Math

Instant, private, and free

Area of a Hemisphere Calculator.

Calculate curved area, total surface area, and volume from radius.

On-device calculationNo signup
01

Set your values

Results update as you type.

Curved surface area: 157.079633 units²

Curved surface area

0.000000units²
Total surface area: 235.619449 units²

Total surface area

0.000000units²
Volume: 261.799388 units³

Volume

0.000000units³

Results update automatically as you type.

Use Cases

Geometry Homework and Exams

Quickly verify your manual calculations for hemisphere surface area and volume, ensuring accuracy in assignments or test preparation.

Example: Check the total surface area of a hemisphere with radius 5 cm.

Design and Construction Projects

Estimate material requirements for dome-shaped structures, such as roofs, tanks, or decorative elements, by calculating surface area and volume.

Example: Find the volume of a hemispherical water tank with radius 2 meters.

Frequently Asked Questions

What does the Area of a Hemisphere Calculator compute?
This calculator takes the radius of a hemisphere and computes three key measurements: the curved surface area (2πr²), the total surface area (3πr²), and the volume (2/3πr³). Simply enter the radius to get all results instantly.
What is the difference between curved and total surface area?
The curved surface area refers only to the dome-shaped part of the hemisphere, excluding the flat circular base. The total surface area includes both the curved surface and the area of the flat circular base, so it is larger by the area of the base (πr²).
Can I use this calculator for any unit of radius?
Yes, you can enter the radius in any unit (e.g., cm, m, inches). The calculator will output the areas in square units and the volume in cubic units corresponding to the unit you used for the radius.

Tips & Common Mistakes

Tips

  • Ensure the radius is measured from the center of the flat base to the edge of the dome, not the diameter.
  • Use consistent units for the radius to get correct area and volume units (e.g., cm for radius gives cm² and cm³).
  • Remember that the total surface area is always 1.5 times the curved surface area, since it adds the base area.
  • For a quick check, use the formulas: curved area = 2πr², total area = 3πr², volume = (2/3)πr³.

Common Mistakes to Avoid

  • Confusing the radius with the diameter – always use the radius, not the diameter, in the input.
  • Forgetting that the volume of a hemisphere is half the volume of a full sphere, so it's (2/3)πr³, not (4/3)πr³.
  • Using the curved surface area when the total surface area is needed, or vice versa, without checking the requirement.

Last updated: August 13, 2026