
Holding every other input at the first worked example, this table changes only radius. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Radius | Curved surface area | Total surface area |
|---|---|---|
| 0.5 | 1.570796 | 2.356194 |
| 1 | 6.283185 | 9.424778 |
| 2 | 25.132741 | 37.699112 |
| 4 | 100.530965 | 150.796447 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Radius: entering "0" shows "Radius must be greater than 0." beside that field and no result.
Choosing between the Hemisphere Surface Area Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Surface Area Calculator](/math/surface-area-calculator/) | shape and a | Surface area |
| [Surface Area of a Cylinder Calculator](/math/surface-area-of-cylinder/) | radius and height | Surface area |
| [Cuboid Surface Area Calculator](/math/cuboid-surface-area/) | length, width and height | Surface area |
| [Area Calculator](/math/area-calculator/) | shape and a | Area |
| [Area of a Circle Calculator](/math/area-of-a-circle/) | i know the and value | Area |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Positive radius
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for radius to confirm this.
Frequently asked questions
What is the volume of a hemisphere?
The volume of a hemisphere is ⅔πr³; for r = 3 that is 56.55.
Is the base included?
In the total area, yes.
What is the area of a dome of radius 3 m?
About 56.55 m² curved.
What is the total surface area for diameter 10?
r = 5, so the total is 3π × 25 ≈ 235.62.
Is the curved area of a hemisphere half the sphere's area?
Yes. A sphere has 4πr² and the curved half has 2πr².
What does the Hemisphere Surface Area Calculator calculate?
Curved and total surface area of a hemisphere. It returns Curved surface area and Total surface area.
What formula does the Hemisphere Surface Area Calculator use?
curved = 2πr²; total = 3πr². Half a sphere's surface plus the circular base for the total.
What do I need to enter in the hemisphere Surface Area Calculator?
You enter Radius.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Positive radius.
What is an example of a hemisphere Surface Area result?
With radius 1, the curved surface area is 6.283185.
Related calculators
- Surface Area Calculator — Surface area of a sphere, cube, cylinder, cone or box.
- Surface Area of a Cylinder Calculator — Surface area and volume of a cylinder.
- Cuboid Surface Area Calculator — Surface area of a cuboid.
- Area Calculator — Area of common two-dimensional shapes.
- Area of a Circle Calculator — Area of a circle from its radius, diameter or circumference.
- Area of a Trapezoid Calculator — Area of a trapezoid from its parallel sides and height.
- Orthocenter Calculator — Orthocenter of a triangle from its vertices.
- Hexagon Calculator — Area, perimeter and angles of a regular 6-sided polygon.
- Pentagon Calculator — Area, perimeter and angles of a regular 5-sided polygon.
Sources
- OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.