What is area?

Area is a measure of how much space there is on a flat surface. For example two sheets of paper have twice the area of a single sheet, because there is twice as much space to write on.

Different shapes have different ways to find the area. For example, in a rectangle we find the area by multiplying the length times the width. In the rectangle above, the area is 2×4 or 8. If you count the small squares you will find there are 8 of them.
(See Area of a rectangle.)


Area is measured in square units. For example in the rectangle above, if the sides are 2 and 4 meters long, then the area is 8 square meters. If the sides were 2 feet and 4 feet long the area would be 8 square feet. The most important thing to remember when calculating area is that

All the dimensions must be in the same units.


We talk about the rectangle above having an area of say 8 square meters, but there is a shorthand way of writing it. We write the letter for the unit with a superscript 2 after it, like this:

"8 square meters"   is written as    8 m2
"8 square feet"   is written as    8 ft2

Converting units

There are many units of area. For example, land area is measured in units like acres and hectares. The easiest way to convert from one unit to another is to use the Google search engine. A little-known feature of it is that if you type in a conversion problem into the search box, it converts it for you if it can figure out what you mean.

For example if you type in "300 sq ft in sq m" it will tell you that 300 square feet equals 27.87 square meters.

Areas of plane shapes

For many shapes there are ways to calculate the area - for example the area of a circle. These are listed below with links to pages that explain each in more depth.

See also

Triangle (SAS)
Given 3 sides
See Heron's formula
Equilateral triangle
Rhombus 3 methods
See Area of a rhombus
where D1, D2 are the diagonals.
Regular polygon 4 methods
See Area of a regular polygon
Segment of a circle See
Area of a circle segment.

Areas on the coordinate plane

If you know the x,y coordinates of the vertices of a shape, there are ways to calculate the area from those coordinates. See Polygons on the coordinate plane.