Parallelogram Calculator
Calculate the area, perimeter, and both diagonals of a parallelogram from two adjacent sides and either an interior angle or a perpendicular height.
Parallelogram dimensions
If both are provided, height takes precedence.
Area
12.9904
- Perimeter
- 16
- Height
- 2.5981
- Interior angle
- 60°
- Diagonal 1
- 7
- Diagonal 2
- 4.3589
Frequently Asked Questions about the Parallelogram Calculator
What is a parallelogram?
A parallelogram is a quadrilateral whose opposite sides are parallel and equal in length. The two adjacent sides are usually called a and b, and the interior angle between them is alpha. A rectangle is the special case where alpha is 90 degrees, and a rhombus is the special case where a equals b.
How do you find the area of a parallelogram?
Area equals the base times the perpendicular height: A = a * h, where h is the distance from side a to its parallel side. If you only have the interior angle alpha, use A = a * b * sin(alpha), since h equals b * sin(alpha). The calculator accepts either input.
What is the perimeter of a parallelogram?
Perimeter sums every side. Because opposite sides are equal, P = 2 * (a + b). You only need the two adjacent side lengths, not the angle or the diagonals.
How are the two diagonals computed?
The diagonals come from the law of cosines on the two triangles formed by each diagonal. Diagonal 1 squared equals a^2 + b^2 + 2 * a * b * cos(alpha), and diagonal 2 squared equals a^2 + b^2 - 2 * a * b * cos(alpha). The two diagonals are equal only when alpha is 90 degrees, in which case the shape is a rectangle.
Why can't the height be larger than side b?
The perpendicular height equals b * sin(alpha), and sin(alpha) never exceeds 1, so the height cannot exceed b. A height greater than b would describe a shape that is not a valid parallelogram, so the calculator rejects it. If you supply both a height and an angle, the height takes precedence and the angle is recomputed from it.