Hemisphere Calculator

What is a Hemisphere?

A hemisphere is half of a sphere, cut by a plane passing through the center of the sphere. It has one flat circular base and one curved surface. The word "hemisphere" comes from Greek: "hemi" meaning half and "sphere" meaning ball. Hemispheres are commonly seen in architecture (domes), cookware (bowls), and nature (half of the Earth).

This hemisphere calculator helps you compute all essential properties: radius (r), base circumference (C), volume (V), curved surface area (A), base surface area (B), and total surface area (K). You can enter any one known dimension and the tool will automatically calculate all remaining properties. For related shapes, try our Sphere Calculator and Cone Calculator.

How to Use the Hemisphere Calculator

Using this hemisphere geometry calculator is simple:

Select Known Value: Choose which hemisphere property you know from the dropdown menu (radius, volume, curved area, total area, or circumference).
Choose Unit: Select your preferred unit of measurement (mm, cm, m, km, in, ft, yd, or none).
Enter Value: Input the known value into the calculator.
Adjust Precision: Set the number of significant figures for the results.

All results update in real-time as you type. The calculator also displays values in terms of pi for exact mathematical representation.

Hemisphere Formulas

The following formulas are used to calculate the properties of a hemisphere where r is the radius:

V = (2/3)πr³

Volume of a hemisphere (half of a sphere)

C = 2πr

Circumference of the base

A = 2πr²

Curved surface area (external dome surface)

B = πr²

Base surface area (circular flat face)

K = A + B = 3πr²

Total surface area (curved + base)

How to Derive Other Values

If you know the volume (V), the radius can be found as r = ³√(3V / (2π)). From the curved area (A), r = √(A / (2π)). From the total area (K), r = √(K / (3π)). From the circumference (C), r = C / (2π). Once the radius is determined, all other properties are computed using the formulas above.

Example Calculation

Example: Find the volume and surface area of a hemisphere with radius r = 6 cm.

Volume: V = (2/3)π x 6³ = 144π = 452.389 cm³
Curved Area: A = 2π x 6² = 72π = 226.195 cm²
Base Area: B = π x 6² = 36π = 113.097 cm²
Total Area: K = 3π x 6² = 108π = 339.292 cm²
Circumference: C = 2π x 6 = 12π = 37.699 cm

Simply select "Radius (r)" from the dropdown, enter 6, and choose cm as the unit. All results will be displayed instantly.

Frequently Asked Questions

What is the difference between curved surface area and total surface area of a hemisphere?

The curved surface area (A = 2πr²) is the area of the dome-shaped curved part only. The total surface area (K = 3πr²) includes both the curved surface and the flat circular base. Since a full sphere has surface area 4πr², half of that (2πr²) is the curved part, plus the base (πr²) gives 3πr² total.

Can I calculate hemisphere properties if I only know the volume?

Yes. If you know the volume (V), you can find the radius using r = ³√(3V / (2π)). Once the radius is determined, all other properties (circumference, curved area, base area, total area) can be calculated using the standard hemisphere formulas.

How is a hemisphere different from a sphere?

A sphere is a perfectly round three-dimensional object where every point on its surface is equidistant from its center. A hemisphere is exactly half of a sphere, created by cutting the sphere through its center. A hemisphere has one flat circular face (the base) and one curved face, while a sphere has only a curved surface with no flat faces.

What is the volume of a hemisphere with radius 10 cm?

The volume of a hemisphere with radius 10 cm is V = (2/3)π x 10³ = (2/3)π x 1,000 = 2,094.40 cm³. The total surface area would be K = 3π x 10² = 300π = 942.48 cm². The curved surface area alone is A = 2π x 10² = 200π = 628.32 cm².

What units does the hemisphere calculator support?

The calculator supports millimeters (mm), centimeters (cm), meters (m), kilometers (km), inches (in), feet (ft), yards (yd), and a "None" option for unitless calculations. Area results use squared units and volume results use cubic units of the selected measurement.

What are some real-world examples of hemispheres?

Real-world examples of hemispheres include domes of buildings, half of the Earth (Northern and Southern Hemispheres), salad bowls, measuring cups, igloos, observatory domes, and the cap of a mushroom. In engineering, hemispherical shapes are used in pressure vessel ends and rocket nose cones.

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