Sphere Surface Area
Worked example: Sphere r = 0.5 m → S = pi m2. Press Try an example to run it live, then adjust anything.
Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.
See also
Hemisphere Total Surface Area: Both use sphere radius.Hemisphere Volume: Both use sphere radius.Sphere Volume: Both use sphere radius.Spherical Cap Volume: Both use sphere radius.Related Rates: Inflating Sphere: Both use sphere radius.Spheres →
Grade 10Grade 10 Math
Test your skills in the Exam Room: new numbers every attempt. Free lessons for students, no sign-up, just pure learning.
Sphere Surface Area explained
A sphere's surface area is exactly four times the area of its great circle: the disc you get by slicing it through the centre. Archimedes proved this with an elegant argument comparing the sphere to its circumscribing cylinder; in modern language, S = 4πr² is simply the derivative of the volume (4/3)πr³ with respect to r, because growing a sphere adds a thin shell whose volume is surface area times thickness.
A worked example: to paint a hemispherical dome of radius 10 m, the curved surface is half a sphere, S = ½ · 4π(10)² ≈ 628 m². At 8 m² per litre you would budget roughly 79 litres per coat. Solving for r takes the principal (positive) square root, the only physically meaningful choice since a radius is a positive length. The square-law scaling is why heat loss, drag, and paint budgets all grow four-fold when the radius merely doubles.
Sphere Surface Area formula
- = Surface area (m²)
- = Radius (m)
Cite this page
formula.expert. (2026, October 16). Sphere Surface Area Formula & Calculator. https://formula.expert/solvers/sphere-surface-area
https://formula.expert/solvers/sphere-surface-area