What is the area of a rectangle?
A rectangle is a four-sided shape with four right angles where opposite sides are equal in length. The two horizontal sides have the same "length"; the two vertical sides have the same "width." Almost every flat surface you measure in everyday life — rooms, paper, screens, walls, tables — is rectangular, which is why this is the most-used area formula in the world.
The area of a rectangle is given by:
A = length × width
Both sides must be in the same units. If length is in feet and width is in feet, the area comes out in square feet (ft²). The "squared" unit reflects the geometric meaning: area is measured in unit squares, and a rectangle of l × w fits exactly l × w of those unit squares inside it.
How to use the rectangle area calculator
- Enter the length in the first field — for example, 10.
- Enter the width in the second field — for example, 6.
- The area appears instantly: 10 × 6 = 60.
- Below the area, you also get the perimeter (2 × (l + w) = 32) and the diagonal (√(100 + 36) ≈ 11.66).
- If length equals width, the calculator notes that you've actually entered a square.
It doesn't matter which value you put in length vs width — multiplication is commutative, so 10 × 6 and 6 × 10 give the same area.
Worked examples
Example 1 — US letter paper (8.5 × 11 in)
A = 8.5 × 11 = 93.5 in². Perimeter = 2(8.5 + 11) = 39 in. Diagonal = √(72.25 + 121) ≈ 13.9 in. Standard US letter paper has nearly 94 square inches of writing surface, which works out to about 603 cm² (594 if you use exact A4-style 8.27 × 11.69 measurements; "letter" is slightly different from A4).
Example 2 — A4 paper (21 × 29.7 cm)
A = 21 × 29.7 = 623.7 cm². Perimeter ≈ 101.4 cm. Diagonal ≈ 36.4 cm. A4 is the international standard outside the US — it's slightly taller and narrower than letter, with the special property that folding it in half gives you exactly an A5 sheet (also half the area). The aspect ratio is √2 ≈ 1.414, which is what makes the half-fold property work.
Example 3 — Plywood sheet (4 × 8 ft)
A = 4 × 8 = 32 ft². Perimeter = 24 ft. Diagonal = √(16 + 64) ≈ 8.94 ft. The standard 4×8 plywood sheet is the construction industry's reference dimension — it's why doors are typically 6'8" or 7' tall (so they cut from one sheet), why ceiling tiles are 4 ft × 2 ft (two fit on a sheet), and why most building frames work in 4-ft modules.
Example 4 — Standard interior door (1.83 × 0.91 m)
A = 1.83 × 0.91 ≈ 1.67 m². Perimeter = 5.48 m. Diagonal ≈ 2.04 m. A typical interior door is roughly 6 feet tall by 3 feet wide. The diagonal tells you the largest object that can pass through — anything longer than 2.04 m (about 6'8") needs to come in at an angle or via a different door.
Perimeter and diagonal — the two extras the calculator gives you
Perimeter: the distance around the outside
P = 2 × (length + width)
Perimeter is what you'd measure if you walked around the rectangle's edges. For a 10 × 6 rectangle: P = 2 × 16 = 32. You need this for fencing, baseboards, picture frames, decorative trim — anything that runs around the outside of a rectangular shape. It's also what you need to know when buying weather stripping for a door or LED strip lighting for a sign.
Diagonal: corner to corner
d = √(length² + width²)
The diagonal is the straight-line distance from one corner to the opposite corner, computed via the Pythagorean theorem (the rectangle splits into two right triangles, and the diagonal is the hypotenuse). For 10 × 6: d = √(100 + 36) ≈ 11.66.
Diagonals matter for screens (TVs, monitors, phones are all measured by their diagonal — a "55-inch TV" has a 55-inch diagonal), for moving large objects through doorways, and for checking whether an item will fit in a rectangular box.
When length equals width: it's a square
A square is a special rectangle where length and width are the same. If you enter equal values in the calculator, it'll note this. The formulas all work — they just simplify:
- Area: A = s² (instead of l × w, with both equal to s)
- Perimeter: P = 4s (instead of 2(l + w) = 2 × 2s)
- Diagonal: d = s√2 (instead of √(s² + s²))
So the rectangle calculator is also a square calculator — just enter the same value for both dimensions.
Real-world use cases
Rooms and flooring
Measuring a room's floor area to know how much flooring (tile, hardwood, carpet) to buy. A 12 × 14 ft room is 168 ft² — order at least 10% extra to allow for cuts and waste, so plan on 185 ft² of material. Most flooring is sold by the box, in increments matched to common room sizes.
Painting walls
For painting, calculate each wall's area: wall length × ceiling height. A typical 12 × 14 ft room with 8 ft ceilings has 4 walls totaling (12+12+14+14) × 8 = 416 ft². Subtract for doors and windows. One gallon of paint covers about 350 ft², so you need 2 gallons for one coat — or 4 if you do two coats (which most paints recommend).
Yards and lawns
Lawn fertilizer, weed killer, and grass seed are sold by the area they cover. A 50 × 80 ft backyard is 4000 ft² — about 0.09 acres. Most "covers 5000 sq ft" bags will do the whole yard with a little extra.
Tablecloths and fabric
Buying a tablecloth requires the table's area plus an overhang. A 6 ft × 3 ft table with a 12-inch (1 ft) drop on each side needs an 8 × 5 ft tablecloth (40 ft²). The math is just adding twice the drop to each dimension.
Garden beds
Mulch, compost, and topsoil are sold by the cubic yard or cubic foot, but you start with the bed's area. A 10 × 4 ft garden bed has 40 ft² of surface area; if you want 3 inches (0.25 ft) of mulch, that's 40 × 0.25 = 10 ft³ of mulch — about a third of a cubic yard.
Common mistakes
- Mixing units. Length in inches × width in feet gives nonsense. Convert one of them first.
- Confusing area with perimeter. Area is what's INSIDE the rectangle (in squared units); perimeter is the distance AROUND it (in linear units). They're entirely different quantities.
- Forgetting to "square" the units. 10 ft × 6 ft is 60 ft², not 60 ft. Area always carries squared units.
- Trying to use diagonal as a side length. The diagonal is a derived measurement — you can't use it as one of l or w in the area formula.
- Assuming all four-sided shapes are rectangles. A rectangle has four right angles. A parallelogram or rhombus does not (unless it's also a rectangle/square). The l × w formula only works for actual rectangles.
What the calculator gives you, summarized
- Area — A = l × w, the interior surface in square units.
- Perimeter — P = 2(l + w), the total distance around the outside.
- Diagonal — d = √(l² + w²), corner-to-corner distance through the interior.
- Square detection — when l = w, the calculator notes that you've entered a square (where the same formulas simplify nicely).
Two inputs, three outputs — and the most-used geometry formula in everyday life.