Answer first
What this calculator tells you
Calculate the volume, curved surface and total surface of a hemisphere from its radius. Size a dome, a bowl or a half-round tank before ordering material. Formula: Volume = ⅔ × π × r³; curved surface = 2 × π × r²; total surface = 3 × π × r². At the worked-example inputs, the volume is 261.8. Holding every other input steady, moving radius from 4 to 6 moves the result from 134 to 452.4.
Transparent method
The formula
Size a dome, a bowl or a half-round tank before ordering material.
Worked example
Example inputs
How to interpret the result
A hemisphere is half a sphere, so its volume is two thirds of pi times the radius cubed, and its curved surface is half the sphere's surface. With a radius of 5 that gives about 262 cubic units of volume and 157 of curved area. A flat base is a separate surface: adding it takes the total to about 236, which is what a solid dome needs and a shell does not.
At the worked-example inputs the volume is 261.8. It rises with radius.
Formulas assume ideal geometric shapes. Real-world measurements carry their own error, and every input must use the same unit: mixing feet and inches silently produces a wrong answer.
Before you rely on it
What to check
Decide whether the flat face counts. Paint for a bowl's outside is the curved area, while a solid dome needs the total.
The common error
Where people go wrong with hemisphere volume calculator
Using the sphere's volume formula and forgetting to halve it. A radius-cubed result with four thirds in front is a full sphere, twice the size of a hemisphere.
Sensitivity evidence
How radius changes the volume
Holding every other input at the worked-example value, moving radius from 4 to 6 moves the volume from 134 to 452.4: a spread of 318.3, or 122% of the worked-example result.
| Radius | Volume | Curved surface area | Total surface area |
|---|---|---|---|
| 4 | 134 | 100.5 | 150.8 |
| 4.5 | 190.9 | 127.2 | 190.9 |
| 5worked example | 261.8 | 157.1 | 235.6 |
| 5.5 | 348.5 | 190.1 | 285.1 |
| 6 | 452.4 | 226.2 | 339.3 |
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Radius | 5 | Enter the radius used in this calculation. |
| Volume | 261.8 | |
| Curved surface area | 157.1 | |
| Total surface area | 235.6 | |
Inputs, definitions and assumptions
Radius
Enter the radius used in this calculation. The prefilled worked-example value is 5.
How to use this calculator
- 1Verify the inputs. Gather radius from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the volume at 261.8. Store your own version of it as Scenario A.
- 3Test one change. Start with radius, the input with the biggest effect here: moving radius from 4.5 to 5.5 takes the volume from 190.9 to 348.5, a swing of 60% of the worked-example figure.
- 4Check the extremes. At half the example radius (2.5) the volume is 32.7; at double (10) it is 2,094.4.
People also ask
Frequently asked questions
How do you calculate hemisphere volume?
Volume = ⅔ × π × r³; curved surface = 2 × π × r²; total surface = 3 × π × r². At the worked-example inputs the volume is 261.8.
What does the hemisphere volume result mean?
Size a dome, a bowl or a half-round tank before ordering material. At the worked-example inputs the volume is 261.8. It rises with radius.
How much does radius change the volume?
Holding every other input at the worked-example value, moving radius from 4 to 6 moves the volume from 134 to 452.4, a spread of 318.3.
What are the limits of this hemisphere volume calculator?
Formulas assume ideal geometric shapes. Real-world measurements carry their own error, and every input must use the same unit: mixing feet and inches silently produces a wrong answer. The tables on this page test radius only from 4 to 6; a value outside that range is not tabulated here.
If I double radius in the hemisphere volume calculator, does the volume double?
Doubling it from 5 to 10 takes the volume from 261.8 to 2,094.4, which is 8.00 times the worked-example figure. So the result grows faster than the input does. Halving it to 2.5 gives 32.7.
Which inputs change the curved surface area in the hemisphere volume calculator?
At the worked-example inputs it is 157.1. Radius takes it from 127.2 to 190.1.
Which inputs change the total surface area in the hemisphere volume calculator?
At the worked-example inputs it is 235.6. Radius takes it from 190.9 to 285.1.
What is the difference between area and perimeter?
Perimeter is the distance around the outside of a shape, in units of length. Area is the surface inside it, in square units. A long thin rectangle and a square can share a perimeter and have very different areas.
How do I find a diagonal of a rectangle or a box?
Use the Pythagorean theorem. A rectangle's diagonal is the square root of length squared plus width squared, and a box's space diagonal adds height squared under the same root.
Sources and evidence
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