Sphere Volume and Surface Area Calculator
Sphere volume (4/3 πr³) and surface area (4πr²) from the radius or diameter, or the radius from a volume or area: a radius of 5 gives 523.5988 and 314.1593. How it works
Use the Sphere Volume and Surface Area Calculator
About the Sphere Volume and Surface Area Calculator
A sphere with a radius of 5 has a volume of 523.5988 cubic units and a surface area of 314.1593 square units, from V = (4/3)πr³ and A = 4πr². This sphere volume and surface area calculator takes the radius and gives both results at once. It also works back from a diameter, a volume or a surface area: a volume of 1,000 gives a radius of 6.2035.
Sphere volume and surface area by radius
| Radius | Volume | Surface area |
|---|---|---|
| 0.5 | 0.5236 | 3.1416 |
| 1 | 4.1888 | 12.5664 |
| 2 | 33.5103 | 50.2655 |
| 2.5 | 65.4498 | 78.5398 |
| 3 | 113.0973 | 113.0973 |
| 5 | 523.5988 | 314.1593 |
| 10 | 4,188.7902 | 1,256.6371 |
Rounded to 4 decimals (4 significant digits for a figure below 1) and grouped with commas, as the page shows them in an English locale. Volume is in cubic units and surface area in square units of the radius unit.
Frequently asked questions
- What is the formula for the volume of a sphere?
- V = (4/3) × π × r³. For r = 3, V = (4/3) × π × 27 = 113.0973, and for r = 10, V = 4,188.7902. The radius can be in any unit, and the volume is in that unit cubed.
- How do you find the surface area of a sphere?
- A = 4 × π × r². For r = 2, A = 4 × π × 4 = 50.2655, and for r = 10, A = 1,256.6371. The surface area is in the square of the radius unit.
- How do I find the volume of a sphere from its diameter?
- Halve the diameter to get the radius, then use V = (4/3)πr³, or choose Diameter under Known value and type it as measured. A ball 10 cm across has r = 5 cm, a volume of 523.5988 cm³ and a surface area of 314.1593 cm².
- What happens to the volume if I double the radius?
- It grows by a factor of 8, because volume depends on r³, while the surface area grows by a factor of 4. Going from r = 1 to r = 2 takes the volume from 4.1888 to 33.5103 and the area from 12.5664 to 50.2655.
- How do I find the radius of a sphere from its volume?
- Rearrange the volume formula: r = ∛(3V ÷ 4π). For V = 523.5988, 3V ÷ 4π is about 125 and its cube root is 5. Choose Volume under Known value and the tool does it: V = 1,000 gives r = 6.2035 and a diameter of 12.407. From a surface area, r = √(A ÷ 4π), so A = 1,256.6371 gives r = 10.
- Can the radius be negative or zero?
- A negative radius shows a message that a sphere cannot have a negative radius, and no result. A radius of 0 gives a volume and a surface area of 0.
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