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How to Calculate Area and Square Footage
The area of a rectangle is length times width. That single formula covers most real-world area problems, from measuring a room for new flooring to figuring out how much paint to buy for a wall. The general formula is:
\[A = l \times w\]A room that measures 12 feet by 15 feet has an area of 12 x 15 = 180 square feet. All area calculations produce a result in square units because you are multiplying two lengths together.
Area formulas for common shapes
Rectangles and squares are the simplest case, but other shapes come up regularly. Each shape has its own formula, and they are all worth knowing.
Rectangle
\[A = l \times w\]Multiply length by width. A rectangular patio that measures 20 feet by 14 feet has an area of 20 x 14 = 280 square feet.
Triangle
\[A = \frac{1}{2} \times b \times h\]The variable b is the base and h is the perpendicular height, measured at a right angle from the base to the opposite vertex. A triangular garden bed with a base of 10 feet and a height of 6 feet has an area of 0.5 x 10 x 6 = 30 square feet. Note that h is always the perpendicular height, not the length of a slanted side.
Circle
\[A = \pi r^2\]The variable r is the radius, which is half the diameter. A circular patio with a diameter of 16 feet has a radius of 8 feet, so its area is 3.14159 x 64 = 201.06 square feet. The area calculator handles circles and other shapes instantly if you want to skip the arithmetic.
Trapezoid
\[A = \frac{(a + b)}{2} \times h\]The variables a and b are the two parallel sides (bases), and h is the perpendicular distance between them. A trapezoidal yard with parallel sides of 30 feet and 20 feet and a height of 12 feet has an area of (30 + 20) / 2 x 12 = 25 x 12 = 300 square feet.
Measuring rooms for square footage
Most rooms are rectangular, so measuring square footage is straightforward. Measure the length and width of the room in feet, then multiply. A bedroom that is 11 feet by 13 feet has an area of 11 x 13 = 143 square feet.
When rooms have closets or alcoves, measure each rectangular section separately and add the results together. A bedroom that is 12 by 14 feet with a 3-by-5-foot closet has a total area of (12 x 14) + (3 x 5) = 168 + 15 = 183 square feet. The room square footage calculator lets you enter multiple sections and sums them automatically.
Always measure to the nearest inch, then convert to decimal feet for the multiplication. Six inches is 0.5 feet, three inches is 0.25 feet, and nine inches is 0.75 feet. A room that measures 11 feet 6 inches by 14 feet 3 inches is 11.5 x 14.25 = 163.88 square feet.
Handling irregular rooms
Rooms with L-shapes, bay windows, or angled walls are not a single rectangle, but they can always be broken down into a combination of rectangles and triangles.
For an L-shaped room, draw an imaginary line that divides the L into two rectangles. Measure each rectangle separately and add the areas. An L-shaped living room might break into one section of 15 x 12 feet and another of 8 x 10 feet, giving a total of 180 + 80 = 260 square feet.
For rooms with an angled wall or a bay window that juts out in a triangle, measure the triangular portion separately using the triangle formula and add it to the rectangular section. The key is to always decompose the shape into pieces you already know how to calculate.
Quick reference table
| Shape | Formula | Example dimensions | Area |
|---|---|---|---|
| Rectangle | l x w | 12 ft x 15 ft | 180 sq ft |
| Square | s x s | 10 ft x 10 ft | 100 sq ft |
| Triangle | (b x h) / 2 | base 8 ft, height 6 ft | 24 sq ft |
| Circle | pi x r squared | radius 7 ft | 153.94 sq ft |
| Trapezoid | ((a + b) / 2) x h | bases 6 ft and 10 ft, height 4 ft | 32 sq ft |
Converting between area units
Area measurements in different units are connected by the square of the linear conversion factor. Because 1 yard equals 3 feet, 1 square yard equals 9 square feet (3 x 3). Because 1 meter equals approximately 3.281 feet, 1 square meter equals approximately 10.764 square feet.
| Conversion | Factor |
|---|---|
| Square feet to square yards | Divide by 9 |
| Square yards to square feet | Multiply by 9 |
| Square feet to square meters | Divide by 10.764 |
| Square meters to square feet | Multiply by 10.764 |
| Square feet to acres | Divide by 43,560 |
A 1,500-square-foot apartment is 1,500 / 9 = 166.67 square yards, or 1,500 / 10.764 = 139.35 square meters. These conversions come up frequently when comparing property listings that use different unit systems.
Area versus perimeter and volume
Area measures the surface inside a two-dimensional shape. It tells you how much material covers a flat surface. Perimeter measures the distance around the outside edge of that same shape. A 12-by-15-foot room has an area of 180 square feet and a perimeter of 54 feet. Area determines how much flooring you need; perimeter determines how much baseboard trim to buy.
Volume extends area into three dimensions. If you know the area of a floor and the height of a space, multiplying them gives you the volume in cubic units. A room with 180 square feet of floor area and 8-foot ceilings has a volume of 1,440 cubic feet. The volume calculator covers common three-dimensional shapes like cylinders, spheres, and cones.