Sphere Volume Calculator
Calculate the volume and surface area of a sphere from its radius. Instant results with step-by-step formulas.
Enter the radius of the sphere
Volume
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Surface Area
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Diameter
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Sphere Formulas
Surface Area = 4 × π × r²
Volume = (4/3) × π × 216 = 288π ≈ 904.7787 cubic units
Surface Area = 4 × π × 36 = 144π ≈ 452.3893 square units
Understanding the Sphere
A sphere is a perfectly round 3D shape where every point on its surface is equidistant from the center. Common real-world examples include balls, planets, and bubbles.
Volume vs Surface Area
| Property | Formula | Measures |
|---|---|---|
| Volume | (4/3)πr³ | Space inside the sphere (cubic units) |
| Surface Area | 4πr² | Total outer surface (square units) |
Frequently Asked Questions
How do I find the volume if I know the diameter?
Divide the diameter by 2 to get the radius, then apply V = (4/3)πr³. Alternatively, V = (π/6) × d³.
Why is the factor 4/3 in the volume formula?
The factor 4/3 comes from integrating circular cross-sections along the diameter. It relates to how a sphere's volume compares to the cylinder that encloses it (the sphere is exactly 2/3 of the enclosing cylinder's volume).
How does doubling the radius affect volume?
Doubling the radius increases the volume by a factor of 8 (since 2³ = 8). Volume scales with the cube of the radius.
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Last updated: 2026-08-08