How rectangle area and perimeter are calculated
Every measurement of a rectangle follows from its length and width.
A = l × w · P = 2 × (l + w) · d = √(l² + w²)
- Area is length times width, in square units.
- Perimeter is the distance around: two lengths plus two widths, or 2 × (l + w).
- The diagonal comes from Pythagoras: √(l² + w²).
- Missing the width? From area, w = A ÷ l. From perimeter, w = P ÷ 2 − l. From the diagonal, w = √(d² − l²).
- To convert area, 1 m² is 10.7639 ft², and 1 ft² is 0.0929 m².
Worked example — A room 4 m long and 3 m wide: A = 4 × 3 = 12 m², P = 2 × (4 + 3) = 14 m and the diagonal is √(16 + 9) = 5 m. That is about 129.17 ft².
Common rectangle sizes
| Length | Width | Measured in | Area | Perimeter |
|---|---|---|---|---|
| 4 m | 3 m | Metres | 12 m² | 14 m |
| 5 m | 4 m | Metres | 20 m² | 18 m |
| 10 cm | 2 cm | Centimetres | 20 cm² | 24 cm |
| 12 ft | 9 ft | Feet | 108 ft² | 42 ft |
| 1.2 m | 0.6 m | Metres | 0.72 m² | 3.6 m |
| 20 m | 10 m | Metres | 200 m² | 60 m |
Swipe the table sideways to see the rest.
Length by width. Each row is worked out by this calculator.
Things to consider
- Measure rooms wall to wall at floor level, and round up when buying flooring.
- Add 5 to 10% to flooring and tile orders for cuts and waste.
- For an L-shaped room, split it into two rectangles and add the areas.
- The diagonal is a quick way to check a corner is square: 3, 4, 5 is the classic test.
Frequently asked questions
What is the formula for the area of a rectangle?
Area = length × width. A 4 m by 3 m rectangle has an area of 12 m².
What is the formula for the perimeter of a rectangle?
Perimeter = 2 × (length + width). A 4 m by 3 m rectangle has a perimeter of 14 m.
How do I find the width from the area and length?
Divide the area by the length. An area of 12 m² with a length of 4 m gives a width of 3 m.
How do I find the diagonal of a rectangle?
Use Pythagoras: d = √(length² + width²). For 4 by 3, √(16 + 9) = 5.
How do I work out the area of a room in square metres?
Measure the length and width in metres and multiply. A 5 m by 4 m bedroom is 20 m², about 215.28 ft².
Is a square a rectangle?
Yes. A square is a rectangle whose length and width are equal, so the same formulas work.
Results are estimates for general information only, not financial, medical or professional advice.