What is the curved surface area (CSA) of a hemisphere?

The curved surface area of a hemisphere is CSA = 2πr², where r is the radius. It covers only the domed outer surface, not the flat circular base.

What is the total surface area (TSA) of a hemisphere?

The total surface area includes both the curved dome and the flat circular base: TSA = 3πr². This equals CSA (2πr²) plus the base area (πr²).

What is the base area of a hemisphere?

The base is a full circle with the same radius r, so its area is πr². When added to the curved surface area, you get the total surface area: TSA = 2πr² + πr² = 3πr².

How do I calculate from the diameter?

If you know the diameter d, the radius is r = d / 2. Substitute into the formulas: CSA = 2π(d/2)² = πd²/2, and TSA = 3π(d/2)² = 3πd²/4.

What units does this calculator support?

You can enter measurements in millimeters, centimeters, meters, inches, or feet. Surface areas are returned in the corresponding square unit (e.g., cm²).

What is the difference between a hemisphere and a sphere?

A hemisphere is exactly half of a full sphere, cut along a great circle. The surface area of a full sphere is 4πr², so the curved surface of a hemisphere (2πr²) is exactly half of that.

Surface Area of a Hemisphere Calculator

Name: Surface Area of a Hemisphere Calculator
Availability: InStock
Author: Nham Vu

Enter the radius or diameter to instantly calculate the curved and total surface area of a hemisphere with step-by-step working.

Calculator Inputs

Input mode

Radius (r)

Unit

Curved Surface Area (CSA)

—

Total Surface Area (TSA)

—

Base Area (flat circle)

—

Hemisphere diagram

r = radius | d = diameter

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Summary

Enter the radius or diameter to instantly calculate the curved and total surface area of a hemisphere with step-by-step working.

How it works

Choose whether to enter the radius or the diameter.
Type the measurement value in the input field.
Select your preferred unit (mm, cm, m, in, or ft).
Click "Calculate" to apply the hemisphere formulas.
Curved surface area, total surface area, and base area results appear with step-by-step working.

Use cases

Geometry homework and exam problems involving hemispheres.
Architecture — estimating material for a dome-shaped roof or ceiling.
Engineering — calculating the exposed area of hemispherical tanks or vessels.
Manufacturing — coating, painting, or finishing hemispherical parts.
Physics problems requiring the surface area of half-sphere objects.
Landscaping — estimating cover material for a dome-shaped topiary or mound.
Classroom demonstrations of the relationship between CSA and TSA.
Verifying manual hemisphere calculations quickly.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu