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Formula for Area of a Circle

Omkar Phatak Mar 5, 2019
If you are looking for the formula for circle area calculation, you need not look any further. Here, the various versions of the formula are discussed.
Circle is one of the most fundamental and simple shapes in Euclidean two-dimensional geometry. While taking your first course in the subject, you are bound to come across a problem of calculating its area. It is also the first instant where you will come across 'Pi (π)', the mysterious quantity that keeps cropping up in various math formulas.

Interesting Geometrical Facts About a Circle

A circle is defined as the set of all points on a two-dimensional plane, that are equidistant from a common point, called the center. The circumference is the total closed curve length of the circle.
Radius is the length of a segment joining the center with any point on the circumference.
Diameter is a straight segment passing through the center and joining two points on the circumference. Naturally, it is twice the radius in length and also the longest distance between any two points situated on the circumference. Area is the numerical measure of the interior expanse of the circle, within its boundaries.
A circle is a special form of ellipse, with both foci coinciding with each other. It is also the conic section created by the intersection of a plane perpendicular to the axis of a cone. For a given perimeter length, circle is the geometrical shape with the largest area, compared to a square or any other shape.
An irrational number comes into calculations associated with a circle and it is Pi (π). It is the ratio of the circumference to its diameter and it has a constant value, which is 3.1415926536 (accurate and rounded up till 10 decimal places).

Forms of Circle Area Formula

Using Radius
If you know the radius, then the formula to be used, is:
Area = π R2

where R is the radius. If radius is measured in meters, then the unit for area will be meter2 (m2).
Using Diameter
Knowing the diameter, you can calculate its area. The formula in terms of diameter is as follows:

Area = π D2 / 4

where D is the diameter.
Using Circumference
Here is a formula to calculate the area from circumference.

Area = C2 / 4π

where C is the circumference.
Memorizing the formula is certainly quite useful. If you practice solving a lot of examples, it will automatically be stored in memory. You won't have to take any extra efforts to remember it that way. Mastering mathematics is all about practice.