Rhombus Area: worked example
| First diagonal | 8 |
|---|---|
| Second diagonal | 6 |
| Area | 24 |
| Side length | 5 |
| Perimeter | 20 |
Rhombus Area: formula
Enter the lengths of the two diagonals, which cross at right angles at the center of the rhombus. The area is half the product of the diagonals, each side is the square root of the sum of the squares of half of each diagonal, and the perimeter is four times the side. Measure the diagonals from corner to opposite corner.
Use the same unit.
Rhombus Area: changing First diagonal
| First diagonal | Area | Side length | Perimeter |
|---|---|---|---|
| 6 | 18 | 4.2 | 17 |
| 7 | 21 | 4.6 | 18.4 |
| 8 (example) | 24 | 5 | 20 |
| 9 | 27 | 5.4 | 21.6 |
| 10 | 30 | 5.8 | 23.3 |
Rhombus Area: compare input ranges
| Input | Tested from | To | Area: low input | Area: high input | Swing |
|---|---|---|---|---|---|
| First diagonal | 7 | 9 | 21 | 27 | 6 (25%) |
| Second diagonal | 5.4 | 6.6 | 21.6 | 26.4 | 4.8 (20%) |
Rhombus Area: individual input comparisons
| Input | Value | Area | Side length | Perimeter |
|---|---|---|---|---|
| First diagonal | 6 | 18 | 4.2 | 17 |
| 7 | 21 | 4.6 | 18.4 | |
| 8 | 24 | 5 | 20 | |
| 9 | 27 | 5.4 | 21.6 | |
| 10 | 30 | 5.8 | 23.3 | |
| Second diagonal | 4.8 | 19.2 | 4.7 | 18.7 |
| 5.4 | 21.6 | 4.8 | 19.3 | |
| 6 | 24 | 5 | 20 | |
| 6.6 | 26.4 | 5.2 | 20.7 | |
| 7.2 | 28.8 | 5.4 | 21.5 |
Rhombus Area: combined input changes
| First diagonal / Second diagonal | 4.8 | 6 | 7.2 |
|---|---|---|---|
| 6 | 14.4 | 18 | 21.6 |
| 7 | 16.8 | 21 | 25.2 |
| 8 | 19.2 | 24 | 28.8 |
| 9 | 21.6 | 27 | 32.4 |
| 10 | 24 | 30 | 36 |
Rhombus Area: which assumptions move the result?
Rhombus Area: values and definitions
| Quantity and definition | Value used |
|---|---|
| First diagonal | 8 |
| Second diagonal | 6 |
| Area | 24 |
| Side length | 5 |
| Perimeter | 20 |
Rhombus Area: half and double First diagonal
| First diagonal | Area |
|---|---|
| 4 | 12 |
| 8 | 24 |
| 16 | 48 |
Common error: Multiplying a side by the other side. A rhombus with the same side lengths can be squashed flat or stood upright, so the sides alone do not fix the area.
A square is a special rhombus with equal diagonals. The diagonals formula requires that you know both diagonals. Units for area are squared, so a diagonal in feet gives an area in square feet.
Convert both diagonal measurements to the same length unit before multiplying them. A numerical product of mixed feet and inches is not already an area expressed in either squared unit.
Geometry calculators: Hemisphere Volume Calculator, Cone Frustum Calculator, Capsule Volume Calculator, Triangular Prism Volume Calculator, Law of Sines Calculator, Cube Calculator.
The two diagonals of a rhombus cross at right angles and cut each other in half, which splits it into four matching right triangles. That makes the area simply half the product of the diagonals: 8 by 6 gives 24. The same triangles give the side as the hypotenuse of 4 and 3, which is 5, so the perimeter is 20.
Measure the diagonals corner to corner through the middle. Measuring along an edge gives the side, not a diagonal, and changes the answer.
See the parallelogram, rectangle and trapezoid calculators for related shapes, the Pythagorean theorem page for the sides, and the triangle area calculator since each diagonal splits a rhombus into triangles. The regular polygon page covers shapes with equal sides and angles.
How do I find the area of a rhombus from its diagonals?
Multiply the two diagonals and divide by two. Diagonals of 8 and 6 give an area of 24.
What are the properties of a rhombus?
All four sides are equal, opposite angles are equal and the diagonals bisect each other at right angles.
Is a square a rhombus?
Yes. A square is a rhombus with four right angles, so its diagonals are equal, and every square is a rhombus though not every rhombus is a square.