Rhombus: - online calculation, formula

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   Rhombus - perimeter and area

Interactive calculator — drag the diagonals or type them in and see the result straight away, with the formula and a live calculation.

Photo

Formula & notes

A = \frac{e \cdot f}{2}

P = 4 a

a = \frac{\sqrt{e^{2} + f^{2}}}{2}

A = area

P = perimeter

a = side "a"

v = height

e = diagonal "e"

f = diagonal "f"

What is it?

A rhombus is a quadrilateral whose four sides all have the same length, which is why it belongs to the family of parallelograms. Its opposite sides are parallel to each other, while adjacent sides are not. Opposite angles of a rhombus are equal and any two adjacent angles always add up to 180 degrees. What makes the shape special is that its diagonals are perpendicular to each other and bisect one another, and each of them also splits the vertex angles it passes through into two equal parts. A square can be understood as a particular case of the rhombus, one that additionally has all of its angles right. Thanks to this symmetry a rhombus has two axes of symmetry, running exactly along its diagonals.

We come across this shape more often than it might seem: the diamonds on playing cards are rhombi, and so are many floor tiles, traffic and warning signs, and the patterns woven into mesh and fabric. In engineering practice the shape is used by so-called rhombic linkages, and it also turns up in crystallography when lattices are described. Knowing its properties therefore pays off not only in school geometry, but also in design, construction and engineering.

Calculator

Length unit

Diagonal e (side to side)cm

Diagonal f (top to bottom)cm

Rhombus area

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Perimeter

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Side a

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Height v

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Diagonals e · f

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Interactive graph

Grab the end of diagonal e or f and drag it Re-center

Frequently asked questions

How do you calculate the area of a rhombus?

The easiest way to get the area of a rhombus is from its diagonals: A = (e × f) ÷ 2, where e and f are the lengths of the diagonals. The formula A = a · v, that is side times height, gives exactly the same result. In the calculator above you can type the diagonals in or drag their endpoints directly with the mouse.

How do you calculate the perimeter of a rhombus?

Because all four sides of a rhombus are the same length, the perimeter is P = 4 · a, where a is the length of the side. You get the side from the halves of the diagonals using the Pythagorean theorem: a = √((e/2)² + (f/2)²).

How do you calculate the side of a rhombus from its diagonals?

The diagonals of a rhombus are perpendicular to each other and bisect one another, so they form a right triangle with legs e/2 and f/2. The side a is its hypotenuse: a = √((e/2)² + (f/2)²). For e = 8 and f = 6 this gives a = √(4² + 3²) = 5.

How does a rhombus differ from a square?

A rhombus has all of its sides the same length, but in general its interior angles are not right angles. A square is a particular case of the rhombus that additionally has all angles right (90°). Every square is therefore a rhombus, but not every rhombus is a square.

Worked example