Rhombus Perimeter Calculator

This rhombus perimeter calculator can calculate the distance around a rhombus, which is the sum of the lengths of all four sides. However, it also offers additional features: if you enter information about one side, the perimeter or both diagonals, or multiple values at once, the tool will calculate the remaining data and also show the area, the two acute angles, and the height. After entering the values and selecting the unit, the perimeter is shown as the main result.

What is the perimeter of a rhombus?

A rhombus is a quadrilateral with all four sides of equal length and opposite sides parallel to each other. It is also known as a diamond shape and can be found in many places, such as playing cards or road signs.

The perimeter is the total length of the boundary of a shape - in other words, it's the distance you would get if you walked all the way around the outside. Since each side is the same length, you don't have to measure all four sides; just knowing one will be enough.

Formula for calculating the perimeter of a rhombus:

Multiply the length of one side by four since a rhombus has four sides of equal length.

In this formula, P is the perimeter and a is the side length. If the rhombus has sides of length 9 cm, then its perimeter is four times that length.

Conversely, if the perimeter is known and the side length is to be calculated, divide the perimeter by four.

For a rhombus with a perimeter of 36 centimeters, the side length would be 9 centimeters, which is the result of dividing 36 by 4. If you enter any value, this calculator will automatically fill in the other value.

Calculating circumference using diagonal:

A rhombus has two diagonals that are perpendicular to each other and bisect each other. Each diagonal cuts the other exactly in half. This is important for a common problem involving rhombuses: calculating the perimeter given the two diagonals.

Half of one diagonal and half of the other diagonal form two sides of a right triangle, with the side of the rhombus being the hypotenuse. Thus the length of each side is (using the Pythagorean theorem) so the perimeter is

First multiply the side length by four to find the perimeter. The formula is summarized as follows:

Consider a rhomboid with diagonal lengths of 6 and 8. Halving each of the two diagonals gives 3 and 4, and the longest side of the right triangle with legs of 3 and 4 is 5, so it's the famous 3-4-5 triangle. So the side length is 5 and the perimeter is 20. If you enter 6 and 8 in the two fields for diagonals, then the side length, perimeter, and area are all shown at once.

Here's how to use this calculator.

Enter the known data and set a unit for each element. Once there is enough information to identify this shape, the calculation tool will complete the remaining data and show the perimeter as the main result. It is not necessary to specify from which measurement you started entering.

If you enter a side or the perimeter, then the perimeter can be directly calculated. The length of the sides can also be determined from the two diagonals, which allows for calculating area, angles and height. A combination of the length of the sides and one diagonal can also be used, since this will allow to deduce the second diagonal. By activating the "Square" option you can see how close this shape is to a square. The inscribed circle option displays an inscribed circle, and by opening the diagram you can observe how perimeter and area change when the rhomboid is enlarged or reduced.

What can't be determined with just one diagonal?

One diagonal is not enough. If you tilt a rhombus on one fixed diagonal, it can become both long and narrow or short and wide. Even if the diagonals remain the same length, the side lengths can change.

To determine this shape, additional measurement data is required. Either the other diagonal or the side length. That's why the calculation tool requires a second input when calculating the perimeter based on a diagonal.

Check all of your measurements for a rhombus together.

Once the shape is determined all other measurements can be derived from the side lengths and diagonals. The following table summarizes the relationships used by the calculator where A represents an acute angle.

Examples of calculations:

The following table shows the perimeter of some rhombuses. Note that the perimeter is calculated by adding all sides together, not multiplying, so it is directly proportional to the length of a side.

Calculations along the diagonals can also be done quickly. If the lengths of the diagonals are 10 and 24, then half their lengths are 5 and 12, which form a Pythagorean triple with 13. So the side length is 13 and the perimeter is 52.

Rhombus, square, diamond

A square is a special type of rhombus where all the angles are right angles. All squares are rhombuses but most rhombuses are not squares. This is because a rhombus can be freely rotated at any angle while its four sides remain equal in length.

Of all rhombuses with a given perimeter (which is to say, of all rhombuses with the same side-length), the square has the largest area. As you flatten out a rhombus while keeping its perimeter constant, its area gradually approaches zero, even though the distance around it stays the same. By turning on the "Square" option, you can see how close your rhombus is to being a square (which would have the maximum possible area).

Angle and height

A rhombus has two acute angles and two obtuse angles, with opposite angles being equal to each other, and the sum of these two types of angles always adding up to 180 degrees. The diagonals determine the angles. One long diagonal and one short diagonal will create a shallow, elongated rhombus, while two equal diagonals will form a square with four right angles.

The height is the vertical distance between two opposite sides and is equal to the value obtained by dividing the area by the length of a side. When arranging rhombus tiles in a row flatwise, the height is important because it determines the vertical space occupied by each tile instead of the length of a side.

Use of the perimeter of a rhombus:

The perimeter answers the everyday question "how long is the border?". It tells us how much material we need to frame a diamond-shaped window or sign, how much fence is required to enclose a diamond-shaped plot of land, or how much ribbon is needed to trim diamond-shaped appliqués on clothing.

The interior of a baseball field is an example of the approximate shape of a rhombus. It consists of a square with one corner on the ground, and the distances between bases are 90 feet. Therefore, the perimeter to go around all the bases is 360 feet. Kites, some crystals, and tiles with a rhombic pattern are also rhombi, and their edge lengths can be measured using the same simple formula.

Tips for accurate results:

Make sure all measurements are in the same units before you begin to use them. You cannot have one side length in centimeters and another in inches for the same triangle. When measuring diagonals, measure from corner to corner through the center point instead of along a side. Remember that in a true rhombus, all four sides will be the same length. If your sides are different lengths, you do not have a rhombus - you have either a general parallelogram or a kite, and different formulas apply.