Enter the base and the height of the parallelogram. The area (base × height) is calculated and shown with a figure and the steps.
Enter the base and the height in the same unit, as numbers greater than 0 (numbers only, without the unit - for 8 cm, enter "8"). The height is the straight (perpendicular) distance between the base and the opposite side, not the length of the slanted side.
Result and figure
Enter the base and the height in the fields on the left and press "Calculate". The result and a figure 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 base and the height, and you get the area of the parallelogram (area = base × height) on the spot
- A figure of the parallelogram is drawn with the result, so you can see which side is the base and where the height is measured
- The height is not the length of the slanted side. The formula explanation walks you through this common mistake
- 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 base and the height in the same unit (both in inches, or both in feet). The areas of other shapes, such as rectangles, triangles and trapezoids, are covered on their own pages.
What is this calculation used for?
Finding the area of a slanted lot or field (real estate and farming)
A lot that runs along a road or a creek at an angle is sometimes shaped more like a parallelogram than a rectangle. For a parallelogram-shaped lot with a base of 80 ft and a height of 50 ft, the area is \(80 \times 50 = 4000\,\mathrm{ft^2}\).
Once you know the area, you can use it directly for property values, price per square foot, or how much seed and fertilizer to buy (often given per 1,000 square feet).
Estimating tiles for slanted and chevron patterns (DIY and interiors)
When you decorate a wall or floor with slanted stripes or a chevron pattern (parallelogram pieces set in a V-shape), each piece is a parallelogram. A piece with a base of 6 in and a height of 3 in has an area of \(6 \times 3 = 18\,\mathrm{in^2}\).
If the area to cover is 12 ft² (= 1,728 in²), you need about \(1728 \div 18 = 96\) pieces (in practice, add a few extra for waste from cutting). This is the most practical use, to avoid buying too much or too little.
Cutting fabric on the bias - bias tape (sewing and crafts)
Bias tape, used to finish the edges of clothing, is made by joining strips of fabric cut at 45 degrees. Each strip is a parallelogram. A strip 2 in wide (the height) and 36 in long (the base) has an area of \(36 \times 2 = 72\,\mathrm{in^2}\).
Add up the area of all the strips you need, and you can check whether your fabric is enough before you start cutting.
Combining two forces or velocities in a diagram (physics, engineering and game development)
In physics, two forces or velocities are combined by drawing a parallelogram (the parallelogram law). Going further, the area of the parallelogram formed by two vectors is the magnitude of their cross product, which is used in structural calculations for machines and buildings and in lighting calculations for 3D graphics and games.
The "base × height" you learn in elementary school is the starting point of calculations that engineers and game developers use every day.
The foundation of the triangle, trapezoid and rhombus formulas (learning and tests)
The triangle area formula "base × height ÷ 2" comes from the fact that two copies of the same triangle fit together to make a parallelogram. The trapezoid and rhombus formulas also start from turning the shape into a parallelogram.
In other words, the area of a parallelogram is the "parent" of the area formulas taught in elementary and middle school, and it is the foundation for area problems on standardized tests and for later problems about rearranging shapes.
Formulas and figures
Area of a parallelogram
Figure
Standard notation
(the usual math form)
\(S\)
\(=\)
\(b\)
\(\times\)
\(h\)
In words
(symbols replaced with words)
③
\(S\): area of the parallelogram
\(=\)
①
\(b\): base
\(\times\)
②
\(h\): height
The formula in words
①
Multiply the
\(b\): base
②
by the
\(h\): height
③
and you get the
\(S\): area of the parallelogram
Quick example
The area of a parallelogram with a base of 8 in and a height of 5 in is
\(S\): area of the parallelogram
\(=\)
base (8 in)
\(\times\)
height (5 in)
\(8 \times 5 = 40\,\mathrm{in^2}\)
Key idea
Why is the area a multiplication, just like a rectangle? Cut off the triangle that sticks out at one end of the parallelogram and move it to the other end. Without changing the area, the parallelogram becomes a rectangle whose width is the base and whose height is the height (rearranging a shape like this keeps its area the same). So the area is "base × height", the same as for a rectangle.
The most common mistake is the height. The height is the distance between the base and the opposite side, measured straight (perpendicular to the base), not the length of the slanted side. If you multiply by the slanted side instead, the answer comes out larger than the true area.
Working back to the height (from the area and the base)
Figure
Standard notation
(the usual math form)
\(h\)
\(=\)
\(S\)
\(\div\)
\(b\)
In words
(symbols replaced with words)
③
\(h\): height
\(=\)
①
\(S\): area of the parallelogram
\(\div\)
②
\(b\): base
The formula in words
①
Divide the
\(S\): area of the parallelogram
②
by the
\(b\): base
③
and you get the
\(h\): height
Quick example
The height of a parallelogram with an area of 40 in² and a base of 8 in is
\(h\): height
\(=\)
area (40 in²)
\(\div\)
base (8 in)
\(40 \div 8 = 5\,\mathrm{in}\)
Key idea
This formula undoes the multiplication "area = base × height" with a division. In the same way, if you know the area and the height and want the base, use \(b = S \div h\).
Watch the units of the answer. You divide an area (in²) by a length (in), so the answer is back in a unit of length (in).
The area of a parallelogram is "base × height". The height is not the length of the slanted side; it is the distance between the base and the opposite side, measured perpendicular to the base. Use the same unit for the base and the height, and the answer is in that unit squared (in² for inches, ft² for feet).
Symbols and terms
Symbols
| \(S\) | S | A letter often used for area. On this page it is the area of the parallelogram. Many US textbooks use \(A\) for area instead, as in \(A = b \times h\); the meaning is the same. |
| \(b\) | b | The length of the base, from the first letter of "base". |
| \(h\) | h | The height, from the first letter of "height". It is the distance between the base and the opposite side, measured perpendicular to the base. |
| \(\mathrm{in^2}\) | 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"). \(1\,\mathrm{ft^2} = 144\,\mathrm{in^2}\). |
Terms
| parallelogram | A four-sided shape whose two pairs of opposite sides are both parallel. Opposite sides are equal in length, and opposite angles are equal in size. Rectangles, squares and rhombuses are all parallelograms too. |
| base | The side you choose to measure the area from. Usually it is the bottom side in the figure, but you may choose any side (then measure the height again, perpendicular to the base you chose). |
| height | The distance between the base and the side opposite it, measured straight (perpendicular to the base). Be careful - it is not the same as the length of the slanted side. |
| perpendicular | Two lines that meet at a right angle (90 degrees). The height is measured perpendicular to the base. |
| 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. |
| rearranging without changing the area | Changing only the shape of a figure while keeping its area. Cut off the triangle at one end of a parallelogram and move it to the other end, and it becomes a rectangle with the same area. This is the reason behind the formula "base × height". |
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) |
|
| Parallel and perpendicular lines, parallelograms (Grades 3–4) |
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| What area means and its units (Grade 3) |
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| Area of a parallelogram (Grade 6) |
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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 parallelogram
| Base (in) | 8 |
| Height (in) | 5 |
| Area of the parallelogram (in²) | =B1*B2 |
Table to work back to the height
| Area of the parallelogram (in²) | 40 |
| Base (in) | 8 |
| Height (in) | =B1/B2 |
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 and "/" is division.
In the first table, for example, B3 shows 8 × 5 = 40 (in², since you entered inches). The second table shows 40 ÷ 8 = 5 in B3. Just replace the input numbers with your own lengths.
"B1" and "B2" in a formula mean "use the number in that cell". "*" is multiplication and "/" is division.
In the first table, for example, B3 shows 8 × 5 = 40 (in², since you entered inches). The second table shows 40 ÷ 8 = 5 in B3. 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 parallelogram
| Base (in) | 8 |
| Height (in) | 5 |
| Area of the parallelogram (in²) | =B1*B2 |
Table to work back to the height
| Area of the parallelogram (in²) | 40 |
| Base (in) | 8 |
| Height (in) | =B1/B2 |
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
base = 8 # length of the base (inches in this example)
height = 5 # height (in the same unit as the base; not the slanted side)
area = base * height # area of the parallelogram (the input unit squared; in2 in this example)
print(f"Area of the parallelogram: {area} in2")
Runs with the standard library only. "*" is multiplication. Change the base and the height at the top and run it. To work back to the height from the area and the base, change it to "height = area / base" ("/" is division).
How to write it in LaTeX and other math languages (copy and paste)
Area of a parallelogram
S = b × h
S = b \times h
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>S</mi>
<mo>=</mo>
<mi>b</mi>
<mo>×</mo>
<mi>h</mi>
</mrow>
</math>
S = b xx h
b*h
S := b*h;
S = b*h;
S = b × h
Working back to the height (from the area and the base)
h = S ÷ b
h = S \div b
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>h</mi>
<mo>=</mo>
<mi>S</mi>
<mo>÷</mo>
<mi>b</mi>
</mrow>
</math>
h = S -: b
S/b
h := S/b;
h = S/b;
h = S ÷ b
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 parallelogram has a base of 8 in and a height of 5 in. Find each of the following: 1. The area of this parallelogram in square inches (in²) 2. If the area stays 40 in² and the base changes to 10 in, what the height becomes in inches 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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Related Features
Area of a Rectangle Calculator (Length × Width)
A parallelogram can be rearranged into a rectangle. Find the area of rectangles and squares here
Area of a Trapezoid Calculator ((a + b) × h ÷ 2)
For a four-sided shape with only one pair of parallel sides (a trapezoid), use this page
Triangle Area Calculator (from Three Sides with Heron's Formula)
Cutting a parallelogram in half along a diagonal gives a triangle. This page finds the area from the three side lengths
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