Area formulas for common shapes
Area measures the flat space inside a shape and is expressed in square units. Each shape has its own formula. A rectangle is length × width, so a 16 by 12 foot room is 192 square feet. A circle is π × radius², so a circular patio with a 6-foot radius covers about 113.1 square feet. A triangle is half the base times the height, measured at right angles to the base, so a triangle with a 10-foot base and 8-foot height is 40 square feet. A trapezoid, a shape with two parallel sides, is the average of the parallel sides times the height between them. An ellipse is π × a × b, where a and b are the two semi-axes, half the longest and shortest widths.
Converting between square units
Square units do not convert like ordinary lengths, because both dimensions change. There are 3 feet in a yard but 9 square feet in a square yard. One meter is 3.28 feet, but one square meter is about 10.76 square feet. This calculator converts your result into square feet, square meters, square yards and acres automatically. For land, one acre is 43,560 square feet, about 4,047 square meters, and one hectare is 10,000 square meters, about 2.47 acres. Carpet is often sold by the square yard in the US, while flooring and paint coverage are usually quoted per square foot or square meter.
Measuring irregular spaces
Real rooms and yards are rarely perfect rectangles. The easiest approach is to split the space into simple shapes, find the area of each, and add them together. An L-shaped room is two rectangles. A room with a bay window is a rectangle plus a trapezoid. A garden bed with a rounded end is a rectangle plus half a circle, so calculate the circle and divide by two. If you need to remove an area, such as a kitchen island from a flooring estimate, calculate it separately and subtract. Sketching the space on paper and labeling each measurement helps avoid mistakes.
Tips for accurate measurements
Use a tape measure or laser measure and record measurements to the nearest inch or centimeter. Measure each wall rather than assuming opposite walls are equal, since older buildings are often slightly out of square. Convert feet and inches to decimal feet before entering them: 12 feet 6 inches is 12.5 feet, and 3 inches is 0.25 feet. When buying materials, always add a waste allowance, typically 5% to 15% depending on the material and the number of cuts. Our square footage calculator adds waste for you and can total several rooms, and the paint and concrete calculators turn areas into quantities to buy.
Frequently asked questions
How do I calculate the area of a room?
Multiply the length by the width. For L-shaped rooms, split them into rectangles and add the areas.
How do I find the area of a circle?
Multiply π (about 3.1416) by the radius squared. The radius is half the diameter.
How many square feet are in a square meter?
About 10.764 square feet.
How many square feet are in an acre?
43,560 square feet.