Parallelogram Calculator

A parallelogram is a quadrilateral (four-sided polygon) where opposite sides are parallel and equal in length. Rectangles, rhombuses, and squares are all special types of parallelograms. The opposite interior angles of a parallelogram are also equal. See also our Right Triangle Calculator.

The area of a parallelogram is calculated as K = a × b × sin(A), where a and b are the side lengths and A is the included angle. Equivalently, K = base × height (K = b × h), where h is the perpendicular height from the base.

The perimeter is simply the sum of all four sides. Since opposite sides are equal, P = 2(a + b), where a and b are the two distinct side lengths.

Using the law of cosines, the diagonals are calculated as: p = √(a² + b² − 2ab·cos(A)) for the shorter diagonal and q = √(a² + b² + 2ab·cos(A)) for the longer diagonal, where A is one of the interior angles. You might also find our Segment Area useful.

In a parallelogram, opposite angles are equal: A = C and B = D. Adjacent angles are supplementary, meaning A + B = 180°. If you know angle A, then angle B = 180° − A.

The height h is the perpendicular distance between the two parallel base sides. It can be calculated as h = a × sin(A), where a is the side length adjacent to the angle A and the base is side b.

A rectangle is a special parallelogram where all four interior angles are exactly 90°. In a general parallelogram, the angles can be any value as long as opposite angles are equal and adjacent angles sum to 180°.

A rhombus is a parallelogram where all four sides are equal in length (a = b). A square is a special case that is both a rhombus and a rectangle — all sides equal and all angles 90°.