# Parallelogram Perimeter Calculator

Created by Hanna Pamuła, PhD
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Feb 02, 2023

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: 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 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 • 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:

1. Determine which part of the calculator is the one you need. Assume it's the 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.

Hanna Pamuła, PhD
Given
sides a
in
b
in
Perimeter
in
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