Calculations at a circle. A circle is the set of all points on a plane with the same distance (the radius) to a certain point, which is called center. Enter one value and choose the number of decimal places. Then click Calculate.
Formulas:
d = 2 r
c = 2 π r
A = π r²
pi:
π = 3.141592653589793...
Radius, diameter and circumference have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
radius
diameter
circumference c, area A
The circle is one of the oldest and most important elements in geometry and has long been considered a perfect shape. The calculation of circumference and area was a difficult problem for thousands of years, which led to ever better approximations and ultimately to the discovery of the number pi. This number is irrational and transcendent, meaning it cannot be represented by either a fraction or a root. The term angle appears for the first time in descriptions of the circle by Thales of Miletus around the year 600 BC. Thales proved that a triangle made from the straight line of a semicircle and a corner lying somewhere else on the circle is always a right triangle.
A circle is point-symmetrical about its center, axisymmetric about any line through its center, and rotationally symmetrical about any angle to one of those lines. This means that the order for rotational symmetry is infinite.
For a long time it was thought that the sun and planets moved in circular orbits. At first it was thought that the sun rotated in a circle and that the planets rotated in superimposed multiple circular orbits around the Earth. It was later believed that the sun is in the center and the earth and other planets rotate in circles around it. The fact that true orbits are ellipses was only discovered by Johannes Kepler in 1609.
The three-dimensional extension of the circle is the sphere.
