Properties of a Parallelogram

This tool calculates the basic geometric properties of a parallelogram. Enter below the shape dimensions. The calculated results will have the same units as your input. Please use consistent units for any input.

 b = h = Additional input (select which): Angle φ1 Length b1 Side α α=b (rhombus)
 b1 =
 α =
 Geometric properties: Area = Perimeter = Lengths: Side α = Diagonal p = Diagonal q = Angles : deg rad φ1 = φ2 = Centroid: xc = yc =

Definitions

Geometry

Parallelogram is a quadrilateral shape with two pairs of parallel sides. The area of a parallelogram is given by the formulas:

$A = b h$

or

$A = ab\sin{\varphi_1}$

where a, b the lengths of the sides and h the height, perpendicular to b.

The perimeter of a parallelogram is simply the sum of the lengths of all sides:

$P = 2\left(a+b\right)$

The length of the left and right sides α, can be expressed in terms of the angle φ1 , using the right triangle, with hypotenuse α (see figure below):

$\alpha = \frac{h}{\sin{\varphi_1}}\\$

Interior angle φ2 is supplementary with φ1 . Therefore:

$\varphi_2 =180^{\circ} -\varphi_1$

There are many ways to find the lengths of diagonals, once the sides or the interior angles are known. Here, a solution employing the Pythagorean Theorem on the highlighted right triangles (see next figure) is presented:

$p = \sqrt{h^2 + \left(b+b_2\right)^2}$

Similarly, the other diagonal is found as:

$q = \sqrt{h^2 + \left(b-b_2\right)^2}$

Centroid

The centroid of parallelogram coincides with the point where diagonals cross each other. Measuring from the left vertex of base, xc and yc distances are:

$\begin{split} & x_{c} = 0.5\left(b+b_1\right)\\ & y_{c} = 0.5 h \end{split}$

where A is the area of the trapezoid.