Rectangle Area Calculator

A = l × w

That is the whole formula. Length times width. Rectangles are the workhorse 2D shape: most rooms, most boards, most sheets of paper, most parcels of land.

Where rectangles show up in measurements:

• A 12 ft × 15 ft bedroom has 180 sq ft of floor. One gallon of paint covers about 350 sq ft per coat, so a gallon does that ceiling twice over. The four walls at 9 ft are a different matter: 2(12 + 15) × 9 = 486 sq ft, which needs two gallons per coat.
• A standard 4 ft × 8 ft sheet of plywood is 32 sq ft. A 200 sq ft project needs at least 7 sheets on paper, so buy 8 and expect to use most of it once the offcuts start.
• The US letter page is 8.5 in × 11 in = 93.5 sq in. A4 is 210 mm × 297 mm = 62,370 sq mm, about 96.7 sq in, so A4 is 3% larger in area while being narrower and taller.

Working with rectangles in practice:

Order materials by area, not perimeter, and be careful because the two move independently. A 10 × 10 room and a 5 × 20 room both hold 100 sq ft of floor, yet one needs 40 ft of baseboard and the other 50. Fix the perimeter instead, at 40 ft, and 10 × 10 gives 100 sq ft while 5 × 15 gives only 75. Neither number predicts the other.

For paint: divide the area by the coverage rate on the tin. Two coats doubles it.

For flooring: add 5 to 15 percent waste depending on the material. Tile run diagonally wastes the most, laminate planks the least, and hardwood with random plank lengths usually wants 10 percent.

Worked example: covering a wall

Wall 14 ft wide × 9 ft tall = 126 sq ft. One door takes 21 sq ft (3 ft × 7 ft) and one window takes 12 sq ft (3 ft × 4 ft). Paintable area = 126 − 21 − 12 = 93 sq ft. Two coats = 186 sq ft of coverage needed. A gallon does 350 sq ft, so one gallon is plenty for two coats with leftover for touch-ups.

Aspect ratio matters for some things, not others:

For flooring or paint, only area matters. For carpets and rugs, the room’s proportions decide which sizes work. A 9 × 12 rug leaves a comfortable border in a 14 × 16 room. Put the same rug in a 30 × 10 hallway and it runs almost wall to wall with 6 in each side, which reads as a fitted carpet that came up short.

Diagonal: d = √(l² + w²). Useful for sizing the longest item you can fit on the diagonal, or for checking if a sheet is actually square (diagonals of a true rectangle are equal).