To find the surface area of a sphere, you mainly need its radius and one key formula:

A=4πr2A=4\pi r^2A=4πr2

where AAA is the surface area and rrr is the radius of the sphere.

Quick Scoop

  • Formula with radius:

A=4πr2A=4\pi r^2A=4πr2

Example: If r=6r=6r=6, then A=4×π×62=144πA=4\times \pi \times 6^2=144\pi A=4×π×62=144π square units.

  • Formula with diameter:
    The diameter d=2rd=2rd=2r, so you can also write

A=πd2A=\pi d^2A=πd2

Example: If d=10d=10d=10, then A=π×102=100πA=\pi \times 10^2=100\pi A=π×102=100π square units.

  • Step-by-step way to do it:
1. Identify the radius (or diameter) from the problem.
2. If you have diameter, divide by 2 to get radius.
3. Plug the radius into 4πr24\pi r^24πr2.
4. Square the radius first, then multiply by 4, then by π\pi π.
5. Round your answer if the question asks (for example, use π≈3.14\pi \approx 3.14π≈3.14).

Mini Walkthrough Example

A sphere has radius 7 cm. Find its surface area.

  1. Radius r=7r=7r=7 cm.
  2. Use A=4πr2A=4\pi r^2A=4πr2.
  3. Compute r2=72=49r^2=7^2=49r2=72=49.
  4. Multiply: A=4×π×49=196πA=4\times \pi \times 49=196\pi A=4×π×49=196π cm2\text{cm}^2cm2.
  5. Using π≈3.14\pi \approx 3.14π≈3.14, A≈196×3.14≈615.4textcm2A\approx 196\times 3.14\approx 615.4\\text{cm}^2A≈196×3.14≈615.4textcm2.

If You Only Know the Volume (Bonus)

Sometimes you’re given the volume and asked for surface area. The volume of a sphere is

V=43πr3V=\frac{4}{3}\pi r^3V=34​πr3

From this you can solve for rrr, then plug that radius into A=4πr2A=4\pi r^2A=4πr2.

There is also a combined formula that goes directly from volume to area:

A=36πV2[3]A=\sqrt{36\pi V^2}[3]A=36πV2​[3]

but in school problems it’s usually simpler to find rrr first.

Tiny Story To Remember It

Think of a basketball completely covered in tiny stickers, each sticker being a tiny square. The surface area is like counting all those sticker squares on the outside of the ball. The rule “4πr24\pi r^24πr2” tells you exactly how many square units of sticker space you need to cover the ball, once you know the radius.

TL;DR:

  • Use A=4πr2A=4\pi r^2A=4πr2 with the radius.
  • Or A=πd2A=\pi d^2A=πd2 with the diameter.
  • Always square the radius/diameter before multiplying by π\pi π.

Information gathered from public forums or data available on the internet and portrayed here.