Every formula you need for circles is on the GED formula sheet. Your job is to know what the parts of a circle are called, find the right formula, and plug in the numbers correctly.
Radius
Diameter
d = 2r
Area
A = π r²
Circumference
C = 2π r or C = π d
The key relationship: The diameter goes all the way across the circle through the center. The radius goes from the center to the edge — exactly half the diameter.
d = 2r r = d ÷ 2
Radius (r)
Diameter (d)
1
2
5
10
10
20
25
50
50
100
Circumference
C = 2π r or C = π d
Use C = π d when given the diameter — faster. Use C = 2π r when given the radius. π ≈ 3.14 on the GED.
Area
A = π r²
Always needs the radius — not the diameter. If given diameter: find r = d ÷ 2 first. Square the radius before multiplying by π.
Common mistake: The area formula uses r² — that means radius squared, not radius times 2. Use the x² button on your calculator. 3.14 × 5² is not the same as 3.14 × 5 × 2.
Worked Example — Given Diameter, Find Area
A circle has a diameter of 10.4 cm. Find the area.
A = π r²
r = 10.4 ÷ 2
r = 5.2
A = 3.14 × 5.2²
A = 3.14 × 27.04
A = 84.91 cm²
Worked Example — Find Radius from Area
A circle has an area of 200.96 cm². Find the radius.