Quick answer
A sphere's volume is V = ⁴⁄₃πr³ and its surface area is 4πr². A radius of 2 gives a volume of 33.5103 and a surface area of 50.2655.
Enter the radius. The calculator returns the volume and surface area.
Related tools: Cylinder Volume Calculator: Volume of a cylinder. Volume of a Hemisphere Calculator: Volume and surface area of a hemisphere. Cone Volume Calculator: Volume, slant height and surface area of a cone.
How to use the Sphere Volume 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 = (4/3)πr³; A = 4πr²
IEEE-754 double precision; shown to at most 6 decimal places.
Standard 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 = 2.
| Result | Value |
|---|---|
| Volume | 33.510322 |
| Surface area | 50.265482 |
Example 2
Inputs: Radius = 1.
| Result | Value |
|---|---|
| Volume | 4.18879 |
| Surface area | 12.566371 |
The first line is the headline result (volume). Below it the sphere Volume Calculator lists surface area, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Worked example
r³ = 8, so V = 4/3 × π × 8 = 33.51. Surface area = 4 × π × 4 = 50.27. Doubling the radius multiplies volume by 8 and area by 4.
Everyday spheres
A basketball (r ≈ 12 cm) has a volume of about 7,238 cm³. The Earth's volume is about 1.08 × 10¹² km³. Use consistent units; volume is in cubic units.
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 | Surface area |
|---|---|---|
| 1 | 4.18879 | 12.566371 |
| 2 | 33.510322 | 50.265482 |
| 4 | 268.082573 | 201.06193 |
| 8 | 2,144.660585 | 804.247719 |
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 Sphere Volume 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 |
| [Volume of a Hemisphere Calculator](/math/volume-of-hemisphere/) | 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 |
| [Cube Volume Calculator](/math/cube-volume-calculator/) | side | 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
- Positive radius
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 sphere with diameter 10?
A diameter of 10 means r = 5, so V = ⁴⁄₃π × 125 ≈ 523.6.
How are sphere and cylinder related?
A sphere is two-thirds of its bounding cylinder.
How do I get radius from volume?
Rearrange V = ⁴⁄₃πr³ to r = ∛(3V ÷ 4π): a volume of 33.51 gives r = 2.
What does the Sphere Volume Calculator calculate?
Volume and surface area of a sphere. It returns Volume and Surface area.
What formula does the Sphere Volume Calculator use?
V = (4/3)πr³; A = 4πr². Standard sphere formulas.
What do I need to enter in the sphere Volume Calculator?
You enter Radius.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Positive radius.
What is an example of a sphere Volume result?
With radius 2, the volume is 33.510322.
Related calculators
- Cylinder Volume Calculator — Volume of a cylinder.
- Volume of a Hemisphere Calculator — Volume and surface area of a hemisphere.
- 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).
- Cube Volume Calculator — Volume, surface area and diagonal of a cube.
- Prism Volume Calculator — Volume of any prism from base area and height.
Sources
- OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.