Parallelogram area, perimeter, diagonals, and angles
The parallelogram area calculator finds the area, perimeter, diagonal lengths, and supplementary angles of a parallelogram from its base, height, side length, and included angle.
Parallelogram formulas
A parallelogram has two pairs of parallel sides. Opposite sides are equal and opposite angles are equal. Consecutive angles are supplementary (they add to 180 degrees).
Area = base * height = base * side * sin(angle). Perimeter = 2 * (base + side). Diagonals are found using the law of cosines: d1 = sqrt(a^2 + b^2 - 2ab*cos(angle)), d2 = sqrt(a^2 + b^2 + 2ab*cos(angle)).
A = b * h
Area from base b and perpendicular height h.
d = sqrt(a^2 + b^2 - 2ab*cos(theta))
Diagonal length via the law of cosines. This is the specific relationship the calculator applies when building the result.
Special cases
When the angle is 90 degrees, the parallelogram is a rectangle. When all four sides are equal, it is a rhombus. When both conditions hold, it is a square. The extra explanation keeps the page useful for searchers who need to understand not just the number, but also the assumption set behind it.
Limitations
The included angle must be between 0 and 180 degrees exclusive. The height must not exceed the side length. The extra explanation keeps the page useful for searchers who need to understand not just the number, but also the assumption set behind it.
Frequently asked questions
How is a parallelogram different from a rectangle?
A rectangle is a special parallelogram where all angles are 90 degrees. In a general parallelogram, angles can be any value as long as opposite angles are equal and consecutive angles sum to 180 degrees.
Do the diagonals of a parallelogram bisect each other?
Yes. The diagonals always bisect each other, but they are not equal in length unless the parallelogram is a rectangle.
How can I check the parallelogram area, perimeter, diagonals, and angles result manually?
The safest manual check is to follow the same formula or rule one step at a time and compare that working with the calculator output. That catches sign errors, bracket mistakes, and input-order mixups without requiring any extra method beyond the underlying maths itself.
