Area of a Circle

The Area of a Circle equation (A = π•r²)CIRCLE PARTS   computes the area of a circle.

INSTRUCTIONS:  Choose units and enter the following:

• (r) - Radius of the circle

Area of a Circle (A): The calculator computes the area (A)  in square meters.  However, this can be automatically converted to many other area units (e.g. square inches) via the pull-down menu.

References

• Light and Matter(Dr. Benjamin Crowell) Chapter 0.5 Basics of the Metric System
• Light and Matter(Dr. Benjamin Crowell) Chapter 1.1 Introduction

Circle Calculators

• Circle Area -  Computes the area of a circle given the radius (A = π r²).
• Area of Circle Arc Segment f(r,θ) - Computes the area of an arc segment of a circle given the radius (r) and angle (θ)
• Area of Circle Arc Segment Area f(r,h) - Computes the area of an arc segment of a circle given radius (r) and the depth (h) into the circle.
• Area of Circle Sector f(r,Θ) - Computes the area of a sector (pie slice) of a circle given the radius (r) and angle (Θ).
• Angle of Circle Sector f(r,h) - Computes the angle in a circle from the radius and depth of the chord.
• Area of Circle Annulus - Computes the area of an annulus (ring) given the inner radius (r) and outer radius (R).
• Radius of Circle from Center and a Point - Computes the radius of a circle given the center point (h,k) and any other point (x,y) on the circle.
• Circumference of Circle -  Computes the circumference of a circle given the radius (C = 2 π r).
• Circle Arc Length - Computes the length of an arc length on a circle given the radius (r) and angle (Θ)
• Circle within a Triangle - Computes the radius of a circle inscribed within a triangle given the length of the three sides (a,b,c) of the triangle.
• Circle around a Triangle - Computes the radius of a circle that circumscribes a triangle given the length of the three sides (a,b,c) of the triangle.
• Circle Diameter from Area - Computes the radius and diameter of a circle from the area. 
• Circle Radius from Circumference - Computes the radius of a circle given the circumference.
• Circle Circumference from Area - Computes the circumference of a circle given the area.
• Circle Radius from Area - Computes the radius of a circle given the area.
• Chord Length: Computes the length of a chord in a circle from the radius and height.
• Chord Length from Arc Length and Radius: Computes the length of a chord on a circle based on the circle's radius (r) and the length of the arc (a).
• Circle Radius from Chord - Computes the radius of a circle based on the length of a chord and the chord's center height.
• Circle Equation from Center and one Point - Develops the general equation of a circle based on the coordinates of the center (h,k) and any point on the circle (x,y).
• Circle Equation from Three Points: Develops the general equation of a circle that goes through three points that are not in a straight line.
• Circle with same Perimeter as an Ellipse - Computes the radius of the circle with the same perimeter of an ellipse defined by the semi-major and semi-minor axes.
• Rectangles to Cover a Circle - Computes the number of rectangles needed to minimally cover a circle based on the circle's diameter and the length and width of the rectangles.

The Math

The formula for the area of a circle is:

          A = π•r²

where:

• A is the area of the circle
• r is the radius of 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.

For other area calculators see:

• Area of Circle - Circle approximates a polygon as the number of sides approaches infinity.
• Area of Triangle -  Three Sides
• Area of Quadrilateral - Four Sides
• Area of Pentagon - Five Sides
• Area of Hexagon - Six Sides
• Area of Heptagon - Seven Sides
• Area of Octagon - Eight Sides
• Area of Nonogon - Nine Sides
• Area of Decagon - Ten Sides
• Area of Hendecagon - Eleven Sides
• Area of Dodecagon - Twelve Sides
• Area of Polygon  -  Any number of sides (n).