Given side lengths
Given one side and diagonals
Given base, height and any parallelogram angle

Parallelogram Perimeter Calculator

By Hanna Pamuła, PhD candidate

If you ever wondered how to find the perimeter of a parallelogram, this parallelogram perimeter calculator can help you in no time. Not only we implemented the easiest well-known equation but also two other parallelogram perimeter formulas. Why not give it a go? Check out also twin brother of that calculator - parallelogram area calculator - to get to know this shape better.

Parallelogram perimeter formula

The most well known formula for parallelogram perimeter comes from perimeter definition: it's simply the sum of the lengths of sides:

  • perimeter = a + b + a + b = 2 * (a + b)

But what if we don't have the length of the two sides?

  • Perimeter given one side and diagonals

    If you know the diagonals and two sides, you can use the formula:

    perimeter = 2 * a² + √(2 * e² + 2 * f²- 4 * a²)

    Where does it come from? It's transformed parallelogram law which states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals:

    2 * a² + 2 * b² = e² + f²

  • Perimeter given base, height and any parallelogram angle

    It's the formula using trigonometric sine function:

    perimeter = 2 * (a + (h/sin(angle)))

    The adjacent angles in the parallelogram are supplementary, so you can choose whichever angle you want because sin(angle) equals sin(180° - angle).

How to find the perimeter of a parallelogram using this calculator?

To use the parallelogram perimeter calculator follow the steps:

  1. Determine which part of the calculator is the one you need. Assume it's second part.
  2. Type the values - in this case, side (a) and two diagonals (e, f): 15 in, 18 in and 24 in, respectively. If you enter the values which can't form the parallelogram, the calculator will tell you about it. (Think for a while, why is it not always possible to create a parallelogram? Take a=1, e=15, f=4, is it possible to create the triangle from a, e/2 and f/2?)
  3. Parallelogram perimeter calculator displays the value. It's 60 in².

What next?

If you are happy with the results from parallelogram perimeter calculator, maybe you want to check our other geometry calculators?

Hanna Pamuła, PhD candidate

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