HesapHanem

Hemisphere Calculator

Find a hemisphere’s volume and surface area.

How it is calculated

The only input is the radius r, which must be greater than zero. Volume is half that of a sphere: V = (2/3) × π × r³. The surface figure is the total surface area: S = 3 × π × r², which is the curved dome 2πr² plus the flat circular base πr². Both are rounded to two decimals. Use any length unit; volume comes out in its cube and the surface in its square. Because the surface value includes the base, it is the right figure for a closed solid, but for an open bowl or a dome sitting on the ground you would use only the curved part, which is two thirds of the displayed value.

Worked example

A hemisphere has a radius of 5. Cube the radius: 5³ = 125. Multiply by 2/3 and π: 2/3 × 3.14159 × 125 is about 261.80, so the volume is 261.80. For the surface, 5² = 25 and 3 × π × 25 is about 235.62. Of this, the curved part is 2 × π × 25, about 157.08, and the flat base is π × 25, about 78.54.

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Common mistakes

  • Entering the diameter as the radius. The radius is half the diameter, and since volume goes with the cube, this error makes the volume 8 times too big.
  • Using the surface result for an open dome or bowl. It includes the flat base; remove πr² if there is no lid.
  • Mixing units, for example a radius in centimeters but expecting liters. The volume is in cubic centimeters; 1,000 cm³ is 1 liter.
  • Applying it to a dome that is less than half a sphere, such as a shallow cap. The formulas are only for an exact half.
  • Forgetting that doubling the radius multiplies volume by 8 and surface by 4.

About this calculator

This calculator finds a hemisphere's volume (⅔πr³) and its total surface area (3πr²), which includes the flat circular base, from a single radius input. The curved dome alone is 2πr², exactly two-thirds of that total, and the flat base is the remaining third (πr²).

It's used in geometry coursework, but also by anyone designing or estimating material for a dome roof, a bowl-shaped tank, a planetarium screen or a rounded storage container, where the flat-base and curved-only surface areas matter for different reasons (painting vs. structural material, for example).

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Comments (1)

  • Editorial team

    For a real bowl or shell, use the inner radius to find what it holds and the outer radius for its outside size. To estimate the material in a thick dome, run the tool twice and subtract. A 30 cm outer radius gives 56,548.67 cm³ and a 28 cm inner radius gives 45,976.16 cm³, so the wall is about 10,572 cm³, near 10.6 litres. Are you measuring a bowl, a tank or a dome roof?

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