Sphere Surface Area Calculator

SA = 4πr². Exactly 4× the area of a great circle of the same radius.

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Result

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General calculation reads

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How to use this calculator

  • Enter radius.
  • Read SA + great-circle area + volume.

About this calculator

Sphere surface area = 4πr², exactly four times the area of a great circle (a cross-section through the center). Archimedes proved this around 250 BCE — and was so proud he had it engraved on his tomb. Earth's surface ≈ 4π × (6371 km)² ≈ 5.1 × 10⁸ km². The sphere has the smallest surface area of any closed surface enclosing a given volume — why bubbles are spherical.

Frequently asked

Why 4× great circle?+
A famous Archimedean result. The lateral surface of the cylinder circumscribing a sphere equals the sphere's surface area, both = 4πr².
Earth surface area?+
4π × 6371² ≈ 510 million km². Land is ~149M km² (29%); ocean ~361M km² (71%).
Hemisphere?+
Curved surface = 2πr² (half of sphere). Add base circle πr² for total = 3πr² for closed hemisphere.
Why is sphere optimal?+
Of all closed surfaces enclosing a given volume, sphere has minimum SA. Proof via calculus of variations.
Real-world spherical SA?+
Solar collectors, satellite antenna design, planetary heat balance, soap-bubble physics.

Related calculators

Cylinder Surface Area Calculator
SA = 2πr² + 2πrh. Two circular ends + lateral wrap.
Cone Surface Area Calculator
SA = πr² + πrl, where l = √(r² + h²) is the slant height.
Cube Surface Area Calculator
SA = 6s². Six identical square faces.
Sphere Volume Calculator
V = (4/3)πr³. Surface area = 4πr².
Cylinder Volume Calculator
V = πr²h. Surface area = 2πr² + 2πrh (top + bottom + side).
Circle Circumference Calculator
C = 2πr (or πd). Area = πr². The fundamental circle formulas.

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SA = 6s². Six identical square faces.

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SA = 2πr² + 2πrh. Two circular ends + lateral wrap.

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SA = πr² + πrl, where l = √(r² + h²) is the slant height.

Sphere Volume Calculator
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V = (4/3)πr³. Surface area = 4πr².

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C = 2πr (or πd). Area = πr². The fundamental circle formulas.

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