Circle Calculator
Enter Any One Known Value
About Circle Calculator
Circle Geometry
A circle is the set of all points equidistant from a center point. The distance from center to edge is the radius (r), the distance across through the center is the diameter (d = 2r), and the distance around is the circumference (C = 2*pi*r). Circles appear everywhere: wheels, pipes, coins, orbits, ripples, clocks, and countless engineered objects. Understanding circle measurements is fundamental to manufacturing, construction, physics, and daily life.
Essential Circle Formulas
Circumference: C = 2*pi*r = pi*d. Area: A = pi*r². Diameter: d = 2r. Arc Length: s = r*theta (theta in radians). Sector Area: A = (1/2)*r²*theta. Pi (approximately 3.14159) is the ratio of circumference to diameter for every circle, regardless of size.
How to Use This Calculator
Enter any one known value (radius, diameter, circumference, or area) and the calculator determines all other measurements. You can also calculate arc length and sector area by providing the central angle. Results include unit conversions for practical applications.
Frequently Asked Questions
What is pi and why is it important?
Pi is the ratio of a circle's circumference to its diameter, approximately 3.14159. It is an irrational number (infinite non-repeating decimals) and appears throughout mathematics, physics, and engineering.
How do I find the area of a semicircle?
A semicircle is half a circle, so its area = (1/2)*pi*r². Its perimeter includes the curved part (pi*r) plus the diameter (2r), totaling pi*r + 2r.
What is the difference between arc length and chord length?
Arc length measures the curved distance along the circle between two points. Chord length is the straight-line distance between the same two points. Arc length is always greater than or equal to chord length.
Related Tools
