A rectangle is the most common shape you measure in real life: a room, a garden bed, a rug, a countertop, a photo frame, a parcel of land. Finding its area takes one multiplication — length times width — yet people still guess, double-count, or forget to convert feet-and-inches before buying carpet, tile, or paint. This rectangle area calculator does the math instantly and also gives you the perimeter and the diagonal, so every dimension you need for ordering material is on one card.
Type your length and width, pick the length unit they are measured in (feet, inches, centimeters, or meters), and the result updates as you type. The engine converts both sides to feet internally, then reports both the converted numbers (area in ft², perimeter in ft, diagonal in ft) and the same results in your chosen unit — so a 12-inch-by-10-inch rectangle shows up as 0.83 ft² on the converted lines and 120 in² on the selected-unit lines. That way you never have to mentally back-convert the answer to the unit your blueprint or tape measure is marked in.
How to Use
- Enter the Length of the rectangle — the long side. Measure it end to end with a tape rule.
- Enter the Width — the short side. Both sides must be in the same unit before you compute.
- Pick the Length Unit for length and width: feet (ft), inches (in), centimeters (cm), or meters (m). The engine applies 1 in = 1/12 ft, 1 cm = 0.0328084 ft, and 1 m = 3.28084 ft.
- Read the Area (ft²) result on the highlighted line — the square footage the rectangle covers. Just below it, Area (in your chosen unit²) gives the same value in inches, centimeters, or meters squared, whichever unit you picked.
- Use the Perimeter (ft) line when you need the total distance around the edge — for baseboards, fencing, trim, or a picture frame. The paired Perimeter (in your chosen unit) line shows the same length in your measured unit.
- Use the Diagonal (ft) line when you need the corner-to-corner distance — for checking that a frame or a room is truly square, or for ordering a diagonal brace. The paired Diagonal (in your chosen unit) line mirrors it.
- If your dimensions are mixed (say, 12 ft 6 in by 10 ft 3 in), convert first: 12 ft 6 in is 12.5 ft and 10 ft 3 in is 10.25 ft, then enter those decimals with the unit set to feet.
The engine applies the three standard rectangle formulas: area = length × width, perimeter = 2 × (length + width), and diagonal = √(length² + width²). It rejects negative inputs outright, because a side length below zero has no physical meaning.
The Rectangle Formulas, Explained
The area of a rectangle is the number of unit squares that fit inside it. If you can tile a 12-by-10 floor with 1-foot squares, you fit 12 rows of 10, which is 120 squares — hence A = l × w. This is the formula Euclid recorded over two thousand years ago, and it has not changed.
The perimeter is the distance around the outside. A rectangle has two lengths and two widths, so P = 2l + 2w = 2(l + w). Walk once around a 12-by-10 room and you have walked 44 feet.
The diagonal splits the rectangle into two identical right triangles, so the Pythagorean theorem applies: d = √(l² + w²). For a 12-by-10 rectangle the diagonal is √(144 + 100) = √244 ≈ 15.62 ft. Builders use this to check square corners: if the two diagonals of a foundation are equal, the corners are 90 degrees.
When to Multiply, When to Add
The single most common mistake is buying material by the perimeter when the job is priced by the area (or vice versa). Carpet, tile, hardwood, sod, paint, and concrete are all quoted per square foot or per square yard — use the area number. Baseboards, fence posts, picture-frame moulding, and lawn edging are quoted by the linear foot — use the perimeter number. Ordering by the wrong number is how contractors end up 30% short or 30% over.
A few practical conversions worth remembering:
- 1 square yard = 9 square feet. Carpet is sold by the square yard; divide your square footage by 9 to get the yardage.
- 1 acre = 43,560 square feet. A 100-by-200-foot lot is 20,000 sq ft, roughly half an acre.
- 1 square meter ≈ 10.764 square feet. Multiply a metric plan by 10.764 to convert into US units.
- Paint coverage is about 350–400 square feet per gallon. Divide your wall area by 350 to estimate gallons, and remember most walls need two coats.
Examples
Example 1 — The default room (12 ft × 10 ft). A rectangular bedroom measures 12 feet long and 10 feet wide. The area is 12 × 10 = 120 square feet, the perimeter is 2 × (12 + 10) = 44 feet, and the diagonal is √244 ≈ 15.62 feet. If mid-range carpet costs $4.50 per square foot installed, the carpet alone is 120 × $4.50 = $540, plus roughly 44 linear feet of baseboard.
Example 2 — A fractional kitchen (12.5 ft × 10.25 ft). You measure a kitchen as 12 ft 6 in by 10 ft 3 in. Converting to decimals gives 12.5 and 10.25. The area is 12.5 × 10.25 = 128.13 square feet. Vinyl plank priced at $3.99 per square foot comes to about $511 for the material, and adding 10% for off-cuts lands the real order near 141 sq ft.
Example 3 — A large rectangular lot (200 ft × 100 ft). A suburban building lot is 200 feet deep by 100 feet wide. The area is 20,000 square feet, which is about 0.46 acre. Fencing the whole perimeter at $18 per linear foot would be 600 ft × $18 = $10,800 — which is why the perimeter number matters so much more than the area number when you are pricing a fence.
Example 4 — Paint for a 10 ft × 12 ft room with 8 ft ceilings. The four walls add up to 2 × (10 + 12) × 8 = 352 square feet of wall area. At 350 sq ft per gallon per coat, two coats need just over 2 gallons of paint — which is why paint stores sell gallon-and-a-half rooms as a "two-gallon minimum."
FAQ
How do I calculate the area of a rectangle?
Multiply the length by the width: Area = length × width. Make sure both measurements are in the same unit first. A 12-foot by 10-foot rectangle has an area of 12 × 10 = 120 square feet. If the result is in square inches and you need square feet, divide by 144; if it is in square yards and you need square feet, multiply by 9.
What is the perimeter of a rectangle and how do I find it?
The perimeter is the total distance around the outside edge. Add the two side lengths and double the sum: Perimeter = 2 × (length + width). For a 12-by-10 rectangle the perimeter is 2 × 22 = 44 feet. Use the perimeter when you are ordering fencing, baseboards, trim, or picture-frame moulding.
How do I find the diagonal of a rectangle?
Apply the Pythagorean theorem: diagonal = √(length² + width²). For a 12-by-10 rectangle the diagonal is √(12² + 10²) = √(144 + 100) = √244 ≈ 15.62 feet. Builders measure both diagonals of a foundation or wall frame: if the two diagonals are equal, the corners are square.
Should I measure in feet, inches, centimeters, or meters?
Pick whichever unit your tape measure is marked in from the Length Unit dropdown, and the calculator converts both sides to feet internally before applying the formulas. All outputs are then reported in feet and square feet: enter inches and you still get square feet (12 in × 10 in becomes 1 ft × 0.83 ft = 0.83 ft²); enter meters and you get 39.37 ft × 32.81 ft ≈ 1,291.67 ft². To convert mixed feet-and-inches, divide inches by 12 and add to the feet: 12 ft 6 in = 12.5 ft, then set the unit to feet.
How much carpet, tile, or paint do I need?
Take the area from this calculator and multiply by the material price per square foot, then add 10–15% for off-cuts, waste, and pattern matching. Carpet is usually priced by the square yard (1 sq yd = 9 sq ft), so divide square feet by 9. Paint covers roughly 350–400 square feet per gallon per coat, and most rooms need two coats.
Is a square a rectangle?
Yes. A square is a special rectangle whose length and width are equal. The same formula applies: a 10-by-10 square has an area of 100 square feet, a perimeter of 40 feet, and a diagonal of √200 ≈ 14.14 feet. This calculator handles squares correctly because it does not assume the two sides are different.
Why does the calculator reject a negative length?
A side length below zero has no physical meaning, so the engine returns an error instead of a nonsense result. If you typed a minus sign by accident, re-enter the dimension as a positive number. Negative numbers inside a rectangle's formulas would produce a "positive" area (because a negative times a negative is positive), which would look correct while being completely wrong — so the calculator refuses them at the door.
Disclaimer
This rectangle area calculator is provided for informational purposes only and does not constitute engineering, construction, or design advice. Results are based on the dimensions you enter and the standard Euclidean formulas for a rectangle; actual building materials, waste factors, and project costs vary by location, product, and contractor. Always double-check measurements on site and confirm material quantities with your supplier before ordering.