Radius of a Circle Calculator
r from circumference or area.
r = C ÷ (2π).
How the Math Works
The Radius of a Circle Calculator uses two fundamental circle formulas to determine radius. When given circumference, it applies r = C/(2π), where C is the circumference and π is approximately 3.14159. When given area, it uses r = √(A/π), where A is the area. These formulas stem from the essential relationships between a circle's linear boundary (circumference) and its enclosed space (area), both directly proportional to the square of the radius.
Practical Applications
To use this calculator practically, first identify whether you have the circle's circumference or area measurement. For circumference problems, measure the total distance around circular objects like wheels, plates, or gardens. For area problems, measure the total space inside the circle, such as a circular tabletop or garden bed. Simply input your known measurement into the appropriate field, and the calculator instantly computes the radius, saving you from manual calculations involving square roots or division by π.
Day-to-Day Use
Knowing a circle's radius proves valuable in everyday scenarios like determining the right size fabric for circular cushions, calculating the amount of paint needed for circular wall sections, or figuring out if a circular rug will fit within a specific room area. It's also helpful for DIY projects involving circular components, such as cutting perfect circle templates for crafts, selecting appropriately sized circular storage containers, or planning circular garden layouts with accurate spacing for plants and pathways.
FAQ
From area?
r = √(A/π).