Calculate radius, diameter, circumference, and area of a circle. Enter any value and get all properties instantly with formulas and visual representations.
A circle is a perfectly round 2D shape where every point on its edge is equidistant from the center. This distance is called the radius. Circles are fundamental in geometry, appearing everywhere in nature, engineering, and mathematics.
The area of a circle is calculated using the formula A = πr², where r is the radius. For example, if the radius is 5 units, the area is π × 5² = 3.14159 × 25 ≈ 78.54 square units.
Circumference = 2πr or πd, where r is the radius and d is the diameter. Since diameter is twice the radius (d = 2r), both formulas give the same result. For a circle with radius 5, C = 2 × π × 5 ≈ 31.42 units.
To find radius from area, use the formula r = √(A/π). For example, if the area is 78.54, then r = √(78.54/3.14159) = √25 = 5 units. Our calculator does this automatically when you select "Area" mode.
Pi (π) is a mathematical constant approximately equal to 3.14159. It represents the ratio of a circle's circumference to its diameter. This ratio is the same for every circle, regardless of size, making π essential for all circle calculations.
The radius is always half the diameter. Simply divide the diameter by 2. For example, if the diameter is 10 units, the radius is 10 ÷ 2 = 5 units. Conversely, diameter = 2 × radius.
Yes! The calculator works with any unit of measurement (inches, feet, meters, centimeters, etc.). Just ensure you're consistent. If you enter radius in meters, all results will be in meters (circumference) and square meters (area).
Circumference and perimeter mean the same thing - the distance around a shape. "Circumference" is specifically used for circles and curves, while "perimeter" is more general and applies to any closed shape (squares, triangles, etc.).
Our calculator uses JavaScript's built-in Math.PI constant (accurate to 15 decimal places) and displays results to 4 decimal places. This is more than sufficient for virtually all practical applications, from homework to professional engineering calculations.
“Perfect for my geometry homework! The ability to enter any property and get all the others is super helpful. The formulas shown make it easy to check my work.”
“As a landscape designer, I use this daily to calculate circular garden beds and fountains. The visual charts help me explain dimensions to clients clearly.”
“Simple, fast, and accurate. I teach middle school math and recommend this to all my students for circle problems. The export feature is great for record keeping!”