Math
Area Calculator
Area and perimeter of eleven shapes, from a room to a circle, in square feet or metric
Pick a shape, choose your unit and type the measurements: this area calculator gives you the area, the perimeter and the square feet instantly, with a drawing of what to measure and the formula we used. It works for rooms, L-shaped floors, yards, circles and ovals.
The key idea
Area is not another perimeter: they grow at different rates
If you double the side of a square, the perimeter doubles, but the area grows 4 times. A 5 ft square has a 20 ft perimeter and 25 sq ft of area; a 10 ft square has 40 ft and 100 sq ft. That is why area comes in square units and cannot be compared with perimeter.
How it is calculated
Pick the shape that looks like yours: the drawing shows which measurement goes in each box. These are the formulas the calculator uses:
- Square and rectangle: A = s² and A = l × w. This is the square footage of most rooms.
- L-shaped room: the full rectangle minus the missing corner, A = a × b − c × d. Its perimeter is the same as the full rectangle's, 2(a + b).
- Triangle: A = b × h / 2 with base and height, or Heron's formula, A = √(s(s − a)(s − b)(s − c)), with the three sides (s is half the perimeter).
- Circle and sector: A = πr², and a slice of θ degrees is that area × θ / 360.
- Ellipse: A = π × a × b, with the two semi-axes (half the long and half the short width). Its perimeter has no exact simple formula: we use Ramanujan's approximation, off by far less than 0.1%.
- Parallelogram: A = b × h, with the height measured straight up, not along the slanted side. Trapezoid: A = (a + b) / 2 × h, with the two parallel sides. Rhombus: A = p × q / 2, with the two diagonals.
Area comes in square units (sq in, sq ft, m²…) and perimeter in the same unit as your measurements. To get square feet we use the exact definition 1 ft = 0.3048 m, so 1 sq ft = 0.09290304 m², 1 sq yd = 9 sq ft and 1 acre = 43,560 sq ft. For the trapezoid perimeter we assume it is isosceles.
How to measure a room: measure wall to wall at floor level, in feet and inches, and turn the inches into feet by dividing by 12 (10 ft 6 in = 10.5 ft). If the room has a closet or a nook, add it as a separate rectangle; for flooring, buy 5 to 10% more for cuts.
Worked example
A 12 × 10 ft room: area = 12 × 10 = 120 sq ft (13.33 sq yd or 11.15 m²) and perimeter = 2 × (12 + 10) = 44 ft. A circle with a 5 ft radius has 78.5398 sq ft of area (about 78.54) and a 31.4159 ft circumference.
Official sources
- NIST Office of Weights and Measures: unit conversion · foot and square foot
Typical cases
Square footage of common room sizes
The area of a rectangular room is its length times its width. These are the sizes you see most in floor plans, for flooring, paint or rent per square foot.
| Room size (ft) | Square feet | Square yards | Square meters | Perimeter |
|---|---|---|---|---|
| 8 × 10 | 80 sq ft | 8.89 sq yd | 7.43 m² | 36 ft |
| 10 × 10 | 100 sq ft | 11.11 sq yd | 9.29 m² | 40 ft |
| 10 × 12 | 120 sq ft | 13.33 sq yd | 11.15 m² | 44 ft |
| 11 × 12 | 132 sq ft | 14.67 sq yd | 12.26 m² | 46 ft |
| 12 × 12 | 144 sq ft | 16.00 sq yd | 13.38 m² | 48 ft |
| 12 × 14 | 168 sq ft | 18.67 sq yd | 15.61 m² | 52 ft |
| 12 × 16 | 192 sq ft | 21.33 sq yd | 17.84 m² | 56 ft |
| 14 × 16 | 224 sq ft | 24.89 sq yd | 20.81 m² | 60 ft |
| 15 × 20 | 300 sq ft | 33.33 sq yd | 27.87 m² | 70 ft |
| 16 × 20 | 320 sq ft | 35.56 sq yd | 29.73 m² | 72 ft |
| 20 × 20 | 400 sq ft | 44.44 sq yd | 37.16 m² | 80 ft |
| 20 × 24 | 480 sq ft | 53.33 sq yd | 44.59 m² | 88 ft |
Save or share this table as an image Typical cases
Area unit conversions: square feet, square meters and acres
How many square feet, square meters and acres are in each area unit, to go from one to another.
| Unit | Square feet | Square meters | Acres |
|---|---|---|---|
| 1 square inch | 0.006944 | 0.0006452 | 0.0000001594 |
| 1 square foot | 1 | 0.0929 | 0.00002296 |
| 1 square yard | 9 | 0.8361 | 0.0002066 |
| 1 square meter | 10.7639 | 1 | 0.0002471 |
| 1 acre | 43,560 | 4,047 | 1 |
| 1 hectare | 107,639 | 10,000 | 2.4711 |
| 1 square mile | 27,878,400 | 2,589,988 | 640 |
Save or share this table as an image Common questions
Frequently asked questions
How do I find the square footage of an L-shaped room?
Measure it as a full rectangle and subtract the missing corner, or split it into two rectangles and add them. For example, 12 × 10 ft plus 6 × 5 ft is 120 + 30 = 150 sq ft. Choose “L-shape” and the calculator does it for you.
How do I find the area of a triangle?
Multiply the base by the height and divide by 2. If you only know the three sides, use Heron's formula, which is what this calculator applies: with sides 3, 4 and 5, the area is 6.
How do I convert square inches to square feet?
Divide by 144, because 1 sq ft is 12 in × 12 in. To go from square feet to square yards, divide by 9.
How many square feet are in an acre?
43,560 square feet, so an acre is about 208.7 × 208.7 ft. A hectare is 10,000 m², about 2.471 acres, and a square mile is 640 acres.
What is the difference between a circle's area and its circumference?
The circumference is the length of the edge, and the area is the surface inside it. So you get the area with πr² and the circumference with 2πr.
How many square feet are in a square meter?
About 10.764 sq ft, because 1 sq ft is exactly 0.09290304 m². Choose meters as the unit and the calculator shows the square feet too.
Geometry and conversions
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