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Geometry

Hemisphere Calculator

Hemisphere properties. Free online Hemisphere Calculator. Calculate hemisphere online — fast, accurate, mobile-friendly, no signup needed.

Half of a sphere; volume = 2/3·π·r³.
Volume
261.799388
Surface area
235.619449

Derivation

  1. ├── 01Givenr = 5
  2. ├── 02FormulaVolume: 2 / 3 × π × t² × t
  3. ├── 03Compute Volume261.799388
  4. ├── 04FormulaSurface area: 3 × π × t²
  5. └── 05Compute Surface area235.619449
Did you know?

Archimedes was reportedly so proud of proving that a sphere has 2⁄3 the volume of its enclosing cylinder that he asked for the diagram carved on his tombstone.

§01What is

Understanding the Hemisphere Calculator

The Hemisphere Calculator computes Volume from 1 input: radius. Hemisphere properties.

Geometry is what turns raw measurements into useful answers about space — how much paint, how big a yard, how much material a project will need. Every craftsperson, architect, and DIYer reaches for these formulas regularly. The Hemisphere Calculator sits in that toolkit — it hemisphere properties. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

Volume = 2 / 3 × π × t² × t | Surface area = 3 × π × t²

Where

r
Radius
Volume
Output value
Surface area
Output value
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Radius = 5.

  1. 01Start by noting the input — Radius: 5.
  2. 02Substitute these values into the formula: Volume = 2 / 3 × π × t² × t | Surface area = 3 × π × t²
  3. 03Compute Volume: the calculator returns 261.799.
  4. 04Compute Surface area: the calculator returns 235.619.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Hemisphere Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Radius halved

r = 2.5 (from 5)

Keep every other input at its default and halve the radius. See how volume responds.

  1. 01New Radius: 2.5
  2. 02Baseline Volume: 261.799
  3. 03New Volume: 32.7249
  4. 04Volume decreases by 87.5% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Radius doubled

r = 10 (from 5)

Keep every other input at its default and double the radius. See how volume responds.

  1. 01New Radius: 10
  2. 02Baseline Volume: 261.799
  3. 03New Volume: 2094.4
  4. 04Volume increases by 700% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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