Circle Calculator

Please provide any value below to calculate the remaining values of a circle.

Geometrically, a circle is a closed curve. In other words, it consists of every point in a plane that lies at the same distance from a fixed point, known as the centre. It can also be described as the path traced by a point that maintains a constant distance from that fixed point while it moves.

Parts of a circle

• Center (or origin): the point within a circle that is equidistant from all other points on the circle.
• Radius: the length measured from the centre of the circle to any point on its edge. This measurement equals one‑half of the diameter.
• Diameter: the greatest straight‑line distance that can be drawn between two points on the circle, which inevitably runs through the centre. Its length is twice that of the radius.
• Circumference: the distance around the circle, or the length of a circuit along the circle.
• Arc: part of the circumference of a circle
  • Major arc: an arc that is greater than half the circumference
  • Minor arc: an arc that is less than half the circumference
• Chord: a straight segment connecting two points on the circumference of the circle. When such a segment goes through the centre, it becomes the circle’s diameter.
• Secant: a line that passes through the circle at two points; it is an extension of a chord that begins and ends outside of the circle.
• Tangent: a line that intersects the circle at only a single point; the rest of the line, except the single point at which it intersects the circle, lies outside of the circle.
• Sector: the portion of a circle bounded by two radii.
  • Major sector – a sector whose central angle exceeds 180°
  • Minor sector – a sector whose central angle is less than 180°

The figures below depict the various parts of a circle:

The constant π

Historically, ancient geometers spent considerable effort trying to “square the circle,” i.e., to construct a square with the same area as a given circle using only a compass and straightedge in a finite number of steps. Although we now know this task is impossible, it wasn’t until 1880 that Ferdinand von Lindemann proved π to be transcendental, finally settling the centuries‑old quest. While their pursuit may appear futile today, the work of those early mathematicians laid the groundwork for many concepts we rely on in modern mathematics.

Circle formulas