# Square meters

A square meter (m^{2}) is a measure of the area of a square with sides of 1 meter.

## What is 1 square meter

1 square meter is the area of a square with a side length of 1 m, as shown in the figure below:

A square area is a measurement made up of two lengths. Square units of area, such as square meters, are a result of multiplying the two lengths. In the case of square meters, each length is measured in meters, so multiplying meters × meters results in meters^{2}.

### How big is a square meter

A square meter is the area formed by a square with side lengths of 1 meter. Below are some examples to help with visualizing how big a square meter is.

- ~5 people can stand in a 1 m
^{2}area - A typical parking space is ~10 m
^{2} - A professional basketball court is 420 m
^{2}

## How to calculate square meters

The most straightforward way to measure square meters is to calculate the length and the width of the area, then multiply them, but this only works if the area is rectangular.

### Multiply length and width

A 4 m × 2 m rectangle has an area of 4 × 2 = 8 m^{2}.

### Break the area down into unit squares

We can easily see why the area of a 4 × 2 rectangle is 8 m^{2} by breaking the rectangle down into unit squares. Since the rectangle in the figure below is made up of 8 squares with an area of 1 m^{2} each, it has an area of 8 m^{2}:

It is possible to estimate the area of any space, even if it is not rectangular, using this method. Simply fill the area with unit squares, and count the number of squares as best you can.

### Measuring non-rectangular rooms

Many spaces are made up of rooms that are either not perfectly rectangular, or are made up of a number of rectangles. If the room is made up of a number of rectangles, calculate the areas of each rectangle separately (using length × width), then find the sum of their areas. This same concept applies to the area of any room; we can find the area by calculating the area of all the individual shapes that make up the room, then find the sum.

Example

Find the area of the following space in square meters.

The area is made up of two rectangular spaces and an area that is half a circle. We will label the green rectangle R_{g}, the red rectangle R_{r}, and the half circle, C. The area of a rectangle is calculated as length × width so the areas of the rectangles are:

The area of a circle is πr^{2}, but since we only want half the area of the circle, we will use the formula πr^{2} ÷ 2:

Thus, summing up all the areas,

The area of the space is 37.534 m^{2}.

## Systems of measurement

A square meter is the base unit of area in the International System of Units (SI), the most widely used system of measurement. Square meters can be converted into larger or smaller measurements of area relatively easily due to the structure of SI, which uses prefixes that indicate a specific power of 10 by which the base unit, in this case the meter, is modified. For example, square centimeters may be used to measure a smaller area. The "centi-" prefix indicates 10^{-2}, so to express an area such as 10 m^{2} in cm^{2} multiply by (10^{2})^{2}, or 10,000. This is because there are 100 centimeters in a meter, and 100^{2} (since we are talking about area not length) is 10,000.

## Convert square meters

To convert from square meters to some other units of area, use the following relationships:

#### Square meter to square feet

square meters × 10.67391 = square feet

#### Square meter to square inch

square meters × 1,550 = square inches

#### Square meters to square centimeters

square meters × 10,000 = square centimeters

#### Square meters to square kilometers

square meters ÷ 1,000,000 = square kilometers

#### Square meters to acres

square meters ÷ 4,046.856 = acres

#### Square meters to square miles

square meters ÷ 2.59 × 10^{6} = square miles

Examples

Convert 57 square meters to square centimeters and square feet.

There are 10,000 cm^{2} in 1 m^{2} and 43,560 ft^{2} in 1 m^{2}, so:

57 × 10,000 = 570,000 cm^{2}

57 × 43,560 = 2,482,920 ft^{2}

It is important to note that when converting SI units of area such as square meters, the linear conversion factor must be squared. For example, there are 100 cm in 1 m, but 100^{2} = 10,000 cm^{2} in 1 m^{2}.

Similarly, when we change the dimensions of an object by some factor, such as halving or doubling the size, this factor must also be squared. For example, the area of a 4 x 4 square is 16 square units. If we double the dimensions of the square, the area of the new square is 64 square units, not 32 square units. Even though we double the dimensions, since we are dealing with area, the increase in area of the square is 2^{2} = 4 such that the new area is 16 × 4 = 64 square units. We can confirm this by actually doubling the dimensions from a 4 × 4 square to an 8 × 8 square and see that 8 × 8 = 64 square units. This is a relatively common trick question!