Parallelogram Perimeter Calculator

Creators

Hanna Pamuła, PhD

Hanna Pamuła

PhD

Website

Research Gate

Hanna (Hania) Pamuła holds a Ph.D. in Bioacoustics / Mechanical Engineering, obtained at AGH University of Science and Technology. She has participated in research work in labs in France and the UK and presented papers at several international conferences. Hania has a penchant for photography and graphic design. When not in the office, she’s probably traveling, hiking, or out in the field, watching birds and recording their calls. See full profile

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Reviewers

Bogna Szyk and Steven Wooding

Steven Wooding

Steven Wooding is a physicist by training with a degree from the University of Surrey specializing in nuclear physics. He loves data analysis and computer programming. He has worked on exciting projects such as environmentally aware radar, using genetic algorithms to tune radar, and building the UK vaccine queue calculator. Steve is now the Editorial Quality Assurance Coordinator here at Omni Calculator, making sure every calculator meets the standards our users expect. In his spare time, he enjoys cycling, photography, wildlife watching, and long walks. See full profile

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

This is very similar to what you will find in our perimeter of a rectangle calculator or perimeter of a square calculator.

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

parallelogram, given sides and an angle between

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 from the 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

parallelogram, given diagonals and an angle between

Perimeter given base, height, and any parallelogram angle

It's the formula using the 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:

Determine which part of the calculator is the one you need. Assume it's the second part.
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?)
Parallelogram perimeter calculator displays the value. It's 60 in².