What this calculator does
A parallelogram is set by two adjacent sides and the angle between them. Area is base times height, but height itself depends on that angle: it is the second side’s length multiplied by the sine of the angle it makes with the base, which is what actually determines how “tall” the shape stands.
A rhombus is the special case where both sides are equal, and this calculator handles it the same way: set the two side lengths equal and the diagonals, area and perimeter all come out correctly for a rhombus, including the useful fact that its diagonals always cross at a right angle.
The formula
Area equals a·b·sin θ, which peaks when θ is 90°: at that point the shape is a rectangle and both diagonals become equal. Away from 90° the shape leans over, the height on side a drops, and the two diagonals split apart: one lengthens as the other shortens, following the law of cosines applied to the triangle each diagonal forms with two sides.
| Term | Meaning |
|---|---|
| a, b | The two adjacent side lengths. |
| θ | The interior angle between sides a and b. |
| Height on a | The perpendicular distance from side a to its opposite side, equal to b·sin θ. |
| Diagonals | The two lines joining opposite corners, of different lengths unless θ = 90°. |
The inputs explained
| Field | What to enter |
|---|---|
| Side a | One side length. |
| Side b | The adjacent side length. Equal to a for a rhombus. |
| Angle between them (°) | The interior angle between sides a and b, in degrees. 90° gives a rectangle. |
When to use it
A sheared or angled panel
Cladding, paving or fabric cut on the diagonal rather than square-cut still has a definite area: this calculator gives it directly from the two edge lengths and the angle between them, no decomposition into triangles required.
Checking whether a frame has racked out of square
A rectangular frame that has been pushed sideways becomes a parallelogram while its side lengths stay the same. The two diagonals, equal only at 90°, are the quickest check for how far it has moved.
Laying out a rhombus or diamond pattern
Floor tiles, kite shapes and diamond-pattern trellis are rhombi. With equal sides, the angle alone controls whether the diamond is tall and narrow or short and wide.
Force and vector diagrams
The parallelogram rule for adding two vectors places them as adjacent sides; the resultant is the diagonal between them, which this calculator’s diagonal figures correspond to directly.
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.
How area and diagonals change with the angle, sides 8 and 5
The two side lengths fixed while the angle between them sweeps from a narrow lean to past a right angle.
| Angle | Area | Diagonals |
|---|---|---|
| 30° | 20.000 | 4.440 and 12.581 |
| 45° | 28.284 | 5.695 and 12.065 |
| 60° | 34.641 | 7.000 and 11.358 |
| 90° | 40.000 | 9.434 and 9.434 |
| 120° | 34.641 | 11.358 and 7.000 |
| 150° | 20.000 | 12.581 and 4.440 |
A rhombus at 60°, side length increasing
Both sides increased together, the rhombus case, at a fixed 60° angle.
| Side length (a = b) | Area | Perimeter | Diagonals |
|---|---|---|---|
| 5 | 21.651 | 20.000 | 5.000 and 8.660 |
| 8 | 34.641 | 26.000 | 7.000 and 11.358 |
| 10 | 43.301 | 30.000 | 8.660 and 13.229 |
| 15 | 64.952 | 40.000 | 13.229 and 18.028 |
| 20 | 86.603 | 50.000 | 18.028 and 22.913 |
Questions
What is the difference between a parallelogram and a rhombus?
A rhombus is a parallelogram with all four sides equal. Every rhombus is a parallelogram, but a parallelogram is only a rhombus when its two side inputs match.
Why does the area use sine rather than the height directly?
Because b·sin θ is the height: the sine converts the angled side b into the perpendicular distance from side a, which is what area actually needs. If you already have the height, base × height works just as well.
Are the two diagonals of a parallelogram ever equal?
Only when the angle is 90°, which makes the parallelogram a rectangle. At any other angle the diagonals differ, and the gap between them grows as the angle moves further from 90°.
Do the diagonals of a rhombus cross at a right angle?
Yes, always, regardless of the angle between the sides. That perpendicular crossing is a property specific to rhombi and is often used as a definition in its own right.
How do I find the area if I only have the diagonals?
For a rhombus specifically, area equals half the product of the diagonals. For a general parallelogram the diagonals alone are not enough: you also need the angle at which they cross.
For four-sided shapes with only one pair of parallel sides, see the trapezoid calculator. For the special right-angled case, use the rectangle calculator.