Circle Calculator

A circle is a basic yet important geometric shape. It consists of all the points on a flat surface that are the same distance from a single central point, known as the center. You can also think of it as the path traced by a point that moves while staying a fixed distance from the center.

Key Parts of a Circle

• Center (Origin): The fixed point at the center of a circle that is equally distant from all points along the edge.

• Radius: The distance from the center to any point on the circle. It’s exactly half the length of the diameter.

• Diameter: The longest distance across the circle, passing through the center. It’s equal to twice the radius.

• Circumference: The total distance around the circle—essentially, the circle’s perimeter.

• Arc: A curved segment of the circle’s circumference.

  • Major Arc: An arc longer than half of the circle’s circumference.

  • Minor Arc: An arc shorter than half of the circle’s circumference.

• Chord: A straight line connecting two points on the circle. If it goes through the center, it’s a diameter.

• Secant: A line that intersects the circle at two points and continues beyond them.

• Tangent: A line that touches the circle at just one point and does not cross into its interior.

• Sector: A slice of the circle created by two radii and the arc between them.

  • Major Sector: A sector with an angle larger than 180°.

  • Minor Sector: A sector with an angle smaller than 180°.
    
    

    The figures below depict the various parts of a circle:

      

Understanding π (Pi)

The radius, diameter, and circumference of a circle are all tied together through the constant π (pi), which is approximately 3.14159. Pi represents the ratio of a circle’s circumference to its diameter. It’s an irrational number, meaning it can’t be exactly written as a simple fraction, and its decimal goes on forever without repeating. It’s also a transcendental number, meaning it’s not a root of any polynomial with rational coefficients.

Historically, ancient mathematicians attempted a famous challenge known as “squaring the circle,” where they tried to construct a square with the same area as a given circle using only a compass and straightedge. Although this task was proven impossible in 1880 when Ferdinand von Lindemann showed that π is transcendental, their efforts laid the groundwork for much of modern geometry.

Formulas for Circle Calculations

Use these essential formulas to solve common circle-related problems:

• Diameter (D):
  D = 2 × R

• Circumference (C):
  C = 2 × π × R

• Area (A):
  A = π × R²

Where:

• R = Radius

• D = Diameter

• C = Circumference

• A = Area

• π ≈ 3.14159