Surface Area of Hemisphere Calculator
Enter a hemisphere's radius, diameter or base circumference to find its total, curved and base surface area.
Updated
Surface Area of Hemisphere Calculator
Our Surface Area of Hemisphere Calculator finds the total surface area of a half ball, the curved dome plus the flat circular base, from whichever measurement you have: the radius, the diameter or the base circumference. It shows the working, the exact answer in terms of π, the curved and base areas on their own, the volume and a drawing.
Quick answer
The total surface area of a hemisphere is 3 × π × radius²: for r = 6 cm, A ≈ 339.29 cm².
- Curved surface only: 2πr², so r = 6 cm gives ≈ 226.19 cm²
- Flat base: πr², so r = 6 cm gives ≈ 113.10 cm²
- From the diameter: A = 3πd² ÷ 4, so 14 cm gives ≈ 461.81 cm²
- Exact form: a radius of 6 gives exactly 108π
What Is the Surface Area of a Hemisphere?
A hemisphere is half of a sphere, cut through the centre. It has two surfaces: a curved surface (the dome) and a flat base, a circle with the same radius r as the sphere. The total surface area A is the two added together, measured in square units. The diameter d = 2r runs across the base, and the base circumference is C = 2πr.
Hemisphere Surface Area Formulas
Use the formula that matches what you know.
| You know | Total surface area |
|---|---|
| The radius | A = 3πr² |
| The diameter | A = 3πd² ÷ 4 |
| Base circumference | A = 3C² ÷ 4π |
| Curved part only | CSA = 2πr² |
The volume of the same hemisphere is V = 2/3 πr³, half of a full sphere.
Why the Formula Is 3πr²
A whole sphere has a surface area of 4πr². Cutting it in half leaves half of that on the dome, 2πr². The cut also makes a new flat face, a circle of area πr². Add them: 2πr² + πr² = 3πr².
So the total surface is exactly three circles of radius r: two for the dome and one for the base.
Surface Area From the Base Circumference
A tape measure around the rim of a bowl or dome gives the base circumference, not the radius. Divide by 2π to get the radius, then use 3πr² as usual. The two steps fold into one formula, A = 3C² ÷ 4π.
r = 60 ÷ 2π ≈ 9.5493 cm
A = 3 × 60² ÷ 4π
A ≈ 859.44 cm²
Hemisphere Surface Area Examples
| Known | Exact total area |
|---|---|
| r = 1 m | 3π ≈ 9.42 m² |
| r = 5 cm | 75π ≈ 235.62 cm² |
| r = 6 cm | 108π ≈ 339.29 cm² |
| r = 10 cm | 300π ≈ 942.48 cm² |
| d = 14 cm | 147π ≈ 461.81 cm² |
| C = 40 cm | 1,200 ÷ π ≈ 381.97 cm² |
Leaving π as a letter keeps the answer exact. Multiply by 3.14159 only at the end, so rounding does not creep in.
Hemisphere Surface Area in Real Life
- Dome roof: a 10 m radius dome has 628.32 m² of curved roof to paint (no base).
- Solid paperweight: a 3 cm radius glass half ball has 27π ≈ 84.82 cm² of surface.
- Tank end caps: a 2 m radius cap with a lid needs about 37.70 m² of steel.
- Half the Earth: one hemisphere of the globe covers about 255 million km².
Common Mistakes
- Halving 4πr² and stopping: 2πr² is only the dome. A solid hemisphere also has a πr² base.
- Adding a base that is not there: an open bowl or a dome roof uses 2πr², not 3πr².
- Using the diameter as r: d = 10 in 3πr² gives 942.48, four times the real 235.62.
- Cubic units: surface area is in square units (cm², m²), not cm³.
- Rounding π too early: 3.14 gives 461.58 instead of 461.81 for r = 7.
Key Terms
- Total area
- Dome plus base, A = 3πr².
- Curved area
- The dome only, CSA = 2πr².
- Base
- The flat circle, area πr².
- Radius
- From the centre of the base to the surface, r.
- Diameter
- Across the base, d = 2r.
How to Use the Surface Area of Hemisphere Calculator
- Choose what you know. Pick Radius, Diameter or Circumference (the base circumference).
- Enter the value. Type the number, such as 6, and pick a unit if you want one (mm, cm, m, km, in, ft, yd or mi). Decimals and fractions such as 3/4 work.
- Read and copy the result. The total surface area appears as you type, with the working, the exact answer in terms of π, the curved surface, the flat base, the volume and the area in other units. Press Copy to copy it, or Clear or Esc to start again.
Example: the rim of a bowl measures 60 cm around. Choose Circumference, enter 60 and pick cm. The total surface area is about 859.44 cm², and the curved part alone is about 572.96 cm².
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
What is the formula for the surface area of a hemisphere?
The total surface area is A = 3πr², where r is the radius: 2πr² for the curved dome plus πr² for the flat base. A radius of 6 cm gives 108π ≈ 339.29 cm².
What is the curved surface area of a hemisphere?
CSA = 2πr², half the surface of a full sphere. A radius of 6 cm gives 72π ≈ 226.19 cm². Use it for open shapes such as a bowl or a dome roof.
How do you find the surface area of a hemisphere from the diameter?
Use A = 3πd² ÷ 4, or halve the diameter and use 3πr². A diameter of 14 cm gives 147π ≈ 461.81 cm².
How do you find the surface area of a hemisphere from the base circumference?
Use A = 3C² ÷ 4π. A rim 60 cm around has a radius of about 9.55 cm and a total surface area of about 859.44 cm².
Why is the surface area of a hemisphere 3πr² and not 2πr²?
Half of a sphere surface, 4πr² ÷ 2, gives the curved part 2πr². Cutting the sphere also makes a flat circular face of area πr², so the total is 2πr² + πr² = 3πr².
What is the surface area of a hemisphere with a radius of 1?
3π, which is about 9.42478 square units. The curved part alone is 2π ≈ 6.28319.
What happens to the surface area if the radius doubles?
It becomes 4 times bigger, because the radius is squared: 2² = 4. The volume grows 8 times.
Is the Surface Area of Hemisphere Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Surface Area of Hemisphere Calculator to get a hemisphere's total, curved and base areas from its radius, diameter or base circumference.