A parallelogram has two pairs of parallel sides. Rectangles and rhombuses are special cases.
How to use the Parallelogram Calculator
- Side a
- Side b
- Angle between sides
Results update as you type, and every field accepts the units shown in its menu.
How it works
The area is base times height, where height = b × sin θ. The diagonals follow from the law of cosines.
Inputs explained
| Field | What to enter |
|---|---|
| Side a | Units: m, cm, mm, km, in, ft … |
| Side b | Units: m, cm, mm, km, in, ft … |
| Angle between sides | In ° |
What each result means
- Area = [Side a]×[Side b]×sin(rad([Angle between sides]))
- Perimeter = 2×([Side a] + [Side b])
- Long diagonal = sqrt([Side a]^2 + [Side b]^2 + 2×[Side a]×[Side b]×abs(cos(rad([Angle between sides]))))
- Short diagonal = sqrt([Side a]^2 + [Side b]^2 – 2×[Side a]×[Side b]×abs(cos(rad([Angle between sides]))))
Example values
How the main result changes when Side a changes and everything else stays at the example values above:
| Side a (m) | Area (m²) |
|---|---|
| 5 | 25.98 |
| 7.5 | 38.97 |
| 10 | 51.96 |
| 12.5 | 64.95 |
| 15 | 77.94 |
| 20 | 103.92 |
Formula
Area = a × b × sin(θ)Diagonals: √(a² + b² ± 2ab cos θ)Worked example
Inputs — Side a: 10 m; Side b: 6 m; Angle between sides: 60 °.
Results — Area = 51.96 m²; Perimeter = 32 m; Long diagonal = 14 m; Short diagonal = 8.72 m.
Frequently asked questions
What if the angle is 90°?
The parallelogram is a rectangle.
Do opposite angles match?
Yes, and adjacent angles add to 180°.
What formula does the Parallelogram Calculator use?
Area = a × b × sin(θ).