What this calculator does
A rhombus is a four-sided shape with all four sides equal in length, a special case of a parallelogram where the two pairs of sides happen to match. The area of a rhombus can be found two different ways, depending on which measurements are actually to hand: from the two diagonals, or from a side length and an interior angle.
This calculator covers both routes, switching between the two methods with a single option, and always returns area of a rhombus as the headline figure regardless of which one you use.
The formula
From the two diagonals, area = ½ × diagonal p × diagonal q, since the diagonals of a rhombus always cross at right angles and split it into four identical right triangles. From a side length and interior angle, area = side² × sin(angle), the same relationship any parallelogram uses, simplified because a rhombus has only one side length to enter.
| Term | Meaning |
|---|---|
| p, q | The two diagonals of the rhombus, which always cross at right angles. |
| s | Side length: all four sides of a rhombus are equal. |
| θ | Interior angle between two adjacent sides. |
The inputs explained
| Field | What to enter |
|---|---|
| Known values | Choose from Two diagonals, Side length and interior angle. |
| Diagonal p, or side length | Diagonal p (for the two-diagonals method), or the side length (for the side-and-angle method). |
| Diagonal q, or interior angle in degrees | Diagonal q (for the two-diagonals method), or the interior angle in degrees (for the side-and-angle method). |
When to use it
A rhombus area formula from measured diagonals
A kite-shaped tile, road sign or garden bed measured along its two diagonals gets its area directly from ½ × p × q, without needing a side length or angle at all.
How to find the area of a rhombus from a side and angle
A rhombus given by its side length and one interior angle, common in trigonometry problems, is solved with the side-and-angle method instead of the diagonals.
Checking a rhombus area result both ways
Since a rhombus’s diagonals and side-angle description both fix the same shape, switching methods on the same rhombus and confirming the areas match is a useful check on either measurement.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Rhombus area formula from the two diagonals
A fixed second diagonal of 6, across a range of values for the first diagonal.
Area of rhombus from a side and interior angle
A fixed side length of 5, across a range of interior angle values.
| Interior angle | Area | Diagonals |
|---|---|---|
| 30° | 12.500 | 9.659 and 2.588 |
| 60° | 21.651 | 8.660 and 5.000 |
| 90° | 25.000 | 7.071 and 7.071 |
| 120° | 21.651 | 5.000 and 8.660 |
| 150° | 12.500 | 2.588 and 9.659 |
Questions
What is the area of rhombus formula using diagonals?
Area = ½ × diagonal p × diagonal q. It works because a rhombus’s diagonals always cross at right angles and bisect each other, splitting the shape into four equal right triangles.
How do you find the area of a rhombus without the diagonals?
Use the side length and one interior angle instead: area = side² × sin(angle). This gives the same area as the diagonal method for the same physical rhombus.
What is a rhombus area formula compared with a square?
A square is a special rhombus with a 90° interior angle, where side² × sin(90°) simplifies to just side², the familiar square area formula.
Do the diagonals of a rhombus always cross at 90°?
Yes, always, regardless of the rhombus’s interior angles. That right-angle crossing is what makes the ½ × p × q area formula work for any rhombus.
For a parallelogram where the sides are not necessarily equal, see the parallelogram area calculator. For area, perimeter and diagonals together, see the full parallelogram & rhombus calculator.