Square Footage Calculator
This calculator estimates the square footage of common shapes, including squares, rectangles, rectangular borders, rectangles with a cut-out, circles, annuli, triangles, trapezoids, ellipses, sectors, caps, and regular polygons with a specified number of sides. It can also be used to estimate cost based on the square footage and quantity of shapes that comprise the space. To use the calculator, please select the shape, provide the dimension values, and click the "Calculate" button.
How to calculate square footage of common shapes?
To calculate the square footage of common shapes, determine the area of the given shape, then multiply the area by the number of shapes that make up the space. The area formulas for common shapes are shown below.
Square
The area of a square is the product of its edges, or:
area = edge2
Given a square with an edge length of 3 feet, the area of the square is:
area = 32 = 9 ft2
If a space is made up of 50 of these squares, the square footage of the space is:
9 × 50 = 450 ft2
Rectangle
The area of a rectangle is the product of its two sides of different lengths, or:
area = length × width
Given a rectangle with a length of 7.5 ft and width of 4 ft, the area of the rectangle is:
area = 7.5 × 4 = 30 ft2
If the space is made up of 20 of these rectangles, the square footage of the space is:
30 × 20 = 600 ft2
Circle
The area of a circle is:
area = πr2
where, π is a constant approximately equal to 3.141593 and r is the radius of the circle. Given a radius of 12 yards, the area of the circle is:
area = π(12)2 = 452.389 yd2
Given that a space is made up of 50 of these circles, the area of the space is:
452.389 × 50 = 22619.45 yd2
Triangle
The area of a triangle is:
| area = |
| bh |
where b is its base and h is its height. Given a triangle with a base of 12 in and a height of 7 in, its area is:
| area = |
| × 12 × 7 = 42 in2 |
If a space is made up of 20 of these triangles, the area of the space is:
42 × 20 = 840 in2
Trapezoid
The area of a trapezoid is:
| area = |
| h(b1 + b2) |
where h is height, b1 is base 1, and b2 is base 2. Given a trapezoid with a height of 5 in and base lengths of 3 in and 2 in, the area of the trapezoid is:
| area = |
| × 5(3 + 2) = 12.5 in2 |
If a space is made up of 20 of these trapezoids, the area of the space is:
12.5 × 20 = 250 in2
Ellipse
The area of an ellipse is:
area = πab
where a is the length of axis a and b is the length of axis b. Given an ellipse that has axis a length of 3 cm and axis b length of 2 cm, the area of the ellipse is:
area = π(3)(2) = 18.8496 cm2
If a space is made up of 30 of these ellipses, the area of the space is:
18.8496 × 30 = 565.488 cm2
Sector
The area of a sector of a circle has different formulas depending on whether the angle is in degrees or radians:
| area (degrees) = |
| πr2 |
| area (radians) = |
| r2 θ |
where r is radius and θ is the sector angle subtended by the arc at the center, as shown in the figure above. Given a sector with radius 12 m and θ = 90°, the area of the sector is:
| area = |
| π(12)2 = 113.09734 m2 |
If a space is made up of 33 of these sectors, the area of the space is:
113.09734 × 33 = 3732.21222 m2
Regular polygon
The area of a regular polygon is dependent on the number of sides in the polygon:
| area = |
|
where n is the number of sides and a is the length of the side. Given a regular 6-sided polygon (hexagon) with side length of 4 ft, the area is:
| area = |
| = 41.5692 ft2 |
If a space is made up of 22 of these shapes, the square footage of the space is:
41.5692 × 22 = 914.5228 ft2
How to calculate square footage of more complex shapes?
More complex shapes do not always have a formula for area calculation. However, many of the times, the area of a complex shape can be calculated by the combination or subtraction of two or more simple shapes. The following are some of such complex shapes.
Rectangular border
The area of a rectangular border is the area of the outer rectangle minus the area of the inner rectangle:
area = lowo - liwi
where lo and wo are the length and width of the outer rectangle and li and wi are the length and width of the inner rectangle. Given an outer length and width of 7 ft and 3 ft respectively, and an inner length and width of 3 ft and 1.5 ft respectively, the area of the rectangular border is:
area = (7)(3) - (3)(1.5) = 16.5 ft2
If a space is made up of 15 of these shapes, the square footage of the space is:
16.5 × 15 = 247.5 ft2
Rectangle with cut-out
The area of a rectangle with a cut-out can be calculated by breaking the larger shape into smaller rectangles using the lengths and widths as specified above.
area = l1(w1 + w2) + l2w1
or
area = w1(l1 + l2) + l1w2
Given l1 = 14 m, w1 = 13 m, l2 = 27 m, and w2 = 6 m, the area of a rectangle with a cut-out is:
area = 14(13 + 6) + 27(13) = 617 m2
Given that a space is made up of 15 of these shapes, the area of the area is:
617 × 15 = 9255 m2
Annulus
The area of an annulus is the area of the outer circle minus the area of the inner circle. Given that the radius of the outer circle is R and the radius of the inner circle is r, the area of an annulus is:
area = π(R2 - r2)
Given that the radius of the outer circle is 15 ft and the radius of the inner circle is 9 ft, the area of the annulus is:
area = π(152 - 92) = 452.3893 ft2
If a space is made up of 35 of these annuli, the square footage of the space is:
452.3893 × 35 = 15833.6255 ft2
Cap
The area of a cap is the area of the sector minus the area of the triangle. Given that the base length of the cap is b, the height of the cap is h.
cap area = sector area - triangle area
where
| sector radius, r = |
| + |
|
| sector area = r2 × asin( |
| ) |
| triangle area = |
|
Given that the cap has a base of 5 ft and height of 2 ft, the area of the cap is: 7.455 ft2
If a space is made up of 35 of these caps, the square footage of the area will be:
7.455 × 35 = 260.925 ft2