Area Calculator
Pick a shape, put in its dimensions, and this gives the area in square feet, metres and yards, along with the formula it used.
Area
120.00sq ft
- Square feet
- 120.00
- Square metres
- 11.15
- Square yards
- 13.33
- Formula
- length × width
- For a shape that is not one of these, split it into rectangles and triangles, work out each one, and add them together.
About the area calculator
Area is how much surface a shape covers, measured in square units. Three shapes cover the overwhelming majority of real questions — rectangles for rooms and plots, circles for anything round, triangles for gables and corners — and anything more complicated can usually be cut into some combination of them.
That cutting-up is the practical technique worth knowing. An L-shaped room is two rectangles. A room with a bay window is a rectangle plus a partial circle or a trapezoid. Work each piece out separately and add them together; the arithmetic stays simple no matter how awkward the outline.
Units matter more here than in linear measurement, because squaring squares the conversion factor too. A square yard is nine square feet, not three — a mistake that turns a flooring order into an expensive surprise. This shows the result in several units at once so the comparison is in front of you.
What it works out
- Rectangles, circles and triangles
- Square feet, metres and yards at once
- The formula used, shown explicitly
- Circumference and diameter for circles
The formula
Rectangle: l × w Circle: π × r² Triangle: ½ × b × h
A rectangle is length times width, and a square is the case where they are equal. This is the one everyone knows, and it is the building block for everything else — the other formulas are essentially statements about how a shape compares to the rectangle around it.
A circle is pi times the radius squared. The radius is half the diameter, and using the diameter by mistake gives an answer four times too large, which is the most common error on this shape. Pi is about 3.14159 and is not a round number in any base, which is why circle areas rarely come out neat.
A triangle is half the base times the perpendicular height — the straight-line distance from the base to the opposite point, not the length of a sloping side. Any triangle is exactly half of the rectangle that encloses it on the same base and height, which is where the half comes from.
For anything else, divide and conquer. Almost any outline can be split into rectangles and triangles, and adding their areas gives the total. For curved edges that are not circular, splitting into thin strips and adding those gets you as close as you need.
- l and w
- Length and width of a rectangle.
- r
- The radius of a circle — half the distance across it.
- b and h
- The base of a triangle and its perpendicular height above that base.
- π
- About 3.14159.
A worked example
A twelve by ten foot rectangle.
That works out to 120.00 sq ft.
- Square feet
- 120.00
- Square metres
- 11.15
- Square yards
- 13.33
- Formula
- length × width
Questions
How do I work out the area of a room?
Length times width for a rectangular room. For an irregular shape, split it into rectangles, work each out separately and add them together.
How many square feet in a square yard?
Nine. Squaring squares the conversion, so although a yard is three feet, a square yard is three times three square feet. Getting this wrong is a classic way to under-order flooring by a factor of three.
What is the area of a circle?
Pi times the radius squared. For a circle 10 feet across the radius is 5, so the area is 3.14159 × 25, which is about 78.5 square feet.
Do I use radius or diameter for a circle?
Radius — half the width across. Using the diameter gives an answer four times too big, because the formula squares whichever you put in.
What height do I use for a triangle?
The perpendicular height: the straight-line distance from the base to the opposite corner, measured at a right angle. Not the length of a sloping side, which is longer and gives too large an answer.
How do I find the area of an L-shaped room?
Split it into two rectangles along the inside corner, work out each one, and add them. The same approach handles almost any shape made of straight lines.