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Rhombus Calculator

Find a rhombus’s area and perimeter from its diagonals.

How it is calculated

You enter the two diagonals d1 and d2 in any one length unit. The tool then computes:

area = d1 × d2 / 2

side = √((d1/2)² + (d2/2)²) and perimeter = 4 × side

The diagonals of a rhombus cross at right angles and cut each other in half, so each side is the hypotenuse of a right triangle with legs d1/2 and d2/2. Both diagonals must be above zero. The area is in the square of your unit and the perimeter in the unit itself. Results are rounded to two decimals, and the side length is not shown separately.

Worked example

A rhombus with diagonals 10 and 24.

  1. Area = 10 × 24 / 2 = 120.00
  2. Half-diagonals are 5 and 12, so side = √(25 + 144) = √169 = 13
  3. Perimeter = 4 × 13 = 52.00

The rhombus covers 120 square units and its boundary is 52 units long.

Try this example →

Common mistakes

  • Entering a side length and a diagonal: both boxes need the two diagonals, not side and height.
  • Multiplying the diagonals without halving: d1 × d2 alone is twice the area.
  • Mixing units, such as one diagonal in cm and the other in m, which makes both results meaningless.
  • Reading the area as a length: area is in square units, while only the perimeter shares the unit you typed.

About this calculator

This calculator finds a rhombus's area and perimeter from its two diagonals, using the geometric property that a rhombus's diagonals are always perpendicular and bisect each other, which makes the area equal to half the product of the diagonal lengths. The perimeter is then found separately from the side length, which the diagonals also let you derive using the Pythagorean theorem on the right triangles they form.

This shape and its diagonal-based formulas come up in geometry coursework when students calculate area from diagonals rather than base and height, which is the more common approach for other quadrilaterals. It's also relevant in design and engineering contexts where rhombus or diamond-shaped tiles, panels, kite frames or decorative patterns are measured and cut based on their diagonal dimensions rather than side lengths, since diagonals are often what's specified or easiest to measure in these applications.

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Comments (1)

  • Editorial team

    Often you know a side and one diagonal rather than both diagonals. Then the other diagonal is 2 × √(side² − (known diagonal ÷ 2)²). With a side of 5 and one diagonal of 6, the other is 2 × √(25 − 9) = 8, and entering 6 and 8 returns an area of 24.00 and a perimeter of 20.00. Are you measuring tiles, panels or a kite frame? Tell us which dimensions you usually have in hand.

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