Square footage calculator

What is square footage?

Square footage is a measurement that shows the amount of surface area or shape in two dimensions, typically measured in square feet or square meters. It quantifies how many square units can fully cover a shape. Square footage is essential in construction, design, engineering, and other fields where estimating dimensions and material volumes is crucial.

Main types of shapes for square footage calculation

There are numerous geometric shapes for which square footage needs to be calculated in various contexts. Here are some of them:

Rectangles and squares

A rectangle is a quadrilateral with opposite sides parallel and equal to each other. A square is a special type of rectangle where all sides are equal. Calculating the square footage of rectangles and squares is important due to their widespread application in construction, interior design, and other fields.

Circles and circle sectors

A circle is the set of all points on a plane at a certain distance from a given point called the center. A circle sector is a part of a circle bounded by two radii and an arc. Knowing the square footage of a circle is necessary for various engineering tasks and calculations in room and site design.

Parallelograms

A parallelogram is a quadrilateral with opposite sides parallel. Calculating the square footage of a parallelogram is significant in applications where these shapes are important, such as construction and machine design.

Regular polygons

A polygon is a shape with more than four sides. Examples of these shapes include pentagons, hexagons, etc. Calculating the square footage of regular polygons is crucial for tasks related to complex projects like landscape design and mosaic floors.

Formulas

Square footage of a rectangle and square

For a rectangle:

$$A = a \times b$$

where $A$ is the area, $a$ is the length, and $b$ is the width.

For a square:

$$A = a^2$$

where $s$ is the length of the side of the square.

Square footage of a circle

$$A = \pi r^2$$

where $r$ is the radius of the circle.

Square footage of a circle sector

$$A = \frac{\theta}{360} \times \pi r^2$$

where $\theta$ is the angle of the sector in degrees.

For calculating the area of a circle sector, when the arc length is known, you can use the circle sector area calculator.

Square footage of a triangle

$$A = \frac{1}{2} \times b \times h$$

where $b$ is the base of the triangle, and $h$ is the height.

For calculating the area of a triangle by other parameters, it is better to use the triangle area calculator.

Square footage of a parallelogram

$$A = b \times h$$

where $b$ is the base, and $h$ is the height.

If you need to calculate the area of a parallelogram, knowing the lengths of the sides and the angle between them, you can use the parallelogram area calculator.

Square footage of a regular polygon

$$A = \frac{1}{4} \times n \times s^2 \times \frac{1}{\tan(\frac{180}{n})}$$

where $n$ is the number of sides, and $s$ is the length of a side.

Square footage of an ellipse

$$A = \pi a b$$

where $a$ and $b$ are the semi-axes.

Square footage of a trapezoid

$$A = \frac{1}{2} \times (b_1 + b_2) \times h$$

where $b_1$ and $b_2$ are the lengths of the bases, and $h$ is the height.

Examples

1. Rectangle: For a rectangle with a length of 16.4 ft and a width of 9.8 ft, the area is: $A = 16.4 \times 9.8 = 160.72 \ \text{ft}^2$.

2. Square: For a square with a side of 13.1 ft, the area is: $A = 13.1^2 = 171.61 \ \text{ft}^2$.

3. Circle: For a circle with a radius of 13.1 ft, the area is: $A = \pi \times 13.1^2 \approx 539.05 \ \text{ft}^2$.

4. Triangle: For a triangle with a base of 19.7 ft and a height of 13.1 ft, the area is: $A = \frac{1}{2} \times 19.7 \times 13.1 = 129.035 \ \text{ft}^2$.

5. Parallelogram: For a parallelogram with a base of 26.2 ft and a height of 16.4 ft, the area is: $A = 26.2 \times 16.4 = 429.68 \ \text{ft}^2$.

6. Regular Hexagon: For a regular hexagon with a side of 9.8 ft, the area is: $A = \frac{1}{4} \times 6 \times 9.8^2 \times \frac{1}{\tan(\frac{180}{6})} \approx 249.748 \ \text{ft}^2$.

7. Ellipse: For an ellipse with semi-axes of 16.4 ft and 9.8 ft, the area is: $A = \pi \times 16.4 \times 9.8 \approx 504.799 \ \text{ft}^2$.

8. Trapezoid: For a trapezoid with bases of 32.8 ft and 19.7 ft and a height of 13.1 ft, the area is: $A = \frac{1}{2} \times (32.8 + 19.7) \times 13.1 = 342.255 \ \text{ft}^2$.

Calculating material costs

This calculator can help not only in determining the square footage but also in calculating material costs for projects such as tiling or flooring. For example, for choosing mosaic tiles for a wall with a height of 9.2 ft and a length of 13.1 ft, the square footage is:

$$A = 9.2 \times 13.1 = 120.52 \ \text{ft}^2$$

If the cost per square foot of tiles is approximately $3.7, the total project cost will be:

$$120.52 \times 3.7 = 445.92 \ \text{dollars}$$

Thus, the calculator allows you to quickly assess how much material is needed and what the project cost will be.

Notes

• Remember that the value of $\pi$ is approximately $3.14159$, but for more accurate calculations, use more decimal places.
• The given formula for regular polygons applies if all sides and angles are equal.
• This calculator can also be used to calculate approximate construction costs by adding cost per square foot or total material cost.

FAQs

How can I calculate the square footage of a shape without a calculator when I don’t have all the parameters?

For some shapes, knowing certain parameters such as the length of a side or radius allows you to use known formulas to calculate the square footage. If parameters are unknown, additional geometric methods or measurement tools may be applied.

Why is it important to know the square footage in everyday life?

Knowing the square footage is important in the context of renovation, construction, interior design, and many other cases. It allows you to estimate the amount of materials, define plot boundaries, and accurately determine surface dimensions.

How to use this calculator for three-dimensional objects?

The formulas discussed here apply solely to two-dimensional shapes. Different formulas and methods are used for calculating the volumes of objects. However, without the accuracy of computerized analysis, mathematical preparation for the analysis of 3D objects would go well beyond the scope of this calculator.

How to find the square footage of two walls, one with dimensions of 9.8 ft height and 16.4 ft length and another with dimensions of 13.1 ft height and 19.7 ft length?

For the first wall with a height of 9.8 ft and a length of 16.4 ft, the square footage is:

$$A_1 = 9.8 \times 16.4 = 160.72 \ \text{ft}^2$$

For the second wall with a height of 13.1 ft and a length of 19.7 ft, the square footage is:

$$A_2 = 13.1 \times 19.7 = 258.07 \ \text{ft}^2$$

The total square footage is:

$$A_{\text{total}} = A_1 + A_2 = 160.72 + 258.07 = 418.79 \ \text{ft}^2$$

What unit of measurement is used for square footage?

For square footage, square feet are usually used in the USA, whereas square meters are used in other regions.