Rhombus Area Calculator

Enter a rhombus's two diagonals to get its area (A = d1 × d2 / 2), side length, perimeter, and height.

Quick Facts

Area formula
A = d1 × d2 / 2
Half the product of the two diagonals.
Side formula
s = √((d1/2)² + (d2/2)²)
The diagonals bisect each other at 90°, so half-diagonals form a right triangle with the side as hypotenuse.
Perimeter formula
P = 4s
Sum of all four equal sides.

Your Results

Calculated
Area
-
A = d1 × d2 / 2
Side Length
-
s = √((d1/2)² + (d2/2)²)
Perimeter
-
P = 4 × side
Height
-
h = Area / side

Ready

Enter both diagonals and a unit, then press Calculate.

Formula and Method for Rhombus Area

A rhombus is a four-sided polygon (quadrilateral) with all four sides of equal length, whose opposite sides are parallel and whose diagonals bisect each other at right angles. Because a rhombus is a parallelogram, its area can be found several equivalent ways — this calculator uses the most common one, the two diagonals: A = (d1 × d2) / 2, where d1 and d2 are the lengths of the two diagonals.

How the calculation works

Enter the lengths of both diagonals and choose the unit they are measured in. The calculator multiplies the two diagonals and divides by 2 to get the area (in square units, such as ft² or m²). It then finds the side length using the Pythagorean theorem: since the diagonals of a rhombus cross at a 90° angle and bisect each other, each side is the hypotenuse of a right triangle with legs d1/2 and d2/2, so s = √((d1/2)² + (d2/2)²). From the side length it derives the perimeter, P = 4s, and the height (the perpendicular distance between a pair of parallel sides) by rearranging the base-times-height area formula: h = A / s.

Common mistakes

  • Confusing side length with diagonal: the diagonals of a rhombus are generally not equal to each other or to the sides (unless the rhombus is also a square) — don't substitute one for the other.
  • Halving only one diagonal: the area formula divides the full product d1 × d2 by 2 once, not each diagonal separately.
  • Rhombus vs. square: every square is a rhombus, but not every rhombus is a square — a rhombus's diagonals are perpendicular but usually unequal in length, while a square's diagonals are also equal.

Real-world applications

  • Tile, parquet, and mosaic patterns often use diamond/rhombus-shaped pieces, where area determines material quantity.
  • Kite and sail design uses the diagonal-based area formula directly, since many kites are rhombus-shaped.
  • Structural trusses and lattice frameworks use rhombus geometry to calculate load-bearing panel areas.
  • Crystallography and materials science use the rhombus (and rhombic lattices) to describe unit-cell cross-sections.

Frequently Asked Questions

What is the formula for the area of a rhombus?
Using the two diagonals, the area of a rhombus is A = (d1 × d2) / 2. For example, a rhombus with diagonals of 10 ft and 6 ft has an area of (10 × 6) / 2 = 30 ft².
How do I find the side length of a rhombus from its diagonals?
A rhombus's diagonals bisect each other at 90°, so each side is the hypotenuse of a right triangle with legs equal to half of each diagonal: s = √((d1/2)² + (d2/2)²). For diagonals of 10 ft and 6 ft, s = √(5² + 3²) = √34 ≈ 5.83 ft.
Can I calculate rhombus area a different way, without diagonals?
Yes. If you know the base (side length) and the perpendicular height, use A = base × height. If you know the side length and one interior angle, use A = s² × sin(θ). All three formulas give the same area for the same rhombus.
How do I find the perimeter of a rhombus?
Since all four sides of a rhombus are equal, the perimeter is P = 4s, where s is the side length. Once you know the side length (from the diagonals or directly), multiply it by 4.

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