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Sphere Surface Area Calculator

Find the surface area and volume of a sphere.

Result

530.93 units²
1,150.35 units³

How it is calculated

A sphere is fully described by its radius r, the distance from the centre to the surface. The tool computes surface area = 4πr² and volume = (4/3)πr³, using the full value of π. The radius must be above zero. Enter the radius, not the diameter, in any single length unit. The results are labelled generically as units² and units³, so read them as m² and m³ when the radius is in metres, cm² and cm³ when in centimetres, and so on. Both results are rounded to two decimals. Surface area grows with the square of the radius and volume with the cube, so doubling r multiplies the area by 4 and the volume by 8.

Worked example

A ball has a radius of 6.5 cm. Square the radius: 6.5² = 42.25. Surface area: 4 × π × 42.25 ≈ 530.93 units², so about 530.93 cm². Cube the radius: 6.5³ = 274.625. Volume: (4/3) × π × 274.625 ≈ 1,150.35 units³, about 1,150.35 cm³ or 1.15 litres. The area is in square units and the volume in cubic units.

Try this example →

Common mistakes

  • Entering the diameter instead of the radius. A 13 cm wide ball has a radius of 6.5 cm; typing 13 makes the area 4 times and the volume 8 times too big.
  • Mixing area and volume units, for example reading the volume in cm² or comparing m² with cm³.
  • Forgetting that the area scales with r². A sphere with twice the radius needs four times as much paint or material, not twice as much.
  • Squaring after multiplying by 4π, as in (4πr)². The square applies to r only.
  • Converting units after the calculation incorrectly. Converting 1 m² to cm² multiplies by 10,000, not 100.

About this calculator

This calculator finds a sphere's surface area, A = 4·π·r², and its volume, V = (4/3)·π·r³, from a single measurement — the radius r — using formulas derived from integral calculus applied to a semicircle rotated through 360° about its diameter. Surface area tells you how much material would be needed to coat or wrap the sphere, while volume tells you how much it can hold or how much space it displaces.

Engineers use these formulas to size spherical tanks and pressure vessels, estimate the material needed for coatings or paint on ball-shaped components, and calculate buoyancy for spherical floats or balloons; manufacturers use them for anything from ball bearings to sporting goods. Geometry and physics students verifying textbook problems, and hobbyists figuring out how much paint or fabric a ball-shaped project needs, use this calculator just as often.

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Comments (1)

  • Editorial team

    For a dome or bowl the sphere's numbers need adjusting. A hemisphere has half the volume and half the curved area, 2 pi r squared, and if it is closed with a flat base you add pi r squared for the disc. With a radius of 10 that means the curved part is about 628.32 and the flat base about 314.16 in the same square units. What are you coating or filling, a ball, a dome or a tank end?

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