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Circle calculator

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This circle calculator takes one known measurement of a circle—radius, diameter, circumference, or area—and automatically calculates the remaining three values.

What is a circle?

A circle is a two-dimensional shape where all points on its boundary are equidistant from a fixed point called the center. This fixed distance is called the radius.

Parts of a circle

  1. Radius (r) – The distance from the center to any point on the circle.
  2. Diameter (d) – The longest distance across the circle, passing through the center. It is twice the radius.
  3. Circumference (C) – The total distance around the circle (the perimeter of a circle).
  4. Area (A) – The total space inside the circle.
  5. Chord – A line segment that connects two points on the circle but does not necessarily pass through the center.
  6. Arc – A portion of the circle’s boundary between two points.
  7. Sector – A region of the circle enclosed by two radii and an arc.
  8. Segment – A region of the circle enclosed by a chord and an arc.
  9. Tangent – A straight line that touches the circle at exactly one point.
  10. Secant – A straight line that intersects the circle at two points.

What is Pi (π)?

The mathematical constant π (pi) is the ratio of a circle’s circumference to its diameter.
It is an irrational number, approximately equal to 3.14159 but continues infinitely without repeating.

\pi = \frac{\text{Circumference}}{\text{Diameter}}

Formulas for circle measurements

  1. Radius (r)
    • If given the diameter: r = \frac{d}{2}​
    • If given the circumference: r = \frac{C}{2\pi}
    • If given the area: r = \sqrt{\frac{A}{\pi}}​
  2. Diameter (d)
    • d = 2r
    • d = \frac{C}{\pi}​
  3. Circumference (C)
    • C = 2\pi r
    • C = \pi d
  4. Area (A)
    • A = \pi r^2

Additional facts about circles

  • A circle is a special case of an ellipse where both foci are at the same point.
  • The unit circle is a circle with a radius of 1, commonly used in trigonometry.
  • Circles are infinitely symmetrical and have no corners or edges.
  • The equation of a circle in a Cartesian coordinate system with center (h,k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2