Circle Calculator

What Is a Circle?

A circle is a simple closed shape consisting of all points in a plane that are exactly the same distance from a fixed central point, called the center. It can also be described as the path traced by a point that moves while staying at a constant distance from the center.

Key Parts of a Circle

• Center (Origin): The fixed point from which all points on the circle are equally distant.

• Radius (R): The distance from the center to any point on the circle. It is half the length of the diameter.

• Diameter (D): The longest straight-line distance between any two points on the circle, passing through the center. It is twice the radius.

• Circumference (C): The total distance around the circle; essentially its perimeter.

• Arc: A segment of the circumference.

  • Minor Arc: Less than half of the circle.

  • Major Arc: More than half of the circle.

• Chord: A line segment that connects two points on the circle. If it passes through the center, it’s the diameter.

• Secant: A line that intersects the circle at two points, extending beyond it.

• Tangent: A line that touches the circle at exactly one point.

• Sector: A “pizza-slice” shaped area enclosed between two radii and the connecting arc.

  • Minor Sector: Central angle less than 180°.

  • Major Sector: Central angle more than 180°.

Understanding π (Pi)

The relationship between the radius, diameter, and circumference of a circle is tied together by the mathematical constant π (pi) — approximately 3.14159.

• π is irrational (its decimal never ends or repeats), and

• π is also transcendental (not the root of any rational polynomial).

Although often estimated as 22/7, π cannot be written exactly as a fraction. Historically, mathematicians tried to “square the circle” — meaning they attempted to create a square with the same area as a given circle using only a compass and straightedge. This was proven impossible in 1882 when Ferdinand von Lindemann proved that π is transcendental.

Essential Circle Formulas

• Diameter:
  D = 2R

• Circumference:
  C = 2πR

• Area:
  A = πR²

Where:
R = Radius
D = Diameter
C = Circumference
A = Area
π ≈ 3.14159

Related Calculators:
Area Calculator, Distance Calculator

External Resources:
Circle Calculator on Calculator.net