# Square feet

A square foot (ft^{2} or sq. ft.) is a unit of measurement of area. 1 square foot is equal to the area of a square with sides that measure 1 foot.

## What is a square foot

A square foot is a measurement of area used in the US customary system. Square feet are most commonly used in the US as a measurement of a flat space such as a room, the amount of floor space in a house or apartment, farm land, and much more. Often, things like materials, flooring, concrete, and more are sold by the square foot, so having an understanding of square footage and being able to measure it is useful in many real-life scenarios.

A square foot can be thought of as the area made up by some number of unit squares. The actual area being measured does not need to be a square or rectangle; any area can be calculated, or estimated, as the area made up by some number of unit squares.

For example, a 4 ft × 2 ft rectangle is made up of 8 squares with an area of 1 ft^{2} each. The rectangle therefore has an area of 8 ft^{2}:

Essentially, we are just finding the area by using the formula for the area of a rectangle, A = length × width. Since both sides are measured in feet, the units of the area are feet × feet, or square feet.

If we have a triangle or some other shape, we can estimate its area by finding the sum of the unit squares that make up the area. Depending on the shape of the space, we may also be able to break the area up into various common shapes whose area formulas are well known.

## How to calculate square feet

The most straightforward way to calculate the square footage of an area is to measure the length and width of the space in feet, given that it is a rectangle. The square footage of the space is the product of the length and the width. This is of course highly dependent on the shape of the space. Below are some square footage examples for various spaces.

### Square footage of a square

To calculate the square footage of a square, find the product of its two sides,

where s is the length of a side of the square measured in feet:

### Square footage of a rectangle

To calculate the square footage of a rectangle, find the product of its length and width,

where both the length and width are measured in feet.

### Square footage of a rectangular border area

The square footage of a rectangular border area is the difference between the area of the outer rectangle and that of the inner rectangle (measured in feet).

The outer length and width are those of the larger rectangle. The inner length and width are those of the inner rectangle (white). To find the square footage of the border area we subtract the white area from the whole rectangle.

### Square footage of a circle

To calculate the square footage of a circle, use the formula

where the radius is measured in feet.

### Square footage of a ring

To calculate the square footage of a ring (also called an annulus), find the difference between the area of the outer circle and the inner circle using the formula

Example

Find the square footage of the following space.

To find the square footage of the space, we calculate the square footage of each room. The area is made up of mostly rectangles with one semicircle. Two of the rooms are squares of the same size that each have a square footage of:

Since there are two rooms of this size,

The rectangle below the two squares has a length of 11 ft and width of 6 ft, so it has a square footage of:

The largest rectangle has length 18 ft and width 8 ft, so it has a square footage of:

The square footage of the semi circle is half the area of a circle with radius 3, so:

The sum of the square footages of the rooms is:

The square footage of the space is therefore 322.137 ft^{2}.

## Systems of measurement

In the US customary system of units, inches, feet, and yards are some of the primary measurements of length. As such, the primary units of area in the US customary system are square inches, square feet, and square yards. These units are used for measuring smaller to medium sized areas. For example, property area (apartment, condominium, house, etc.) in the US is most commonly measured using square feet. For significantly larger measurements of area, the US also uses acres, or even square miles.

Outside of the US, most countries use the International System of Units (SI). The standard unit of length in SI is the meter (or metre), so the standard unit of area is square meters (m^{2}). While some countries may use other measurements of area (including square feet, also usually for measuring property area), most use square meters. As such, it is important to be able to convert between US customary and SI units of area, the two most widely used systems of measurement around the world.

Below are the relationships between square feet and some other measurements of area.

### Square feet to square inches

To convert square feet to square inches, multiply ft^{2} by 144 to get in^{2}.

### Square feet to square yards

To convert square feet to square yards, multiply ft^{2} by 0.11111 to get yd^{2}.

### Square feet to square meters

To convert square feet to square meters, multiply ft^{2} by 0.092903 to get m^{2}.

### Square feet to acres

To convert square feet to acres, multiply ft^{2} by 0.00002295684 to get ac^{2}.

Note that for units in the US customary system, if you know the relationships between inches, feet, and yards, you can determine the relationships between square inches, square feet, and square yards by squaring the units. Since there are 12 inches in 1 foot, there are 144 inches in 1 square foot. Similarly, there are 3 feet in a yard, so there are 9 square feet in 1 square yard.

Examples

Convert the following areas between square feet and square meters.

1. 3,560 ft^{2}:

3,560 ÷ 10.764 = 330.732 m^{2}

2. 4459.346 m^{2}:

4459.346 × 10.764 = 48,000.4 ft^{2}