Rhombus Area
A = (d₁·d₂)/2P = 4·√((d₁/2)²+(d₂/2)²)The area of a rhombus is the product of its two diagonals divided by two.
The formula works because a rhombus’s diagonals cross at right angles and bisect each other. That splits the figure into four identical right triangles, and their sum comes to exactly half of the rectangle enclosing the diagonals.
The perimeter comes from Pythagoras applied to half of each diagonal, multiplied by four — since all four sides of a rhombus are equal.
A rhombus is the quadrilateral with four equal sides. If its angles are also right angles, it is a square — so every square is a rhombus, but not every rhombus is a square.
What is commonly called a "diamond" is the same figure, merely resting on a vertex instead of a side. There is no geometric difference, only orientation.
Because all sides are equal, a rhombus is also a parallelogram. The base times height formula still applies — but measuring the diagonals is usually easier in practice.
- Tiles laid in a diagonal pattern, very common in wall and floor coverings.
- Warning road signs in some countries.
- Chain-link fencing, whose mesh forms rhombuses.
- Fabric pieces cut on the bias in sewing.
Frequently asked questions
Yes. A rhombus only requires four equal sides; a square adds the requirement of right angles. Every square satisfies both conditions.
It works via the parallelogram formula, base times height, since a rhombus is a special case of one. This calculator uses the diagonals, which are usually easier to measure.
No, except in the case of a square. They cross at right angles and bisect each other, but have different lengths.
None geometrically. It is the same figure, merely resting on a vertex rather than a side.