What this calculator does
A parallelogram has two pairs of parallel sides, and its area of parallelogram depends on the base and the perpendicular height between the parallel sides, the same principle as a rectangle but allowing the sides to lean. The slant of the sides changes the shape without changing the area, as long as the base and height stay the same.
This calculator covers the two common ways a parallelogram’s area is actually known: directly from a base and height, or from two adjacent sides and the angle between them, when no height has been measured separately.
The formula
With a base and height known, area of parallelogram is simply base × height, the same as a rectangle. With two sides and the included angle instead, area = a × b × sin(angle), since the height works out to b × sin(angle) once the angle between the sides is known, and multiplying by the base a gives the same area.
| Term | Meaning |
|---|---|
| Base, height | One side of the parallelogram and the perpendicular distance to the opposite side. |
| a, b | Two adjacent sides, used with the included angle when no height is known. |
| θ | The interior angle between sides a and b. |
The inputs explained
| Field | What to enter |
|---|---|
| Known values | Choose which measurements you know: base and height, or two sides and the angle between them. |
| Base, or side a | The base (for base and height), or side a (for the two-sides method). |
| Height, or side b | The height (for base and height), or side b (for the two-sides method). |
| Included angle in degrees (two-sides method only) | The included angle in degrees, used only for the two-sides method. |
When to use it
A sloped panel or garden bed with a known height
A parallelogram-shaped garden bed, panel or paved area with a measured base and perpendicular height uses the base and height method directly, the fastest route to the area.
How to find the area of a parallelogram without a height
When only two adjacent side lengths and the angle between them are known, common in trigonometry and vector problems, the two-sides method finds the area without a separate height measurement.
Checking a parallelogram area formula against a rectangle
Shearing a rectangle into a parallelogram, sliding the top edge sideways while keeping the base and height fixed, does not change the area at all, only the side lengths and angles.
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.
Parallelogram area formula from base and height
A fixed height of 5, across a range of base lengths, using the base-and-height method.
Area of a parallelogram from two sides and the angle between them
Two sides fixed at 8 and 5, with the angle between them varying, using the two-sides method.
| Included angle | Area | Height (relative to side a) |
|---|---|---|
| 30° | 20.000 | 2.500 |
| 60° | 34.641 | 4.330 |
| 90° | 40.000 | 5.000 |
| 120° | 34.641 | 4.330 |
| 150° | 20.000 | 2.500 |
Questions
What is the area of parallelogram formula?
Area = base × height, using the perpendicular height between the base and its opposite side, not the length of the slanted adjacent side.
How do you find the area of a parallelogram without the height?
Use two adjacent sides and the angle between them instead: area = a × b × sin(angle). This avoids needing a separate perpendicular height measurement.
How is parallelogram area different from a rectangle’s?
It is not, once base and height are known: both use base × height. The difference only shows up in the side lengths and angles, since a parallelogram’s sides can lean while a rectangle’s cannot.
Is a rhombus just a special parallelogram?
Yes. A rhombus is a parallelogram where all four sides happen to be equal in length. Its area can still be found from base and height or from sides and angle, though the dedicated rhombus area calculator also offers a diagonals-based method.
For a parallelogram with all four sides equal, see the rhombus area calculator. For area, perimeter and diagonals together, see the full parallelogram & rhombus calculator.