Square Inches and Square Feet Converter

Square Inches and Square Feet Converter

This converter allows for conversion between two commonly used units of area within the imperial system, namely the square inch or the square foot.

Start by choosing between the American or British spelling of the text on the site.

Next, choose your input value in the ‘CONVERT FROM’ section. The choice can be made out of two options, either square inches (in²) or square feet (ft²).

The output value can be selected in the ‘CONVERT TO’ section, out of the same two options.

An alternative way to select the input and output units is to just keep the pre-selected options or to use the icon with the two arrows in opposite directions, which allows you to swap the input and output units.

If you are happy with your choice of units, move toward the ‘VALUE TO CONVERT’ part of the converter and enter your input value as a decimal number.

The final choice lies in choosing the number of decimal places you would like your result rounded toward. After that, click on the ‘CONVERT’ button and you will receive your result in the output value of your choice, rounded to the desired number of decimal places.

Additionally, you will also receive the conversion rate between the two converted units and an option to easily copy your result by using the ‘COPY’ icon next to it.

Converting Square Inches and Square Feet Manually

Both of the units belong to the imperial system, which makes the relationship between them, and hence the conversion rates, quite neat.

A square unit is always defined as the area of a square with a side length of 1 measure of said unit.

That means that a square inch is equivalent in area to a square with a side length of 1 inch, while a square foot is equivalent in area to a square with a side length of 1 foot.

This definition helps us find the conversion rates, as we know that the relationship between the units of length is that 1 foot is equivalent to 12 inches, while 1 inch is equivalent to about 0.083 feet.

If we square these relationships, we work with the fact that 1² is still equal to 1.

This will help us find the squared values of the units of length, leading to the conversion rates of the units of area.

We start by squaring the relationship of 1 ft = 12 in. We get 1 ft² = 12² in² = 144 in².

Squaring the second relationship of 1 in = 0.083 ft will yield 1 in² = 0.083² ft² = 0.0069 ft², rounded to 4 decimal places.

We can now derive 2 formulae.

in^2 = ft^2 * 144

ft^2 = in^2 * 0.0069

Applying the formulae manually is demonstrated in the two examples below.

EXAMPLE 1: A sheet of paper has an area of exactly 2.25 ft². What is the area of this sheet of paper in square inches?

We will apply the first formula, as our output is in in², which is the subject of the said formula. We substitute 2.25 for ft² and calculate the equivalent number of in².

in^2 = ft^2 * 144 \\= 2.25 * 144 \\= 324 ~in^2.

EXAMPLE 2: A coffee table has an area of 400 in². What is the area of that table in ft²?

We will use the second formula, where we substitute 400 for in². This will lead to a simple calculation of an equivalent value in ft².

ft^2 = in^2 * 0.0069 \\= 400 * 0.0069 \\= 2.76 ~ft^2.

How to Convert Square Inches to Square Feet More Accurately

Based on the guide before, we might notice that there is a quicker way to convert the units. We see that the conversion rate asks us to multiply by 144 when converting from ft² to in². However, the approximate number 0.0069 is not the easiest to remember, while also being a rounded version of the real conversion rate.

We know that this number comes from the reverse operation, where we divided 1 by 144. Hence, an easier solution might be to simply operate using this concept and change the formula to the following one.

ft^2 = in^2 \div 144

As an example, solving the conversion from EXAMPLE 2 would lead to 400 ÷ 144 = 2.78 ft².

The result itself is rounded to two decimal places, however, it is a more accurate result, as working with 0.0069 leads to further inaccuracies.

Whenever is the conversion rate defined by whole numbers, the division is a better option, as it will yield more accurate results. 

How Big is a Square Inch?

To get a perception of the size of a square inch, you can have a look at the list below, with some everyday items and their usual areas in in².