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.
Parallelogram area formulas
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)
.
How to use this parallelogram area calculator?
Are you still not sure our parallelogram area calculator works? We will show you step by step:

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.

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.

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.
FAQ
How do I find the area of a parallelogram given its adjacent sides?
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.
How do I find the area of a parallelogram given diagonals?
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)
.
How do I find the area of a parallelogram without height?
It is possible to find the area of a parallelogram without height! For instance, it suffices to know one of the following things:
 The length of adjacent sides and the angle between them – use trigonometry.
 The length of diagonals and the angle between them, using the formula – use trigonometry.
 The length of diagonals and one side – use Heron's formula.
What is the area of a parallelogram with perpendicular diagonals of length 10 and 15?
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
.