Sphere Calculator
Enter a radius below to instantly get the volume and surface area of a sphere.
Sphere Formulas
Volume = (4/3)πr³. Surface area = 4πr². Both formulas depend only on the radius, r.
A common mistake is squaring the radius instead of cubing it when solving for volume, or using the diameter where the formula calls for the radius. Since volume scales with r³, doubling the radius doesn't double the volume — it multiplies it by 8 (2³).
Worked example
A sphere with radius 6.
Volume = (4/3) × π × 6³ = (4/3) × π × 216 ≈ 904.78
Surface area = 4 × π × 6² = 4 × π × 36 ≈ 452.39
A second example, with radius 2.
Volume = (4/3) × π × 2³ = (4/3) × π × 8 ≈ 33.51
Surface area = 4 × π × 2² = 4 × π × 4 ≈ 50.27
Keep going
- Every cross-section through a sphere's center is a circle; the circle calculator finds the area and circumference of that same 2D slice. Circle Calculator
Frequently Asked Questions
What is the formula for the volume of a sphere?
Volume = (4/3) × π × r³, where r is the radius. Doubling the radius multiplies the volume by 8, since volume scales with the cube of the radius.
What is the formula for the surface area of a sphere?
Surface area = 4 × π × r², where r is the radius.
How is a sphere different from a circle?
A circle is a flat, two-dimensional shape. A sphere is the three-dimensional version — every point on its surface is the same distance from its center, in every direction.
How does a sphere's volume compare to the cylinder around it?
A sphere's volume is exactly two-thirds the volume of the smallest cylinder that contains it (radius r, height 2r). That cylinder's volume is πr² × 2r = 2πr³, and two-thirds of that is (2/3) × 2πr³ = (4/3)πr³ — the sphere formula exactly. Archimedes considered this ratio one of his greatest discoveries.
Related Calculators
- Cylinder Calculator — Geometry & Trigonometry
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