Sphere volume calculator.
Find the volume of a sphere. Enter the radius or the diameter and the calculator returns the volume, the surface area and the diameter of the sphere.
Sphere size
LiveVolume equals four thirds times pi times the radius cubed. Enter a radius or diameter and pick which one it is.
Volume
523.599
four thirds pi r cubed
Uses pi to full floating-point precision. Units match whatever unit you enter. Calculations run in your browser; nothing you enter is stored.
How it works
Four thirds pi r cubed
The volume of a sphere is four thirds times pi times the radius cubed. Because the radius is cubed, volume grows very fast as a ball gets bigger: doubling the radius makes the sphere eight times the volume.
A sphere with a radius of 5 has a volume of about 523.60. Its surface area, four times pi times the radius squared, is about 314.16. The calculator gives both from a radius or a diameter.
Reference
Sphere volume examples.
The volume for a few radius values, using pi.
| Radius | Volume |
|---|---|
| 1 | 4.19 |
| 2 | 33.51 |
| 5 | 523.60 |
| 10 | 4188.79 |
| 0.5 | 0.52 |
The full guide
The complete guide to sphere volume.
Where the formula comes from, how it scales, and how surface area differs.
The volume formula
A sphere is the set of all points a fixed distance, the radius, from a centre. Its volume is four thirds pi r cubed, a result that goes back to Archimedes. The cube on the radius is what makes spheres fill space so quickly as they grow.
Enter the radius, or a diameter that the calculator halves, and keep your units consistent for a result in those units cubed.
How volume scales
Because volume depends on the radius cubed, scaling matters a lot. Double the radius and the volume rises eightfold; triple it and the volume is twenty-seven times larger. That is why small increases in size mean large increases in capacity.
This cube law explains why large bubbles, planets and balloons hold so much more than they appear.
Volume versus surface area
Volume is the space inside the sphere; surface area is the skin around it, four pi r squared. As a sphere grows, volume outpaces surface area, which is why large objects have relatively little surface for their size.
The calculator reports both so you can compare capacity with covering.
Where it is used
Sphere volume comes up with balls, tanks, planets, droplets and bubbles. To convert a centimetre-based volume to litres, divide by 1000. For tubes and cans, use the cylinder volume calculator instead.
A sphere holds the most volume for the least surface area of any shape, which is why drops and bubbles are round.
The formula
Four thirds
pi r cubed.
A sphere’s volume is four thirds pi times the radius cubed; its surface area is four pi r squared.
Cylinder volume ›# Sphere
volume = 4/3 × pi × r^3
surface = 4 × pi × r^2
# r=5
V = 523.60Questions
Sphere questions.
How do I calculate the volume of a sphere?
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Multiply four thirds by pi by the radius cubed. Enter the radius or diameter above and the calculator returns the volume and surface area.
What is the formula for sphere volume?
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V equals four thirds pi r cubed, where r is the radius. If you know the diameter, halve it to get the radius first.
How does doubling the radius change the volume?
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It makes the volume eight times larger, because volume depends on the radius cubed and two cubed is eight.
What is the surface area of a sphere?
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The surface area is four pi r squared. The calculator shows it alongside the volume.
Is this sphere volume calculator free?
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Yes. It is completely free with no sign-up, and every calculation runs locally in your browser, so nothing you enter is stored or sent anywhere.
About the developer
Jean Borg
Jean builds and maintains every calculator on freecalculators.pro from Malta, with a focus on tools that are fast, free and show their working. The sphere volume calculator works from a radius or diameter and shows the surface area too.