Surface Area of Sphere Calculator
Surface Area
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Volume
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Great Circle Circumference
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How to Calculate the Surface Area of a Sphere
The surface area of a sphere is SA = 4πr², where r is the radius. This means a sphere's surface area is exactly four times the area of its great circle (the largest circle that can be drawn on the sphere). This formula was first proven by Archimedes.
The volume of a sphere is V = (4/3)πr³. The great circle circumference — the distance around the sphere at its widest point — is C = 2πr, the same as any circle with that radius.
Sphere calculations are used in sports (ball sizes), astronomy (planet dimensions), engineering (tank design), and medicine (dosage spheres). The sphere has the smallest surface area of any shape enclosing a given volume, making it nature's most efficient container.
Frequently Asked Questions
What is the surface area formula for a sphere?
Surface area = 4πr². A sphere with radius 5 has surface area = 4 × π × 25 ≈ 314.16 square units.
How do you calculate the volume of a sphere?
Volume = (4/3)πr³. A sphere with radius 3 has volume = (4/3) × π × 27 ≈ 113.1 cubic units.
What is a great circle?
A great circle is the largest circle that can be drawn on a sphere's surface, passing through the center. The equator is a great circle of the Earth.
How do you find the radius from the surface area?
r = √(SA / 4π). Take the surface area, divide by 4π, then take the square root.