Rhombus Calculator

Calculate the area, perimeter, side, diagonals, and angles of a rhombus. Enter two diagonals, or a side and angle. Free online rhombus calculator.

Rhombus Properties

Area

24

square units

Perimeter

20

units

Side5
Diagonal d16
Diagonal d28
Acute Angle73.7398°

Input Mode

Diagonals

Formulas Used

  • Area = (d1 × d2) / 2 = (6 × 8) / 2 = 24
  • Side = √((d1/2)² + (d2/2)²) = 5
  • Perimeter = 4 × side = 20
  • Acute angle = 2 × arctan(min(d1,d2) / max(d1,d2)) = 73.7398° (obtuse = 180° − acute)

Quick Answer

To calculate rhombus properties from two diagonals: Area = (d1 x d2) / 2, side = sqrt((d1/2)^2 + (d2/2)^2), Perimeter = 4 x side. For diagonals 6 and 8: Area = 24 square units, side = 5, Perimeter = 20 units, angles of 73.74 and 106.26 degrees. Alternative input with a side and angle: Area = side^2 x sin(angle).

Key Facts

  • Formula: Area = (d1 x d2) / 2 (half the product of the diagonals)
  • Formula: Perimeter = 4 x side
  • Formula: Area = side^2 x sin(angle) when a side and angle are known
  • Diagonals 6 and 8 give area 24, side 5, perimeter 20
  • The diagonals of a rhombus always bisect each other at 90 degrees
  • All four sides of a rhombus are equal; opposite angles are equal
  • A square is a rhombus with 90-degree angles

Frequently Asked Questions

From the two diagonals: Area = (d1 x d2) / 2. Diagonals 6 and 8 give area 24 square units. From a side and angle: Area = side^2 x sin(angle). Both formulas always agree for the same rhombus.

The diagonals bisect each other at right angles, so each side is the hypotenuse of a right triangle with legs d1/2 and d2/2: side = sqrt((d1/2)^2 + (d2/2)^2). Diagonals 6 and 8 give side = sqrt(9 + 16) = 5.

All four sides are equal, so Perimeter = 4 x side. With side 5, the perimeter is 20 units. From the diagonals, first compute the side with the Pythagorean theorem, then multiply by 4.

Yes. This is the defining property that makes the area formula work: the diagonals split the rhombus into four congruent right triangles, each with area (d1/2)(d2/2)/2, totaling (d1 x d2)/2.

A rhombus requires four equal sides; a square adds four 90-degree angles. Every square is a rhombus, but a rhombus is only a square when its angles are all right angles (equivalently, when d1 = d2).

From the diagonals, the angle at the vertex where d1 meets the side follows from arctan(d2/d1); the full interior angle is 2 x arctan(d2/d1) or its supplement. Diagonals 6 and 8 give angles of 73.74 and 106.26 degrees. From a side and one angle, the opposite angle is equal and adjacent angles sum to 180.