Key takeaways
- The area of a rhombus is A = (d₁ × d₂) / 2, using the two diagonals.
- The diagonals of a rhombus always cross at a right angle.
- A square is a special rhombus with equal diagonals.
- This formula needs diagonals, not the equal side lengths.
In this guide
What is a rhombus?
A rhombus is a parallelogram where all four sides are the same length, but the corners aren't necessarily right angles. Its two diagonals cross each other at a right angle in the middle.
Why does the area of a rhombus matter?
Rhombus shapes appear in kites, diamond floor tiles, and quilting patterns, and their area is unusually easy to find using nothing but the two diagonals.
The two diagonals of a rhombus always cross at exactly 90°, splitting the shape into four identical right triangles. Multiplying the diagonals and halving the result adds up the area of all four triangles at once — which is exactly why the formula divides by 2.
The formula
| Symbol | What it means | Example |
|---|---|---|
| A | The area you want to find | 60 m² |
| d₁ | The length of the first diagonal | 10 m |
| d₂ | The length of the second diagonal | 12 m |
How to find the area step by step
- 1Measure the first diagonal, d₁. From one corner to the opposite corner.
- 2Measure the second diagonal, d₂. Connecting the other two corners.
- 3Multiply the two diagonals together.
- 4Divide the result by 2.
Now try it yourself. Change the two diagonals in the calculator below and watch the area update, with every step shown.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Forgetting to divide by 2. The diagonals split the rhombus into four right triangles, which is why the result is halved.
- Confusing a rhombus with a general [parallelogram](/calculator/area-parallelogram). A general parallelogram uses base × height instead, since its diagonals aren't perpendicular.
- Assuming the diagonals are equal. Unless the rhombus is also a square, the two diagonals usually have different lengths.
Tips and tricks
- If both diagonals end up equal, the rhombus is actually a square, and either area formula gives the same answer.
- Working backwards from area and one diagonal? Multiply the area by 2 and divide by the known diagonal to find the other one.
Where you'll use it in real life
- Crafts: working out the area of a rhombus-shaped kite.
- Flooring: tiling with diamond-shaped floor tiles.
- Quilting: checking fabric needed for a rhombus quilt patch.
- Jewelry design: estimating the face area of a diamond-cut gem outline.
Quick summary
To find the area of a rhombus, multiply its two diagonals together and divide by 2. The diagonals always cross at a right angle, which is why this shortcut works. Use the calculator above to check your own rhombus instantly.
Worked example
You're planting a rhombus-shaped (diamond-shaped) flower bed, with diagonals measuring 10 meters and 12 meters. How much ground space does the flower bed cover?
- 01A = (d₁ × d₂) / 2
- 02A = (10 × 12) / 2
- 03A = 120 / 2
- 04A = 60 m²
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I find the area of a rhombus if I only know the side length and an angle?
Use the parallelogram-style formula instead: area = side² × sin(angle), since a rhombus is a special parallelogram with equal sides.
Why does the rhombus area formula divide by 2?
The two diagonals of a rhombus cross at right angles and split it into four equal right triangles. Multiplying the diagonals and halving gives the combined area of all four triangles.
Is a square a type of rhombus?
Yes, a square is a rhombus where the angles also happen to be 90°. Its diagonals are equal in length, and the same area formula still works.
Does it matter which diagonal I call d₁ and which I call d₂?
No, since multiplication doesn't depend on order, d₁ × d₂ gives the same result either way.
