Quick answer
A hemisphere of radius r has volume ⅔πr³, curved surface area 2πr² and total surface area 3πr². For r = 3: volume 56.5487, curved area 56.5487 and total area 84.8230.
Enter the radius. The calculator returns the volume, curved surface area and total surface area.
Related tools: Cylinder Volume Calculator: Volume of a cylinder. Rectangular Prism Volume Calculator: Volume of a rectangular prism (box). Sphere Volume Calculator: Volume and surface area of a sphere.
How to use the Volume of a Hemisphere Calculator
- Enter radius (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Radius | A number | > 0 |
Formula and method
Formula
V = (2/3)πr³; curved area = 2πr²; total surface = 3πr²
IEEE-754 double precision; shown to at most 6 decimal places.
Half of the sphere formulas.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Radius = 3.
| Result | Value |
|---|---|
| Volume | 56.548668 |
| Curved surface area | 56.548668 |
| Total surface area | 84.823002 |
Example 2
Inputs: Radius = 1.
| Result | Value |
|---|---|
| Volume | 2.094395 |
| Curved surface area | 6.283185 |
| Total surface area | 9.424778 |
The first line is the headline result (volume). Below it the volume of a Hemisphere Calculator lists curved surface area and total surface area, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Half a sphere
The sphere's volume ⁴⁄₃πr³ = 113.097, and half is 56.549. The curved area equals the volume numerically here only because r = 3 makes 2πr² = ⅔πr³ (r = 3 is the special case).
Practical use
Dome volumes, bowls and half-spherical tanks. Total surface area adds the flat circular face πr² = 28.27 to the curved area. Radius must be positive.
How the result changes with radius
Holding every other input at the first worked example, this table changes only radius. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Radius | Volume | Curved surface area | Total surface area |
|---|---|---|---|
| 1.5 | 7.068583 | 14.137167 | 21.20575 |
| 3 | 56.548668 | 56.548668 | 84.823002 |
| 6 | 452.389342 | 226.194671 | 339.292007 |
| 12 | 3,619.114737 | 904.778684 | 1,357.168026 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Radius: entering "0" shows "Radius must be greater than 0." beside that field and no result.
Choosing between the Volume of a Hemisphere Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Cylinder Volume Calculator](/math/cylinder-volume-calculator/) | radius and height | Volume |
| [Rectangular Prism Volume Calculator](/math/rectangular-prism-volume/) | length, width and height | Volume |
| [Sphere Volume Calculator](/math/sphere-volume-calculator/) | radius | Volume |
| [Cone Volume Calculator](/math/cone-volume-calculator/) | radius and height | Volume |
| [Pyramid Volume Calculator](/math/pyramid-volume-calculator/) | base length, base width and height | Volume |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Radius must be positive
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for radius to confirm this.
Frequently asked questions
What is the volume of a hemisphere with r = 1?
With r = 1 the volume is ⅔π ≈ 2.0944.
How do I find capacity in litres?
Convert cubic cm by dividing by 1,000.
What is a spherical cap?
A part of a sphere cut by a plane.
What does the Volume of a Hemisphere Calculator calculate?
Volume and surface area of a hemisphere. It returns Volume, Curved surface area and Total surface area.
What formula does the Volume of a Hemisphere Calculator use?
V = (2/3)πr³; curved area = 2πr²; total surface = 3πr². Half of the sphere formulas.
What do I need to enter in the volume of a Hemisphere Calculator?
You enter Radius.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Radius must be positive.
What is an example of a volume of a Hemisphere result?
With radius 3, the volume is 56.548668.
Related calculators
- Cylinder Volume Calculator — Volume of a cylinder.
- Rectangular Prism Volume Calculator — Volume of a rectangular prism (box).
- Sphere Volume Calculator — Volume and surface area of a sphere.
- Cone Volume Calculator — Volume, slant height and surface area of a cone.
- Pyramid Volume Calculator — Volume of a pyramid from its base area and height (rectangular base).
- Triangular Prism Volume Calculator — Volume of a triangular prism.
Sources
- Standard Euclidean geometry formulas (e.g. NIST Digital Library of Mathematical Functions §4, CRC Standard Mathematical Tables)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.