ConverterHub

Rhombus Calculator

Find the area and perimeter of a rhombus.

Result

240.00 units²
68.00 units

How it is calculated

Given the diagonals d1 and d2 of a rhombus, the tool returns its area and perimeter:

area = (d1 × d2) / 2

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

The two diagonals meet at 90° and split each other in half, which turns each quarter of the rhombus into a right triangle whose hypotenuse is a side. Both diagonals must be positive. The results are labelled generically as units and units², so read them in whatever length unit you entered (cm, m, inches). Two decimals are shown.

Worked example

Diagonals of 16 and 30.

  1. Area = 16 × 30 / 2 = 480 / 2 = 240.00 units²
  2. Half-diagonals 8 and 15: side = √(64 + 225) = √289 = 17
  3. Perimeter = 4 × 17 = 68.00 units

So the rhombus has an area of 240 and a perimeter of 68 in the unit you used.

Try this example →

Common mistakes

  • Typing the side and height instead of the diagonals: this tool needs both diagonals only.
  • Forgetting to divide by 2 in the area when calculating by hand: the product of the diagonals is twice the area.
  • Using a square's side for both diagonals: a square is a rhombus, but its diagonals are about 1.41 times the side, not equal to it.
  • Taking the label "units" literally: no conversion is done, so the unit of the answer is whatever unit you typed in.

About this calculator

A rhombus is a parallelogram with four equal sides whose diagonals are perpendicular bisectors of each other, so its area reduces to the elegant formula Area = (d₁ × d₂) / 2 — half the product of the diagonals — while the perimeter is simply four times the side length, itself found from the diagonals via the Pythagorean relation s = √((d₁/2)² + (d₂/2)²).

The diagonal-based formula shows up constantly outside the classroom: it's how draftsmen and machinists check diamond-shaped plates, tile setters lay out lozenge patterns, and civil engineers compute the area of rhombus-shaped road signs or kite-shaped land parcels without ever measuring an angle directly.

Geometry students, drafting and CAD professionals, and hobbyist woodworkers or quilters cutting diamond shapes all reach for this relationship because diagonals are usually easier to measure on a physical rhombus than its interior angles.

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