Radius of a Circle Calculator
Created by: Emma Collins
Last updated:
Calculate circle radius from circumference, area, or diameter with our free online calculator. Get instant results with step-by-step solutions and interactive circle visualization for geometry problems, construction planning, and educational purposes.
What is a Circle Radius Calculator?
A circle radius calculator is a mathematical tool that determines the radius of a circle using known measurements such as circumference, area, or diameter. The radius is the fundamental measurement of a circle, representing the distance from the center point to any point on the circle's edge. This calculator provides instant, accurate results for various geometric and practical applications.
Understanding how to calculate radius is essential in mathematics, engineering, construction, and design fields. Whether you're planning a circular garden, designing architectural elements, or solving geometry problems, knowing the radius allows you to determine all other circle properties including area, circumference, and diameter.
Circle Radius Formulas
The radius can be calculated using different known circle measurements:
- From Circumference: r = C ÷ 2π
- From Area: r = √(A ÷ π)
- From Diameter: r = d ÷ 2
Where r = radius, C = circumference, A = area, d = diameter, and π ≈ 3.14159. These formulas are derived from the fundamental circle equations: C = 2πr and A = πr².
How to Calculate Circle Radius: Examples
Example 1: Finding Radius from Circumference
If a circular track has a circumference of 628 meters, what is its radius?
Solution: r = C ÷ 2π = 628 ÷ 6.283 = 100 meters
Example 2: Finding Radius from Area
If a circular pizza has an area of 201.06 square inches, what is its radius?
Solution: r = √(A ÷ π) = √(201.06 ÷ 3.14159) = √64 = 8 inches
Common Applications
Circle radius calculations are essential in numerous practical situations:
- Construction and Architecture: Designing circular structures, arches, and curved elements
- Landscaping: Planning circular gardens, patios, and irrigation systems
- Engineering: Calculating pipe dimensions, gear specifications, and mechanical components
- Education: Solving geometry problems and understanding circle properties
- Manufacturing: Quality control for circular products and components
Frequently Asked Questions
How do I find the radius of a circle if I know the circumference?
To find radius from circumference, divide the circumference by 2π (approximately 6.283). The formula is r = C ÷ 2π. For example, if circumference is 31.4 units, radius = 31.4 ÷ 6.283 = 5 units.
What is the formula for calculating radius from area?
To find radius from area, use the formula r = √(A ÷ π). First divide the area by π (3.14159), then take the square root. For example, if area is 78.54 square units, radius = √(78.54 ÷ 3.14159) = √25 = 5 units.
What is the difference between radius and diameter?
Radius is the distance from the center to any point on the circle's edge, while diameter is the distance across the entire circle through its center. Diameter is always exactly twice the radius: d = 2r.
When would I need to calculate a circle's radius?
Circle radius calculations are used in engineering design, architecture, construction planning, area calculations for gardens or pools, determining material requirements for circular projects, and solving geometry problems in education and professional applications.
Sources and References
- National Institute of Standards and Technology, "Circle Geometry Formulas", NIST Handbook
- American Mathematical Society, "Fundamentals of Geometry", Educational Standards
- International Organization for Standardization, "Mathematical Notation Standards", ISO 31-11