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Parallelogram Calculator
Computes the area of a parallelogram from base and height and, when the slanted side is given, its perimeter, the acute angle between base and side in degrees, and both diagonals.
When to use
You need the area, perimeter, angles or diagonals of a quadrilateral whose opposite sides are parallel (including rhombi).
Do not use when: All angles are right angles (use rectangle) or only one pair of sides is parallel (use trapezoid).
Formula
area = base × height; perimeter = 2 × (base + side); angle_deg = asin(height / side); diagonals = √(base² + side² ± 2·base·√(side² − height²))
Inputs
| Parameter | Type | Unit | Required | Description |
|---|---|---|---|---|
base | number | units | yes | Length of one side chosen as the base. Range: > 0 |
height | number | units | yes | Perpendicular distance between the base and its opposite side. Range: > 0 |
side | number | units | no | Length of the slanted side adjacent to the base (optional; must be at least the height). Range: > 0 |
Outputs
| Output | Type | Unit | Description |
|---|---|---|---|
area | number | units² | base × height. |
perimeter | number | units | 2 × (base + side), only when side is given. |
angle_deg | number | degrees | Acute angle between base and side = asin(height / side); the obtuse angle is 180° minus this. |
diagonal_long | number | units | √(base² + side² + 2·base·√(side² − height²)). |
diagonal_short | number | units | √(base² + side² − 2·base·√(side² − height²)). |
Example
Base 8, height 5, side 6: {"base":8,"height":5,"side":6} → {"area":40,"perimeter":28,"angle_deg":56.4427,"diagonal_long":12.372,"diagonal_short":6.8508}
Base 10, height 3: {"base":10,"height":3} → {"area":30}
GET https://tttkmbb.com/api/v1/calculate/parallelogram?base=8&height=5&side=6
Machine access
- API:
GET https://tttkmbb.com/api/v1/calculate/parallelogram(query parameters) orPOSTwith a JSON body{"inputs": {...}} - Schema: https://tttkmbb.com/api/v1/calculators/parallelogram · Markdown: https://tttkmbb.com/geometry/parallelogram.md · JSON definition: https://tttkmbb.com/geometry/parallelogram.json
- MCP: server
https://tttkmbb.com/mcp, toolrun_calculator with calculator_id="parallelogram" - OpenAPI operationId:
calculate_parallelogram_properties - Freshness:
static. Authentication: none. Rate limit: fair use (see rate limits).
Sources
- Wikipedia – Parallelogram (reference)
- Wolfram MathWorld – Parallelogram (reference)
FAQ
Why must the side be at least the height?
The height is the perpendicular distance between the parallel sides, so the slanted side can never be shorter than it; side = height gives a rectangle.
How do I compute a rhombus?
Enter side = base. The area is still base × height, or you can use diagonal_long × diagonal_short / 2.
Related calculators
- Rectangle Calculator — Special case with right angles.
- Trapezoid Calculator — Only one pair of parallel sides.
- Triangle Area Calculator — Half a parallelogram cut along a diagonal.