Parallelogram Area Calculator

If you have any problems with the geometry of a parallelogram, check this parallelogram area calculator (and also its twin brother, parallelogram perimeter calculator).

Whether you want to calculate the area given base and height, sides and angle, or diagonals of a parallelogram and angle between them, you are in the right place. Don't ask how to find the area of a parallelogram; just give the calculator a try!

Below you can find out how the tool works – the parallelogram area formulas and neat explanation are all you need to understand the topic.

A parallelogram is a simple quadrilateral with two pairs of parallel sides. Every rectangle is a parallelogram, as well as every rhombus and square. Remember, it doesn't work the other way around!

Which formulas does the parallelogram area calculator use?

• Area given base and height

  area = base × height

  Did you notice something? The formula for the area of a parallelogram is pretty much the same as for a rectangle! Why is it so? Have a look at the picture: a parallelogram can be divided into a trapezoid and a right triangle and rearranged to the rectangle.

  Learn more about rectangle area with our area of a rectangle calculator.

• Area given sides and the angle between them

  area = a × b × sin(angle)

Does it ring a bell? This formula comes from trigonometry and is used, for example, in our triangle area calculator – the parallelogram may be seen as two congruent triangles. The adjacent angles in the parallelogram are supplementary, so you can choose whichever angle you want because sin(angle) = sin(180° - angle).

• Area given diagonals of a parallelogram and the angle between them

  area = ½ × e × f × sin(angle)

  The formula comes from trigonometry as well. Do you want to know where it comes from?

  Divide the parallelogram into two triangles, and assume that our e diagonal is the "base" for both new triangles.

  What's the height of that triangle? Use the sine function. It's (f/2) × sin(angle)!

  The area of the triangle is equal to our "base" e times height: e × (f/2) × sin(angle)

  The parallelogram consists of two such triangles, so the area equals e × f × sin(angle).

Are you still not sure our parallelogram area calculator works? We will show you step by step:

1. Have a look at your exercise. What is given, what is unknown? Choose the right calculator part for your needs. Assume that we want to calculate the area knowing the diagonals of a parallelogram and the angle between diagonals.

2. Enter the given values to the right boxes. Assume 5 in, 13 in, and 30° for the first diagonal, the second one, and the angle between them, respectively.

3. The calculator displays the area of a parallelogram value. It's 32.5 in² in our case.

Check out our area calculators for other shapes, such as rhombus area calculator, circle area calculator, and trapezoid area calculator.

To determine the area given the adjacent sides of a parallelogram, you also need to know the angle between the sides. Then you can apply the formula: area = a × b × sin(α), where a and b are the sides, and α is the angle between them.

The area of a parallelogram can be determined from its diagonals, provided that you also know the angle between the diagonals.

If e and f are the lengths of the diagonals and φ is the angle between them, then the area can be calculated as follows: area = ½ × e × f × sin(φ).

It is possible to find the area of a parallelogram without height! For instance, it suffices to know one of the following things:

1. The length of adjacent sides and the angle between them – use trigonometry.
2. The length of diagonals and the angle between them, using the formula – use trigonometry.
3. The length of diagonals and one side – use Heron's formula.

The answer is 75. We use the formula that says the area is equal to ½ times the product of the lengths of the diagonals times the sine of the angle between them. As our diagonals are perpendicular, the angle between them is 90° and sin 90° = 1. Hence, the calculation we need to perform is ½ × 10 × 15 = 75.