GeomBench

Rhombus Area Calculator

Half the product of the diagonals.

Diagonal d₁

Diagonal d₂

Area

Side length: 5
Perimeter: 20

What you entered

Diagonal d₁: 8Diagonal d₂: 6

1
Area = ½ × diagonal₁ × diagonal₂
0.5 × 8 × 6= 24
2
Side length (diagonals bisect at 90°)
√((8/2)² + (6/2)²)= 5
3
Perimeter
4 × 5= 20

Result

Area: 24

A rhombus with diagonals 8 and 6 has an area of 24, side length 5, and perimeter 20.

Rhombus area, side and perimeter from the diagonals

Area is half the product of the two diagonals. Because the diagonals bisect each other at right angles, the side follows from Pythagoras on half of each.

Diagonal 1	Diagonal 2	Area	Side	Perimeter
6	8	24.00	5.000	20.000
8	10	40.00	6.403	25.612
10	12	60.00	7.810	31.241
12	16	96.00	10.000	40.000
14	20	140.00	12.207	48.826
16	24	192.00	14.422	57.689

Rows one and four give whole-number sides because halving those diagonals produces the 3-4-5 and 6-8-10 right triangles. All four sides of a rhombus are equal, so the perimeter is simply four times the side. The diagonals are not equal to each other unless the shape is a square, which is the special case where both diagonals match and the area formula reduces to half the diagonal squared.

Why diagonals are enough

A rhombus's diagonals always bisect each other at a right angle, splitting it into 4 congruent right triangles. That's why area = ½ × d₁ × d₂ works without needing an angle or height.

Finding the side length too

Because the diagonals cross at 90°, each side is the hypotenuse of a right triangle with legs d₁/2 and d₂/2 — so the Pythagorean theorem gives you the side length for free.

Frequently asked questions

How do I calculate the area of a rhombus?

Area = ½ × d₁ × d₂ (half the product of the two diagonals). A rhombus with diagonals 10 and 14: Area = ½ × 10 × 14 = 70. Alternatively, Area = side² × sin(angle) if you know a side and an angle.

What is the difference between a rhombus and a square?

A square is a special rhombus where all angles are 90°. A rhombus has all four sides equal but angles can vary. Both have diagonals that bisect each other at right angles, but a square's diagonals are also equal in length.

How do I find the side length from the diagonals?

Side = √((d₁/2)² + (d₂/2)²). The diagonals of a rhombus bisect each other at 90°, creating four right triangles. Each side is the hypotenuse of a triangle with legs d₁/2 and d₂/2. Diagonals 6 and 8: side = √(9 + 16) = 5.