Rhombus Area Calculator
Find a rhombus's area from its diagonals.
Results update as you type.
How it works
A rhombus is a four-sided shape with all sides equal, like a slanted square, and this calculator finds its area, side, and perimeter from its two diagonals. You enter the lengths of the two diagonals, and it returns the area, the length of each side, and the perimeter. The area formula is elegantly simple: half the product of the diagonals. This works because a rhombus's diagonals cross at right angles and cut each other exactly in half, dividing the rhombus into four identical right triangles. Because all four sides of a rhombus are the same length, once you find one side you know the perimeter is four times it. Each side is found using the Pythagorean theorem on the half-diagonals, since the half-diagonals form the two legs of a right triangle with the side as the hypotenuse. Rhombuses appear in tiling patterns, jewelry, kites, crystal structures, and many designs, and knowing their measurements is useful in geometry, construction, and craft projects. Using the diagonals is often more practical than using the side and an angle, since diagonals are straightforward to measure directly. Both diagonals must be positive lengths. Enter the two diagonals to find the rhombus's area, side length, and perimeter.
Area = (d₁ × d₂) / 2 ; side = √((d₁/2)² + (d₂/2)²)
A rhombus's diagonals bisect each other at right angles, so its area is half the product of the two diagonals. Each side is the hypotenuse of a right triangle formed by the half-diagonals, found with the Pythagorean theorem, and the perimeter is four times that side since all sides of a rhombus are equal.
Source:Geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter diagonal 1 (d₁) and diagonal 2 (d₂).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Area updates instantly as you type — no button to press.
Frequently asked questions
How do you find the area of a rhombus?
The simplest way is to multiply the two diagonals and divide by two. This works because the diagonals of a rhombus intersect at right angles and bisect each other, splitting the shape into four congruent right triangles. If you know the diagonals, the area is immediate; the calculator computes it along with the side and perimeter.
How is the side of a rhombus calculated from diagonals?
Each half-diagonal is a leg of a right triangle whose hypotenuse is a side of the rhombus. Using the Pythagorean theorem, the side equals the square root of the sum of the squares of the two half-diagonals. Since all sides of a rhombus are equal, this single value applies to every side.
Why do the diagonals meet at right angles?
It is a defining geometric property of a rhombus that its diagonals are perpendicular and bisect each other. This follows from the equal side lengths, which make the diagonals axes of symmetry. This right-angle intersection is exactly what allows the area to be computed as half the product of the diagonals.
Is a square a rhombus?
Yes. A square is a special rhombus in which all angles are right angles as well as all sides being equal. For a square, the two diagonals are equal, and the area formula of half the product of diagonals still holds, giving the same result as side squared. So every square is a rhombus, but not every rhombus is a square.
Why use diagonals instead of side and angle?
Diagonals are often easier to measure directly than an interior angle, especially on a physical object, and the area formula using diagonals is simpler than one requiring trigonometry. If you happen to know a side and an angle instead, the area can also be found as side squared times the sine of the angle, but the diagonal method is usually more convenient.