About the Hemisphere Calculator
A hemisphere is exactly half of a sphere, cut through its centre: a curved dome sitting on a flat circular base. This hemisphere calculator finds its volume, the curved (dome) surface area, the area of the flat base and the total surface area, starting from whichever measurement you have — radius, diameter, volume, curved area, total area or base circumference.
It is handy for geometry homework and for practical jobs such as working out how much a hemispherical bowl holds, how much concrete or paint a dome needs, or what radius a half-sphere planter must have to hold a set volume. Working back from volume or area to the radius is done for you.
Use any length unit you like: areas come out in square units and volumes in cubic units of the same kind. With centimetres, the volume in cm³ equals millilitres; divide by 1,000 for litres.
With the default inputs, the volume is 261.7994 cu units. Change any value above to recalculate instantly.
How to use the hemisphere calculator
- 1Choose which measurement you know.
- 2Enter its value in any consistent unit.
- 3Read the volume and the curved, base and total surface areas.
- 4Use the curved area for open domes or bowls and the total area for solid half-spheres.
Formula and method
A hemisphere has half the volume of the full sphere, so V = ½ × (4/3)πr³ = (2/3)πr³. Its curved surface is half the sphere’s surface, 2πr², and the flat cut face is a circle of area πr². Adding the two gives the total surface area 3πr² — use the curved area alone for an open bowl or dome, and the total for a solid half-ball.
When you start from another value the calculator inverts these formulas: r = ∛(3V ÷ 2π) from volume, r = √(A ÷ 2π) from curved area, r = √(A ÷ 3π) from total area and r = C ÷ 2π from the base circumference.
- r
- Radius of the hemisphere (and of its base circle)
- V
- Volume
- A
- Surface area
- C
- Circumference of the flat base
Worked examples
Hemisphere with radius 5
V = (2/3) × π × 125 ≈ 261.80. The dome is 2π × 25 ≈ 157.08, the base π × 25 ≈ 78.54, so the total surface is about 235.62 square units.
A 3 cm diameter half-ball
r = 1.5 cm, so V = (2/3) × π × 3.375 ≈ 7.07 cm³ and the total surface is 3π × 2.25 ≈ 21.21 cm².
Bowl that holds 1,000 cm³ (1 litre)
r = ∛(3 × 1,000 ÷ 2π) ≈ 7.82 cm, so a hemispherical bowl about 15.6 cm across holds one litre when filled to the rim.
Frequently asked questions
What is the formula for the volume of a hemisphere?+
V = (2/3)πr³, which is half of the sphere volume (4/3)πr³. For r = 3, V = (2/3) × π × 27 ≈ 56.55 cubic units.
What is the total surface area of a hemisphere?+
Total surface area = 3πr²: the curved part 2πr² plus the flat circular base πr². For r = 4 that is 3π × 16 ≈ 150.80 square units.
What is the curved surface area of a hemisphere?+
The curved (lateral) area is 2πr², half of a full sphere’s 4πr². It is the area to use for an open bowl, dome roof or the outside of a half-shell.
How do you find the radius of a hemisphere from its volume?+
Multiply the volume by 3, divide by 2π and take the cube root: r = ∛(3V ÷ 2π). A 1,000 cm³ hemisphere has a radius of about 7.82 cm.
Is a dome a hemisphere?+
Only if its height equals its base radius. Shallower domes are spherical caps; use the spherical cap calculator when the height is less than the radius.