Sphere Volume Calculator
Calculate the volume and surface area of a sphere from its radius.
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How to use this tool
- Enter radius in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your volume and the full breakdown beneath it.
Calculate sphere volume (4/3 × π × r³) and surface area (4 × π × r²).
Formula
Volume = 4/3 π r3
Surface area = 4 π r2
volume = (4/3) * Math.PI * r³ surface_area = 4 * Math.PI * r²
How it works
This calculator computes the volume and surface area of a perfect sphere from its radius using the classical geometric formulas derived from integral calculus. Both results depend on π (≈ 3.14159) and the radius raised to the appropriate power. The formulas assume a mathematically ideal sphere; for real-world objects, slight deviations in shape will introduce error.
Worked example
- Enter radius r = 3.
- Volume = (4/3) × π × 3³ = (4/3) × π × 27 = 36π ≈ 113.0973.
- Surface area = 4 × π × 3² = 4 × π × 9 = 36π ≈ 113.0973.
- Notice that for r = 3, volume and surface area are numerically equal (both equal 36π).
Volume ≈ 113.0973 cubic units; Surface area ≈ 113.0973 square units.
Common mistakes to avoid
- Using diameter instead of radius in the formula; since volume scales with r³, this error multiplies the result by 8.
- Forgetting the 4/3 coefficient and computing π × r³ instead of (4/3) × π × r³.
- Confusing surface area (4πr²) with volume ((4/3)πr³) when the problem asks how much material covers the sphere vs how much it holds.
Key terms
- Radius
- The distance from the centre of the sphere to any point on its surface.
- Volume
- The amount of three-dimensional space enclosed inside the sphere, in cubic units.
- Surface area
- The total area of the outer surface of the sphere, in square units.
- Pi (π)
- The mathematical constant ≈ 3.14159, representing the ratio of a circle's circumference to its diameter.
Frequently asked questions
- How do you calculate sphere volume?
- Volume = (4/3) × π × r³. Surface area = 4 × π × r². For r=3: V = 4π×9 = 36π ≈ 113.10.