Circle Formulas: Area, Circumference, Diameter Explained
A deep dive into the interconnected formulas of circle geometry. Learn how deriving one measurement unlocks all the others.
A circle is a shape of perfect symmetry. Because of this, knowing just one metric allows you to unlock every other property. Let's break down the relationships.
Radius and Diameter
Diameter
The diameter is simply twice the radius.
The radius (r) is the distance from the center to the edge. The diameter (d) is the distance edge-to-edge through the center.
Circumference
Circumference
Alternatively: C = π × d
The circumference is the perimeter of the circle. The number Pi (π) is actually defined as the ratio of a circle's circumference to its diameter (C/d = π).
Finding Radius from Area
If you know the area but need the radius, you have to work backwards using algebra:
Radius from Area
Divide the area by Pi, then take the square root.
Our main calculator handles all these conversions automatically.