VolLab

Sphere Volume Calculator

The 4/3 · π · r³ formula, instantly.

Radius

Volume

523.599

V = 4/3 · π · r³

Surface area: 314.159

What you entered

Radius: 5

1
Volume
4/3 × π × 5³= 523.5988
2
Surface area
4π × 5²= 314.1593

Result

Volume: 523.599

A sphere with radius 5 has a volume of 523.599 and a surface area of 314.159.

Sphere volume and surface area by radius

Volume is four thirds pi r cubed; surface area is 4 pi r squared.

Radius	Volume	Surface area
1	4.19	12.57
2	33.51	50.27
3	113.10	113.10
4	268.08	201.06
5	523.60	314.16
6	904.78	452.39
8	2144.66	804.25
10	4188.79	1256.64
12	7238.23	1809.56

At a radius of 3 the two figures are identical at 113.10, and that one is a genuine identity rather than a coincidence: four thirds pi r cubed equals 4 pi r squared exactly when r = 3. Below that radius the surface area is larger, above it volume runs away. A sphere encloses more volume for a given surface area than any other shape, which is why bubbles and droplets form spheres and why storage tanks are often spherical.

Why r³ this time

Like the cube, a sphere's volume scales with the cube of its radius — a basketball with twice the radius of a tennis ball holds 8 times the volume, not twice as much.

Everyday spheres

Balls, balloons, planets, and scoops of ice cream are all approximated as spheres — this formula estimates their volume from a single radius measurement.

Frequently asked questions

How do I calculate the volume of a sphere?

Volume = (4/3) × π × r³. A sphere with radius 6 cm: V = (4/3) × π × 216 = 904.8 cm³. If you know the diameter, halve it for the radius first. The formula comes from calculus (integrating circular cross-sections).

How do I find the surface area of a sphere?

Surface area = 4 × π × r². A ball with radius 10 cm has surface area 4 × π × 100 = 1,256.6 cm². That's exactly 4 times the area of its great circle — a surprising and elegant relationship.

How much water does a spherical tank hold?

Calculate volume in cm³ using V = (4/3)πr³, then divide by 1,000 for liters. A spherical tank with 50 cm radius: V = (4/3) × π × 125,000 = 523,599 cm³ = 523.6 liters ≈ 138.2 US gallons.