Radius Of A Circle
Find the radius of a circle from circumference, area, or diameter using r = C/(2pi), r = sqrt(A/pi), or r = d/2. Free geometry calculator with chart and results.
About This Calculator
About the Radius Of A Circle Calculator
Our Radius Of A Circle Calculator is a versatile geometry tool designed for anyone who needs to find the radius of a circle quickly and accurately. Whether you are a student learning circle geometry, a teacher preparing lesson materials, an engineer working on circular components, or a DIY enthusiast measuring round objects, this calculator handles all common radius scenarios. You can compute the radius from three different known measurements: circumference, area, or diameter -- whichever you have on hand.
How the Radius Is Calculated
The radius of a circle is calculated using one of three formulas depending on the input you provide. From circumference C, the radius is r = C / (2pi). From area A, the radius is r = sqrt(A / pi). From diameter d, the radius is simply r = d / 2. The calculator automatically selects the correct formula based on your chosen input mode and displays not only the radius but also the derived diameter, circumference, and area for a complete picture of the circle's properties.
Why Use This Calculator
Manual circle calculations can be error-prone, especially when working with pi and square roots. This calculator eliminates math errors, saves time, and provides a visual chart for comparing the circle's key measurements. It supports any positive numeric input and displays results with up to 4 decimal places for precision. The results update instantly, and you can share your calculation via a unique URL containing your inputs.
Practical Applications
Finding the radius of a circle is useful in many real-world scenarios. Students use it for geometry homework and exam preparation. Engineers and architects calculate radii when designing circular components like wheels, pipes, arches, and round tables. Construction professionals measure the radius of curved walls, arches, and circular patios. In manufacturing, workers determine radii of cylindrical parts and circular cutouts. The versatile input options make this calculator suitable for anyone working with circles in any field.
Frequently Asked Questions
How do you find the radius of a circle from the circumference?
To find the radius of a circle from its circumference, use the formula r = C / (2pi), where C is the circumference and pi is approximately 3.14159. For example, a circle with circumference 31.42 units has a radius of 31.42 / (2 x 3.14159) = 5 units.
How do you calculate the radius from the area of a circle?
To find the radius from the area of a circle, use the formula r = sqrt(A / pi), where A is the area. For example, a circle with area 78.54 square units has a radius of sqrt(78.54 / 3.14159) = sqrt25 = 5 units.
What is the formula for radius from diameter?
The radius is exactly half the diameter. The formula is r = d / 2, where d is the diameter. This is the simplest way to find the radius -- just divide the diameter by 2.
What is the radius of a circle?
The radius of a circle is the distance from its center point to any point on the circle's boundary. It is half the diameter and is used in all circle formulas including circumference C = 2pir, area A = pir^2, and diameter d = 2r.
Can I calculate the radius if I only know the circumference?
Yes, you can calculate the radius from the circumference alone using the formula r = C / (2pi). Simply select the circumference input mode on our calculator, enter your circumference value, and the radius will be computed instantly.
Is this radius calculator free to use?
Yes, all calculators on Calculy are completely free to use with no registration or download required.
What is the difference between radius and diameter?
The radius is the distance from the center of a circle to its edge, while the diameter is the distance across the entire circle passing through the center. The diameter is always twice the length of the radius (d = 2r).
How accurate are the radius calculations?
Our radius calculator uses high-precision JavaScript math with up to 4 decimal places displayed. The calculations use the mathematical constant pi (pi) accurate to 15 decimal places, ensuring reliable results.