Rhombus Area & Perimeter Calculator
Rhombus Area & Perimeter Calculator
A rhombus is a four-sided shape with all sides equal, whose diagonals always cross at right angles and bisect each other. Enter the two diagonals, and this calculator finds the area, the side length, and the perimeter, along with a diagram and the full step-by-step working.
The area formula works because the two diagonals always split a rhombus into four congruent right triangles — multiplying the diagonals together and halving the result is mathematically equivalent to summing those four triangle areas, which is a cleaner shortcut than computing each triangle individually. The side length falls out of the same right-triangle structure via the Pythagorean theorem, since each half-diagonal pair forms the two legs of one of those right triangles, with the rhombus's side as the hypotenuse.
- Area = (p × q) / 2, so diagonals of 8 and 6 give an area of (8 × 6) / 2 = 24 square units - this works because the diagonals split the rhombus into four congruent right triangles.
- Side = √((p/2)² + (q/2)²), found via the Pythagorean theorem, since each half-diagonal forms a right triangle with a side - for diagonals 8 and 6, the side is √(4² + 3²) = √25 = 5.
- Perimeter = 4 × side, since all four sides are equal - for a side of 5, that's 4 × 5 = 20 units.
How do I find the area of a rhombus from its diagonals?
Use Area = (p × q) / 2, where p and q are the two diagonals. For diagonals 8 and 6: (8 × 6) / 2 = 24.
Is a rhombus the same as a square?
A square is a special rhombus where the diagonals are also equal in length (making all angles 90°) - a general rhombus can be "squashed" at any angle while keeping all four sides equal.
Rhombus Area & Perimeter Calculator
A rhombus is a four-sided shape with all sides equal, whose diagonals always cross at right angles and bisect each other. Enter the two diagonals, and this calculator finds the area, the side length, and the perimeter, along with a diagram and the full step-by-step working.
The area formula works because the two diagonals always split a rhombus into four congruent right triangles — multiplying the diagonals together and halving the result is mathematically equivalent to summing those four triangle areas, which is a cleaner shortcut than computing each triangle individually. The side length falls out of the same right-triangle structure via the Pythagorean theorem, since each half-diagonal pair forms the two legs of one of those right triangles, with the rhombus's side as the hypotenuse.
- Area = (p × q) / 2, so diagonals of 8 and 6 give an area of (8 × 6) / 2 = 24 square units - this works because the diagonals split the rhombus into four congruent right triangles.
- Side = √((p/2)² + (q/2)²), found via the Pythagorean theorem, since each half-diagonal forms a right triangle with a side - for diagonals 8 and 6, the side is √(4² + 3²) = √25 = 5.
- Perimeter = 4 × side, since all four sides are equal - for a side of 5, that's 4 × 5 = 20 units.
How do I find the area of a rhombus from its diagonals?
Use Area = (p × q) / 2, where p and q are the two diagonals. For diagonals 8 and 6: (8 × 6) / 2 = 24.
Is a rhombus the same as a square?
A square is a special rhombus where the diagonals are also equal in length (making all angles 90°) - a general rhombus can be "squashed" at any angle while keeping all four sides equal.