# Circle Calculator

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Lets first understand, what is a circle and how we can find different properties of a circle?

Circle

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, called the center of the circle.

Circle is the curve traced out by a point that moves in a plane so that its distance from a given point (center of the circle) is constant.

The distance between any point of the circle and the centre is called the radius.

A circle is a simple closed curve that divides the plane into two regions: an interior and an exterior.

Definition of circle

A circle is a plane figure bounded by one curved line and such that all straight lines drawn from a certain point within it to the bounding line are equal. The bounding line is called its circumference and the point, its centre.

Formulas

Let the Radius the Circle be \(R\) units.

Diameter (D) of the Circle will be \(2R\) units.

Circumference of the circle

The ratio of a circle's circumference to its diameter is \(\pi\), a constant approximately equal to 3.14159.

Circumference of the Circle will be \(2\pi R(=\pi D)\) units.

Area of the circle

Area of the Circle will be \(\pi R^2\) square units.

The circle is the plane curve enclosing the maximum area for a given arc length.

Equation of a circle

The circle with centre \((x_0,y_0)\) and radius 'r' is the set of all points \((x, y)\) such that

$$(x-x_0)^2+(y-y_0)^2=r^2,$$This equation is known as the equation of the circle.

If the circle is centred at the origin (0, 0) and with radius 'r' then the equation will

$$x^2+y^2=r^2$$For calculating different properties of the circle using above circle calculator, you have to just write the values in the given input boxes and press the calculate button, you will get the result.