Rhombus Area Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/10/2026
The area of a rhombus is calculated with A = (D × d) ÷ 2, where D and d are the lengths of its two diagonals. For a rhombus whose diagonals measure 8 m and 6 m, the area is 24 m².
Explanation
A rhombus is a quadrilateral whose four sides have the same length — a special case of parallelogram. Unlike a rectangle, whose area is calculated from its length and width, a rhombus's area is most simply calculated from its two diagonals, which always intersect perpendicularly at their midpoints: the area is half the product of their lengths, exactly as if the four right triangles bounded by the diagonals were rearranged to form a rectangle with sides D and d/2. This same partition into right triangles also recovers the length of a side from the diagonals, by the Pythagorean theorem: each side is the hypotenuse of a right triangle whose two legs are the halves of the two diagonals — so this calculator also displays the side length and the resulting perimeter. The rhombus shares its diagonal-based area formula with the kite (another quadrilateral with perpendicular diagonals), but differs from it by its four equal-length sides; it in turn differs from the square, a special rhombus whose diagonals are also equal in length and whose angles are all right angles.
Example: diagonals of 8 m and 6 m
Inputs
Long diagonal: 8 m. Short diagonal: 6 m.
Calculation
Area = (8 × 6) ÷ 2 = 48 ÷ 2 = 24 m². Side = √((8÷2)² + (6÷2)²) = √(16 + 9) = √25 = 5 m. Perimeter = 4 × 5 = 20 m.
Result
This rhombus has an area of 24 m², a side of 5 m, and a perimeter of 20 m.
Frequently asked questions
Why do a rhombus’s diagonals always intersect perpendicularly?
It is a consequence of the rhombus's symmetry: since its four sides are equal in length, the figure is symmetric about each of its two diagonals, which are therefore axes of symmetry. And the axis of symmetry of a figure made of two isosceles triangles joined at their base necessarily crosses that base at a right angle — exactly the configuration formed by the two diagonals of a rhombus.
Does this formula also work for a square?
Yes: a square is a special rhombus whose two diagonals have the same length. The formula A = (D × d) ÷ 2 therefore applies unchanged, and simplifies to A = D² ÷ 2 since D = d in that case — a result consistent with the usual formula A = side², given that the diagonal of a square is side × √2.
How do you calculate a rhombus’s area if I only know a side and an angle?
In that case, another formula applies: A = side² × sin(angle), where the angle is one of the rhombus's angles (the result is the same whichever angle is chosen, since opposite angles are equal and adjacent angles supplementary). This calculator uses only the diagonal method, the most direct when those two lengths are known.