How to Find the Radius of a Circle
The radius of a circle is the distance from the center to any point on the circumference. It is one of the most fundamental measurements in geometry and can be derived from several other circle properties.
Radius Formulas
From Circumference
Divide the circumference by 2 times pi.
r = C / (2 * pi)
From Area
Take the square root of the area divided by pi.
r = sqrt(A / pi)
From Diameter
Simply divide the diameter by 2.
r = d / 2
Circle Properties
Once you know the radius, you can find every other property of the circle:
- Diameter: d = 2r -- the longest chord passing through the center
- Circumference: C = 2 * pi * r -- the total distance around the circle
- Area: A = pi * r^2 -- the total space enclosed by the circle
Real-World Applications
- Engineering: designing wheels, gears, pipes, and circular components
- Architecture: planning domes, arches, and circular floor plans
- Astronomy: calculating orbital paths and celestial body sizes
- Everyday life: determining ring sizes, pizza area, circular garden beds