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Math Calculators

Hemisphere Calculator

Verified formula Updated Jun 2026 Private — runs on your device

Enter details
units
Verified formula Private

Volume

452.3893

Total surface area
339.2920

For general information only — not financial, tax, legal or medical advice. Verify before you rely on it.

How to use the Hemisphere Calculator

The Hemisphere Calculator works out your volume, along with 1 related figure in an instant. Enter radius and the result updates as you type — it is free, needs no sign-up, and runs entirely in your browser so your figures stay private.

  1. Enter the radius.
  2. Read off your volume, together with total surface area — the calculator updates automatically, with no button to press.

Formula

The Hemisphere Calculator uses the formula:

Volume = 2 ÷ 3 × 3.141592653589793 × Radius ^ 3

Worked example

For example, with radius of 6 units, the volume is 452.3893.

Inputs used
Radius 6 units
Results
Volume 452.3893
Total surface area 339.2920

Results are estimates for educational use, not professional advice.

Key terms explained

Surface area
The total area of all the outer faces of a three-dimensional object.
Radius
The distance from the centre of a circle or sphere to its edge.
Volume
The amount of three-dimensional space an object occupies, measured in cubic units.
Area
The amount of two-dimensional space a shape covers, measured in square units.

Frequently asked questions

It is half a sphere's volume: V = 2⁄3 πr³. A hemisphere of radius 6 has a volume of about 452.39 cubic units.

Total surface area is 3πr², which is the curved half plus the flat circular base. For radius 6 it is about 339.29 square units.

The curved surface is 2πr², and adding the flat circular base of πr² gives 3πr² in total.

It is exactly half of a sphere, like a dome or a bowl shape cut through the centre.

The Hemisphere Calculator uses the formula: Volume = 2 ÷ 3 × 3.141592653589793 × Radius ^ 3. For example, with radius of 6 units, the volume is 452.3893.

Enter the radius. Read off your volume, together with total surface area — the calculator updates automatically, with no button to press.

Hemisphere Table: Volume by Radius

Reference table of volume for Hemisphere across a range of radius values — exact, engine-computed figures you can read off at a glance.

1 min read

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