Hemisphere Formulas
3D Solids
Hemisphere
- Volume
- V = (2 ⁄ 3) πr3
- Curved surface area
- CSA = 2πr2
- Total surface area
- TSA = 3πr2
- r radius
Hemisphere formulas explained
A hemisphere is half a sphere. Its total surface area includes the curved dome plus the flat circular base. Below are all the hemisphere formulas with what each letter means, a worked example and a free calculator.
- Volume:
V = (2 ⁄ 3) πr³ - Curved surface area:
CSA = 2πr² - Total surface area:
TSA = 3πr²
Hemisphere calculator
Live calculator
Hemisphere calculator
Worked example: volume of a hemisphere
Given Radius r = 3 cm, substitute the values into each hemisphere formula:
- V = (2 ⁄ 3) × π × 3³ = 56.55 cm³
- CSA = 2 × π × 3² = 56.55 cm²
- TSA = 3 × π × 3² = 84.82 cm²
Hemisphere Formula SheetFormulas, variables, a worked example and practice questions with answers.Download PDFOpen
Hemisphere formulas FAQ
What is the formula for the volume of a hemisphere?
The volume of a hemisphere is V = (2 ⁄ 3) πr³, where r is the radius.
What is the formula for the curved surface area of a hemisphere?
The curved surface area of a hemisphere is CSA = 2πr², where r is the radius.
What is the formula for the total surface area of a hemisphere?
The total surface area of a hemisphere is TSA = 3πr², where r is the radius.
Can I download the hemisphere formulas as a PDF?
Yes. Use the Download PDF button on this page for a free printable hemisphere formula sheet with a worked example and practice questions.