Sphere Surface Area Calculator — 4πr²
Find the surface area of a sphere by entering its radius. The formula 4πr² gives the total outer area — equal to exactly four great circles.
units
Total outer area of the sphere — equal to four great circles
- 1
Square the radius
5 × 5 = 25 - 2
Great-circle area
π × 25 = 78.5398The sphere surface equals exactly four great-circle areas. - 3
Surface area
4 × π × 25 = 314.1593
How does this calculator work?
Sphere surface area = 4πr². For r = 5: area = 4π × 25 ≈ 314.16 square units. This equals four great-circle areas (each πr²). Diameter = 2r. Surface area scales with r², so doubling the radius gives four times the area.
Formula
How this is calculated
The surface area of a sphere is the total area of its outer skin — the amount of material needed to cover the sphere completely. The exact formula is A = 4πr², where r is the radius and π ≈ 3.14159. An elegant geometric fact: this equals precisely four times the area of the sphere's great circle (the largest circle that fits on the sphere, with area πr²). Archimedes first proved this by showing that a sphere's surface equals the lateral area of its circumscribed cylinder.
Enter the radius in any single consistent length unit (metres, centimetres, feet, etc.) — the result comes back in that unit squared. The calculator also reports the diameter (2r), the great-circle area (πr²), and the great-circle circumference (2πr). These are useful in physics, packaging design, and astronomy.
The formula assumes a perfect mathematical sphere with zero thickness. For a hollow spherical shell, compute outer and inner surface areas separately and add them. Surface area scales with the square of the radius: doubling the radius quadruples the surface area, while tripling the radius gives nine times the surface area.
Frequently asked questions
2πr² is only the curved surface of a hemisphere (half a sphere). A full sphere has twice that dome area, giving 4πr². Equivalently, the sphere surface equals four times the great-circle area πr².
Rearrange the formula: r = √(A / (4π)). For example, if the surface area is 314.159 square units, then r = √(314.159 / 12.566) = √25 = 5 units.
A great circle is the largest circle that can be drawn on a sphere — it passes through the sphere's centre. Its area is πr² and its circumference is 2πr. The remarkable fact is that the sphere's surface equals exactly four of these great circles.
Also known as
TG we-Calculate Editorial Team. (2026). Sphere Surface Area Calculator — 4πr² [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/area-of-sphere-calculator
TG we-Calculate Editorial Team. "Sphere Surface Area Calculator — 4πr²." TG we-Calculate. 2026. https://we-calculate.com/calculator/area-of-sphere-calculator.
TG we-Calculate Editorial Team, "Sphere Surface Area Calculator — 4πr²," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/area-of-sphere-calculator
@misc{wecalculate_area_of_sphere_calculator, title = {Sphere Surface Area Calculator — 4πr²}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/area-of-sphere-calculator}}, year = {2026}, note = {TG we-Calculate} }
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