What this calculator does
The surface area of a sphere is the total area of its curved outer surface, the figure needed for painting, coating or wrapping a spherical shape, as distinct from the volume the same sphere encloses. It follows a strikingly simple rule: exactly four times the area of a flat circle with the same radius.
This calculator leads with that surface area, taking just a radius and returning the area of a sphere directly, with the diameter, the great-circle circumference and the volume given underneath for whichever secondary figure the same job also needs.
The formula
The surface area of a sphere formula is A = 4πr², four times the area of a circle sharing the same radius, πr². That factor of four is a fixed geometric relationship: it holds for a sphere of any size, from a ball bearing to a planet.
| Term | Meaning |
|---|---|
| A | Surface area: the total area of the sphere’s curved outer surface, 4πr². |
| r | Radius: the distance from the centre of the sphere to its surface. |
| π | Pi, approximately 3.14159, the constant linking a sphere’s radius to its surface area and volume. |
The inputs explained
| Field | What to enter |
|---|---|
| Radius | The radius of the sphere, from its centre to the surface. |
When to use it
Coating or painting a spherical tank or dome
A spherical tank, dome or pressure vessel needs its surface area, not its volume, to work out how much paint, insulation or cladding will cover it.
Sizing material for a ball, globe or sphere shell
A moulded ball, globe or hollow sphere shell uses an amount of material tied to its surface area of sphere figure, useful once a thickness or coverage rate per unit area is known.
Working a surface area of a sphere formula problem
A geometry or physics question giving a radius and asking for surface area is solved directly here, without separately squaring the radius and multiplying by 4π by hand.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does sphere surface area change with the radius?
The surface area and volume of a sphere across a range of radius values.
| Radius | Surface area | Volume |
|---|---|---|
| 1 | 12.566 | 4.189 |
| 2 | 50.265 | 33.510 |
| 5 | 314.159 | 523.599 |
| 10 | 1,256.64 | 4,188.79 |
| 15 | 2,827.43 | 14,137.17 |
| 20 | 5,026.55 | 33,510.32 |
Questions
What is the surface area of a sphere formula?
A = 4πr², where r is the radius. It is exactly four times the area of a flat circle sharing the same radius.
How do you find surface area of sphere from the diameter instead of the radius?
Halve the diameter to get the radius first, then apply A = 4πr² as usual. Using the diameter directly in place of the radius would overstate the surface area by a factor of four.
What is the difference between area of a sphere and its volume?
Surface area measures the outer skin, in square units, useful for coatings and material wrapping the outside. Volume measures the enclosed space, in cubic units, useful for capacity. The two grow at different rates as a sphere scales up.
Why does surface area of sphere grow slower than volume as the sphere gets bigger?
Surface area is proportional to the radius squared while volume is proportional to the radius cubed, so as a sphere scales up, its volume accelerates away from its surface area, the same reason a larger sphere holds more relative to its outer skin than a smaller one.
For volume as the headline figure instead, see the sphere volume calculator. For both volume and surface area together from a single radius, see the full sphere calculator.