Enter the length and the width of the rectangle. The area (length × width) is shown, along with the area converted between cm² and m².
Enter the length and the width in the same unit, as numbers greater than 0 (numbers only, without the unit - for 150 cm, enter "150").
Result and figure
Enter the length and width in the fields on the left and press "Calculate". The result will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formulas and figures
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Symbols and terms
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Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter the length and the width, and you get the area of the rectangle (area = length × width) on the spot
- The area is also converted to other units (square feet when you enter inches, square inches when you enter feet). Switch "Units" to Metric to get cm² and m² instead
- Enter the same number for the length and the width, and it works for the area of a square too
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
Enter the length and the width in the same unit (both in inches, or both in feet). The areas of other shapes, such as triangles and circles, are covered on their own pages.
What is this calculation used for?
Measuring a room to choose furniture and rugs (home and moving)
A room 12 ft long and 10 ft wide has a floor area of \(12 \times 10 = 120\,\mathrm{ft^2}\). An 8 × 10 ft rug covers \(8 \times 10 = 80\,\mathrm{ft^2}\), which is two-thirds of the floor.
Compare the area of the room with the areas of rugs, carpets and beds, and you can check with numbers how much of the room they will fill before you buy.
Reading the size of land and homes - square feet and acres (real estate)
A rectangular lot 100 ft wide and 150 ft deep has an area of \(100 \times 150 = 15000\,\mathrm{ft^2}\). Land is also measured in acres, and 1 acre = 43,560 ft², so \(15000 \div 43560 \approx 0.34\) acre.
Home listings give the living area in square feet, so being able to work out the area helps you compare homes and prices (the price per square foot).
Estimating paint or wallpaper (DIY)
To paint a wall 8 ft high and 12 ft wide, the area is \(8 \times 12 = 96\,\mathrm{ft^2}\), or 192 ft² for two coats. A paint can label gives the area it covers, often about 350 to 400 square feet per gallon for one coat, so you can work out how much to buy before you go to the store.
Wallpaper, flooring, insulation and other materials sold by area all use this calculation. It is the one you need most often to avoid buying too much or too little.
Planning a vegetable garden (gardening and farming)
A 4 × 8 ft raised bed has an area of \(4 \times 8 = 32\,\mathrm{ft^2}\). Garden guides and seed packets give spacing such as "4 lettuce plants per square foot", so for the whole bed that is \(32 \times 4 = 128\) plants. Knowing the area tells you how many plants or seeds you need.
Fertilizer and other products are also often given as an amount per square foot (or per 1,000 square feet), so area is the starting point for any growing plan.
Checking if you have enough fabric (sewing and crafts)
Fabric is sold as a rectangle: a fixed width (often 44 inches) cut to the length you ask for, by the yard. If you buy 1.5 yards (54 inches) of 44-inch fabric, the area is \(44 \times 54 = 2376\,\mathrm{in^2}\) (16.5 ft²).
Compare it with the area your pattern pieces need, and you can decide how much to buy before you get to the cutting counter.
Formulas and figures
Area of a rectangle
Figure
Standard notation
(the usual math form)
\(S\)
\(=\)
\(l\)
\(\times\)
\(w\)
In words
(symbols replaced with words)
③
\(S\): area of the rectangle
\(=\)
①
\(l\): length
\(\times\)
②
\(w\): width
The formula in words
①
Multiply the
\(l\): length
②
by the
\(w\): width
③
and you get the
\(S\): area of the rectangle
Quick example
The area of a rectangle 5 in long and 8 in wide is
\(S\): area of the rectangle
\(=\)
length (5 in)
\(\times\)
width (8 in)
\(5 \times 8 = 40\,\mathrm{in^2}\)
Key idea
Why does multiplying give the area? Area counts how many squares with 1-inch sides (1 in², one square inch) fit inside. A rectangle 5 in long and 8 in wide holds 5 rows of 8 such squares with no gaps, \(5 \times 8 = 40\) squares in all. So the area is 40 in².
Always use the same unit for the length and the width. Inches times inches gives square inches (in²), and feet times feet gives square feet (ft²).
Area of a square (a special rectangle)
Figure
Standard notation
(the usual math form)
In words
(symbols replaced with words)
\(S\)
\(=\)
\(l\)
\(2\)
③
\(S\): area of the square
\(=\)
①
\(l\): side length
②
squared (the length times itself)
The formula in words
①
Take the
\(l\): side length
②
find it
squared (the length times itself)
③
and you get the
\(S\): area of the square
Quick example
The area of a square with 6-inch sides is
\(S\): area of the square
\(=\)
side length (6 in)
squared
\(6 \times 6 = 36\,\mathrm{in^2}\)
Key idea
A square is a rectangle whose length and width are equal. So if you put \(l = w\) into the rectangle formula \(S = l \times w\), you get the square formula \(S = l^2\). This calculator also finds the area of a square if you enter the same number for the length and the width.
Converting area units (in² → ft²)
Figure
Standard notation
(the usual math form)
\(S_{\mathrm{ft^2}}\)
\(=\)
\(S_{\mathrm{in^2}}\)
\(\div\)
\(144\)
In words
(symbols replaced with words)
③
\(S_{\mathrm{ft^2}}\): area in ft²
\(=\)
①
\(S_{\mathrm{in^2}}\): area in in²
\(\div\)
②
\(144\): square inches in 1 ft²
The formula in words
①
Divide the
\(S_{\mathrm{in^2}}\): area in in²
②
by the
\(144\): square inches in 1 ft²
③
and you get the
\(S_{\mathrm{ft^2}}\): area in ft²
Quick example
A 5 × 8 ft rug measured in inches is 60 in × 96 in = 5,760 in². In square feet, that is
area in ft²
\(=\)
area in in² (5760)
\(\div\)
square inches in 1 ft² (144)
\(5760 \div 144 = 40\,\mathrm{ft^2}\)
Key idea
The conversion factor for area is the square of the conversion factor for length. Since \(1\,\mathrm{ft} = 12\,\mathrm{in}\), \(1\,\mathrm{ft^2} = 12\,\mathrm{in} \times 12\,\mathrm{in} = 144\,\mathrm{in^2}\). It is 144, not 12. This is the point people most often get wrong.
To go from ft² back to in², multiply by 144. Larger units work the same way: \(1\,\mathrm{yd^2} = 3\,\mathrm{ft} \times 3\,\mathrm{ft} = 9\,\mathrm{ft^2}\). In metric units, \(1\,\mathrm{m^2} = 100\,\mathrm{cm} \times 100\,\mathrm{cm} = 10000\,\mathrm{cm^2}\).
The area of a rectangle is "length × width". Use the same unit for both, and the answer is in that unit squared (in² for inches, ft² for feet). To convert in² to ft², just divide by 144.
Symbols and terms
Symbols
| \(S\) | S | A letter often used for area. On this page it is the area of the rectangle (or square). Many US textbooks use \(A\) for area instead, as in \(A = l \times w\); the meaning is the same. |
| \(l\) | l | The length, from the first letter of "length". |
| \(w\) | w | The width, from the first letter of "width". |
| \(l^2\) | l squared | The number \(l\) multiplied by itself (\(l \times l\)). The small raised 2 is an exponent that says "use it as a factor twice". |
| \(\mathrm{in^2}\) | square inch | A unit of area. The area of a square with 1-inch sides is 1 in². It is also written "sq in". |
| \(\mathrm{ft^2}\) | square foot | A unit of area. The area of a square with 1-foot sides is 1 ft² (also written "sq ft"). \(1\,\mathrm{ft^2} = 144\,\mathrm{in^2}\). Room and home sizes in the US are given in square feet. |
Terms
| rectangle | A four-sided shape whose four angles are all right angles. Opposite sides are equal in length. It is the most common shape around us, from notebooks to doors to rooms. |
| square | A four-sided shape with four right angles and four sides of equal length. It is a special rectangle whose length and width are equal. |
| area | How much flat space a shape covers, given as a number. It is measured by how many unit squares (such as 1 in² squares) fit inside. |
| right angle | An angle of 90 degrees, the angle that fits exactly into the corner of a sheet of paper. All four angles of a rectangle are right angles. |
| unit conversion | Writing the same amount in a different unit. For area, the key point is that the area factor is the square of the length factor (1 ft = 12 in, so 1 ft² = 144 in²). |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Multiplication (Grades 3–4) |
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| Rectangles and squares (Grades 2–3) |
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| What area means and its units (Grade 3) |
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| Multiplying decimals (Grade 5) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to find the area of a rectangle
| Length (in) | 60 |
| Width (in) | 96 |
| Area of the rectangle (in²) | =B1*B2 |
Table to find the area of a square
| Side length (in) | 6 |
| Area of the square (in²) | =B1^2 |
Table to convert in² to ft²
| Area in in² | 5760 |
| Area in ft² | =B1/144 |
After pasting, column A has the labels and column B has the numbers. The upper rows are your inputs, and the formula in the last row is calculated automatically from them.
"B1" and "B2" in a formula mean "use the number in that cell". "*" is multiplication, "/" is division and "^" raises to a power (how many times to multiply).
In the first table, for example, B3 shows 60 × 96 = 5760 (in², since you entered inches). The second table shows 36 in B2, and the third shows 40 in B2. Just replace the input numbers with your own lengths.
"B1" and "B2" in a formula mean "use the number in that cell". "*" is multiplication, "/" is division and "^" raises to a power (how many times to multiply).
In the first table, for example, B3 shows 60 × 96 = 5760 (in², since you entered inches). The second table shows 36 in B2, and the third shows 40 in B2. Just replace the input numbers with your own lengths.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the area of a rectangle
| Length (in) | 60 |
| Width (in) | 96 |
| Area of the rectangle (in²) | =B1*B2 |
Table to find the area of a square
| Side length (in) | 6 |
| Area of the square (in²) | =B1^2 |
Table to convert in² to ft²
| Area in in² | 5760 |
| Area in ft² | =B1/144 |
The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace the input numbers with your own lengths.
How to calculate it in Python
length = 60 # length (inches in this example)
width = 96 # width (in the same unit as the length)
area = length * width # area of the rectangle (the input unit squared; in2 in this example)
area_ft2 = area / 144 # when you entered inches, the area in ft2
print(f"Area of the rectangle: {area} in2")
print(f"In square feet: {area_ft2} ft2")
Runs with the standard library only. "*" is multiplication and "/" is division. Change the length and the width at the top and run it (this example uses inches; if you enter feet instead, multiply by 144 to get in²).
How to write it in LaTeX and other math languages (copy and paste)
Area of a rectangle
S = l × w
S = l \times w
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>S</mi>
<mo>=</mo>
<mi>l</mi>
<mo>×</mo>
<mi>w</mi>
</mrow>
</math>
S = l xx w
l*w
S := l*w;
S = l*w;
S = l × w
Area of a square (a special rectangle)
S = l²
S = l^{2}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>S</mi>
<mo>=</mo>
<msup><mi>l</mi><mn>2</mn></msup>
</mrow>
</math>
S = l^2
l^2
S := l^2;
S = l^2;
S = l^2
Converting area units (in² → ft²)
S[ft²] = S[in²] ÷ 144
S_{\mathrm{ft^2}} = S_{\mathrm{in^2}} \div 144
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>S</mi><mrow><msup><mi mathvariant="normal">ft</mi><mn>2</mn></msup></mrow></msub>
<mo>=</mo>
<msub><mi>S</mi><mrow><msup><mi mathvariant="normal">in</mi><mn>2</mn></msup></mrow></msub>
<mo>÷</mo>
<mn>144</mn>
</mrow>
</math>
S_(ft^2) = S_(in^2) -: 144
sIn2/144
sFt2 := sIn2/144;
s_ft2 = s_in2/144;
S(ft²) = S(in²)/144
How to have ChatGPT do the calculation
You are a math calculation assistant. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). A rectangle is 60 inches long and 96 inches wide. Find each of the following: 1. The area of this rectangle in square inches (in²) 2. That area converted to square feet (ft²) Show the formulas you used and the numbers from the execution result.
How to Use
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1Enter your numbersType the numbers you want to calculate with into the input fields
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2CalculatePress the "Calculate" button
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3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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