Circle Calculator

vCalc Reviewed
Calculator / Last modified by KurtHeckman on 2019/03/15 16:24
Circle Area Circle Circumference
Segment Area f(r,`theta`) arc length
Segment Area f(r,h) circle within a triangle
Sector Area f(r,`theta`) circle around a triangle
area of annulus Radius from Circumference
Radius from Center to a Point Circumference from Area
Radius from Chord Radius from Area

The Circle Calculator provides the area, circumference, radius and diameter equations employing many different length and area units CircleStack.png          Circles and
    Circle segments
as follows:

The Circle

A circle is a simple shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance from a given point, the center; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the center is called the radius.
A circle is a simple closed curve which divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is the former and the latter is called a disk.
A circle may also be defined as a special ellipse in which the two foci are coincident and the eccentricity is 0, or the two-dimensional shape enclosing the most area per unit perimeter, using calculus of variations.Triangle-in-Circle.jpgcircle around triangleCircleInTriangle.jpg  circle within triangle  Circle_Radius_from_Cord_Length.png Radius of circle from cord length and height


The word "circle" derives from the Greek κίρκος/κύκλος (kirkos/kuklos), itself a metathesis of the Homeric Greek κρίκος (krikos), meaning "hoop" or "ring".  The origins of the words "circus" and "circuit" are closely related.

The circle has been known since before the beginning of recorded history. Natural circles would have been observed, such as the Moon, Sun, and a short plant stalk blowing in the wind on sand, which forms a circle shape in the sand. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy, and calculus.

Early science, particularly geometry and astrology and astronomy, was connected to the divine for most medieval scholars, and many believed that there was something intrinsically "divine" or "perfect" that could be found in circles.

Some highlights in the history of the circle are:

  • 1700 BCE – The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 25681 (3.16049...) as an approximate value of π
  • 300 BCE – Book 3 of Euclid's Elements deals with the properties of circles.
  • In Plato's Seventh Letter there is a detailed definition and explanation of the circle. Plato explains the perfect circle and how it is different from any drawing, words, definition or explanation.
  • 1880 CE– Lindemann proves that π is transcendental, effectively settling the millennia-old problem of squaring the circle.


  • wikipedia -


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