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Hemisphere Calculator

Get hemisphere volume and surface areas from the radius

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How to use

  1. 1.Enter the radius (r) of the hemisphere in the field, using any consistent unit such as cm, inches, or meters. If you have the diameter, halve it first.
  2. 2.The tool computes instantly — no button to press.
  3. 3.Read the volume along with the curved surface area, base area, and total surface area, each with its formula shown.

About Hemisphere Calculator

A hemisphere is exactly half of a sphere, and this hemisphere calculator turns a single number — the radius r — into every measurement you need. Type the radius and it instantly returns four results: the volume V = (2/3)πr³, the curved surface area of hemisphere = 2πr², the flat circular base area = πr², and the total surface area = 3πr². There is no button to press and nothing is sent to a server — every number is computed in your browser using Math.PI for full precision.

Each formula follows directly from the sphere it comes from. A full sphere has volume (4/3)πr³ and surface area 4πr²; slice it in half through the center and the volume halves to (2/3)πr³ while the rounded (curved) surface halves to 2πr². The cut exposes a flat circular face — a disk of area πr² — that a full sphere does not have. That single distinction is the most common source of confusion, so this tool reports the curved part and the total part separately.

The key difference to keep straight: the curved surface area (2πr²) is only the dome — the smooth, rounded outside. The total surface area (3πr²) adds the flat circular base to that dome, because 2πr² + πr² = 3πr². Use the curved area when the flat side is open or joined to something else (a dome roof, a bowl interior, a half-pipe). Use the total area when the object is a solid closed half-ball and you need to paint, coat, or wrap the whole thing including the flat face.

Units follow whatever you enter. Keep the radius in one unit and the volume comes out in that unit cubed — centimeters give cubic centimeters (cm³, equal to milliliters), inches give cubic inches, meters give cubic meters. All three areas come out in that unit squared (cm², in², m²). If you only know the diameter, halve it first: r = d ÷ 2.

These numbers appear anywhere a rounded half-shape shows up: the capacity of a bowl, dome, or hemispherical tank; the material to cover a planetarium or observatory dome; the glaze on a half-round decorative object; and geometry homework. As a quick sanity check, a hemisphere holds exactly half the volume of the sphere with the same radius and twice the volume of a cone that shares that radius and a height equal to r.

The calculator accepts whole numbers and decimals, treats a radius of 0 as zero for every result, and flags negative or non-numeric entries so a typo never returns a misleading answer. Extremely large inputs that would overflow are caught rather than shown as a broken result.

Frequently asked questions

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. It is exactly half the volume of a full sphere, which is (4/3)πr³. Keep r in one unit and the volume comes out in that unit cubed.
What is the curved surface area of a hemisphere?
The curved surface area of a hemisphere is 2πr² — just the rounded dome, with no flat face. It is half of a sphere's surface area (4πr²). Use this when the flat side is open or attached to something else.
What is the difference between curved and total surface area?
The curved surface area (2πr²) is only the dome. The total surface area (3πr²) adds the flat circular base (πr²) to that dome, since 2πr² + πr² = 3πr². Use the total when you need to cover the whole closed half-ball, base included.
How do I calculate a hemisphere from the diameter?
Convert the diameter to a radius first by halving it: r = d ÷ 2. Then use V = (2/3)πr³ and the area formulas. For example, a 10 cm diameter gives a 5 cm radius. Enter that radius and the calculator does the rest.
What units does the hemisphere calculator use?
It is unit-agnostic: enter the radius in whatever unit you like. The volume comes out in that unit cubed (cm³, which equals milliliters; cubic inches; cubic meters) and the three areas come out in that unit squared (cm², in², m²).

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