Solve a circle from radius, diameter, circumference or area — any one gives the rest.
A circle is completely defined by a single measurement: its radius. Every other property follows directly from r. The diameter is twice the radius. The circumference (perimeter) is 2πr ≈ 6.28318·r. The area enclosed is πr² ≈ 3.14159·r². π (pi) is an irrational constant approximately equal to 3.14159265.
Diameter
d = 2r
Circumference
C = 2πr = πd
Area
A = πr²
π is the ratio of a circle's circumference to its diameter — it's approximately 3.14159265. It appears in every circle formula because it's the fundamental constant connecting a circle's linear dimensions (radius) to its rotational measures (arc length, area).
First find the radius from the area: r = √(A/π). Then compute C = 2πr. For example, if A = 100, then r = √(100/π) ≈ 5.642, and C = 2π × 5.642 ≈ 35.45.
They mean the same thing: the total length of the boundary. 'Perimeter' is the general term for polygons; 'circumference' is specifically used for circles and curved shapes.