Sphere Volume and Surface Area

Written byOleh Soloninupdated 27 September 2026

Known value

Value

Units

A known volume or area is in cubic or square units of the chosen length.

Result

Volume523.598776
Surface area314.159265
Radius5
Diameter10
Great circle area78.539816
Equator length31.415927
Volume in litres0.523599
Unitslengths in cm, areas in cm², volume in cm³
WorkingV = 4/3 · π · 5³ ≈ 523.5988; S = 4 · π · 5² ≈ 314.1593

One number is enough

The volume of a sphere, V = 4/3πr³, and its surface area, S = 4πr², from the radius, diameter, volume, surface area or the edge of a cube it sits inside, with the working, the volume in litres and a table of values.

A sphere's volume is four thirds of π times the radius cubed, V = 4/3 · π · r³, and its surface area is four π times the radius squared, S = 4 · π · r². A ball of radius 5 cm holds 523.6 cm³, a little over half a litre, with a surface of 314.16 cm².

A sphere is fixed by a single number, so any one measurement leads to all the others. You can enter the volume or the area instead of the radius and the calculator works back to it.

How to use

Choose what you know: radius, diameter, volume, surface area or the edge of the cube the ball is inscribed in.
Enter the number and pick millimetres, centimetres or metres to see the volume in litres as well.
Read the volume, surface area, radius, diameter and a line of working with your numbers in it.

The formulas

From the radius: V = 4/3 · π · r³, S = 4 · π · r². From the diameter, since r = d ÷ 2: V = π · d³ ÷ 6, S = π · d². Backwards: r = ∛(3V ÷ 4π) from the volume, r = √(S ÷ 4π) from the area.

Volume grows with the cube of the radius and area with the square. Double the radius and the area goes up four times, the volume eight. A radius 10% larger gives 1.1³ ≈ 1.331 times the volume, 33% more.

Worked out with this calculator. At radius 3 volume and area are the same number: 4/3 · π · 27 = 4 · π · 9 = 36π.
Radius, cm	Volume, cm³	Surface area, cm²	Volume, l
1	4.19	12.57	0.0042
2	33.51	50.27	0.0335
3	113.1	113.1	0.1131
5	523.6	314.16	0.5236
10	4,188.79	1,256.64	4.1888
15	14,137.17	2,827.43	14.1372
20	33,510.32	5,026.55	33.5103
50	523,598.78	31,415.93	523.5988

A ball inscribed in a cube

A ball inscribed in a cube touches every face, so its diameter equals the cube's edge: r = a ÷ 2. Its volume is V = π · a³ ÷ 6, which is π/6 ≈ 52.36% of the cube. A cube with a 10 cm edge holds a 523.6 cm³ ball out of its 1,000 cm³.

Choose "Edge of the cube the ball is inscribed in" and the calculator shows the radius, the ball's volume and the share of the cube it fills.

What this calculator shows

The volume of the ball and the surface area of the sphere
Radius and diameter, even when you entered a volume, area or cube edge
The volume in litres when a length unit is chosen
Great circle area and equator length
A line of working with your numbers

What to keep in mind

The formulas are exact, V = 4/3 πr³ and S = 4πr²; results are rounded to six decimal places.
A litre is a cubic decimetre: 1 l = 1,000 cm³.

FAQs

How do I find the volume of a sphere?

Cube the radius, multiply by π and by 4/3: V = 4/3 · π · r³. For a 5 cm radius: 4/3 · 3.1416 · 125 ≈ 523.6 cm³.

How do I find the volume from the diameter?

V = π · d³ ÷ 6. For a 10 cm diameter: 3.1416 · 1,000 ÷ 6 ≈ 523.6 cm³, the same as from a 5 cm radius.

How do I find the surface area of a sphere?

S = 4 · π · r². For a 5 cm radius: 4 · 3.1416 · 25 ≈ 314.16 cm², exactly four great circles of the same radius.

How do I find the radius from the volume?

Take the cube root of 3V ÷ 4π. Choose "Volume" in the calculator, enter it, and the radius follows.

What is the volume of a ball inscribed in a cube?

The radius is half the edge, so V = π · a³ ÷ 6. A cube with a 6 cm edge holds a ball of π · 216 ÷ 6 = 36π ≈ 113.1 cm³.

What is the difference between a sphere and a ball?

A sphere is only the surface; a ball is the surface together with everything inside. That is why we speak of a sphere's area and a ball's volume.

Worked example

A ball of radius 5 cm

Input: Radius 5 cm

Output: Volume 523.6 cm³, surface area 314.16 cm²

Note: V = 4/3 · π · 125 ≈ 523.6 cm³, which is 0.52 litres. The surface is exactly four times the area of its great circle, 78.54 cm².

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Sphere Volume and Surface Area

Result

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