Parallelogram Calculator

A parallelogram is a four-sided shape where opposite sides are parallel and equal in length. The two adjacent sides are labeled a and b, and alpha is the interior angle between them. Rectangles are the special case where alpha equals 90 degrees, and rhombuses are the special case where a equals b.

Area equals base times perpendicular height: A = a x h. If you have the interior angle instead of the height, use A = a x b x sin(alpha), because h = b x sin(alpha). The calculator accepts either a direct height value or an angle and converts automatically.

Because opposite sides are equal, perimeter is just P = 2 x (a + b). You only need the two adjacent side lengths, since the angle and the diagonals play no part in the perimeter formula.

Each diagonal is found using the law of cosines on the two triangles the diagonal cuts the parallelogram into. Diagonal 1 = sqrt(a^2 + b^2 + 2 x a x b x cos(alpha)), which is the longer diagonal when alpha is less than 90 degrees. Diagonal 2 = sqrt(a^2 + b^2 - 2 x a x b x cos(alpha)), which is the shorter one. The two diagonals are equal only when alpha is exactly 90 degrees, making the shape a rectangle.

Height equals b x sin(alpha), and sin(alpha) never exceeds 1, so height can be at most equal to b, which happens at alpha = 90 degrees. A height greater than b is geometrically impossible for a valid parallelogram, so the calculator rejects it. If you enter both a height and an angle, the height takes precedence and the angle is recomputed from it using the acute solution.