Rhombus Calculator
Enter the two diagonals of a rhombus to find its area, side length and perimeter.
units
units
- 1
Side = √((p⁄2)² + (q⁄2)²)
√((8 ÷ 2)² + (6 ÷ 2)²) = 5Diagonals bisect at right angles, making each side the hypotenuse of a right triangle. - 2
Perimeter = 4 × side
4 × 5 = 20 - 3
Area = p × q ÷ 2
8 × 6 ÷ 2 = 24
Formula
How this is calculated
The calculator takes the two diagonals of a rhombus, p and q, expressed in the same length unit (any consistent unit works since the result is purely geometric). In a rhombus the diagonals always cross each other at right angles and bisect one another, so each one is split into two equal halves of length p⁄2 and q⁄2.
The area follows directly from this perpendicular-diagonal property: Area = (p × q) ⁄ 2, reported in square units. Because the crossing point divides the shape into four congruent right triangles, each side is the hypotenuse of a triangle with legs p⁄2 and q⁄2, giving Side = √((p⁄2)² + (q⁄2)²) by the Pythagorean theorem. All four sides are equal, so the perimeter is simply 4 × side.
The tool assumes a true (non-degenerate) rhombus, so both diagonals must be positive; zero or negative inputs are rejected. It does not compute the interior angles, and when the two diagonals are equal the rhombus is a square.
Examples
| Input | Result |
|---|---|
| p = 8, q = 6 | Area = 24, Side = 5, Perimeter = 20 |
About this calculator
A rhombus is a quadrilateral with all four sides equal in length, often described as a "diamond" shape. Its diagonals always intersect at right angles and bisect each other, which makes the area simply half the product of the two diagonals.
Because the diagonals cut the rhombus into four congruent right triangles, each side equals the hypotenuse formed by half of each diagonal — √((p⁄2)² + (q⁄2)²). The perimeter is then four times that side length, since all sides are equal.
Frequently asked questions
Multiply the two diagonals and divide by two: Area = (p × q) ÷ 2. Diagonals of 8 and 6 give an area of 24 square units.
The diagonals meet at right angles, so each side is the hypotenuse of a right triangle: side = √((p⁄2)² + (q⁄2)²).
A square is a special rhombus with equal diagonals and right angles. A general rhombus has equal sides but its angles need not be 90 degrees.
Also known as
TG we-Calculate Editorial Team. (2026). Rhombus Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rhombus-calculator
TG we-Calculate Editorial Team. "Rhombus Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/rhombus-calculator.
TG we-Calculate Editorial Team, "Rhombus Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rhombus-calculator
@misc{wecalculate_rhombus_calculator, title = {Rhombus Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rhombus-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?