Rhombus Calculator
Find a rhombus's area, side length, perimeter, and height from its two diagonals.
Area
24
Area = (d₁ × d₂) / 2. Diagonals of 6 and 8 give an area of 24 square units.
Side length
5
Perimeter
20
Height
4.8
Each side comes from the half-diagonals: side = √((d₁/2)² + (d₂/2)²). Diagonals of 6 and 8 give a side of 5 and a perimeter of 20.
How it works
A rhombus is a four-sided shape with all sides equal — think of a square that's been pushed over. Its two diagonals cross at right angles and cut each other exactly in half, which is what makes the diagonals such a handy way to describe it.
The area is the easiest part: multiply the two diagonals and halve the result, so area = (d₁ × d₂) / 2. Because the half-diagonals form a right triangle, each side equals √((d₁/2)² + (d₂/2)²), and the perimeter is four of those sides. Divide the area by a side and you get the height.
Diagonals of 6 and 8, for example, give an area of 24, a side of 5, and a perimeter of 20 — the classic 3-4-5 right triangle hiding inside each quarter of the shape.
Frequently asked questions
How do I find the area of a rhombus from its diagonals?
Multiply the two diagonals and divide by two: area = (d₁ × d₂) / 2. The diagonals split the rhombus into four right triangles, and this formula adds them all up in one step.
How do I get the side length from the diagonals?
Each side is the hypotenuse of a right triangle whose legs are half of each diagonal, so side = √((d₁/2)² + (d₂/2)²). All four sides of a rhombus are equal, so one calculation covers them all.
Is a square a rhombus?
Yes. A square is a special rhombus where the two diagonals are equal, which forces all four angles to be right angles. Any rhombus with unequal diagonals is a slanted, non-square version.