Parallelogram Calculator
Calculate area, perimeter & diagonal of any parallelogram instantly
Calculation Results
Enter parallelogram measurements to calculate properties.
Base (b): units
Height (h): units
Area (A): square units
Perimeter (P): units
Diagonal (d): units
Side (s): units
Angle (
Angle (
Parallelogram Diagram
The Parallelogram: A Versatile Geometric Shape
A parallelogram is a four-sided polygon (a quadrilateral) where opposite sides are parallel and equal in length. The opposite angles are also equal, and adjacent angles are supplementary.
Key Properties of a Parallelogram
- Base (b) - One of the sides used as the reference for height.
- Height (h) - The perpendicular distance from the base to the opposite side.
- Area (A) - The space enclosed within the parallelogram (A = b × h).
- Perimeter (P) - Total distance around the shape (P = 2(a + b) where a and b are adjacent sides).
- Diagonals - Parallelograms have two diagonals that bisect each other but are not necessarily equal.
- Angles - Opposite angles are equal, and adjacent angles add up to 180°.
Mathematical Equations of a Parallelogram
- Area
A = b × h - Perimeter
P = 2(a + b) - Diagonal 1 (d₁)
d₁ = √(a² + b² + 2ab cosθ) - Diagonal 2 (d₂)
d₂ = √(a² + b² - 2ab cosθ)
Why Are Parallelograms Important?
- Engineering - Parallelogram linkages are used in mechanical arms and devices.
- Architecture - Parallelogram shapes appear in trusses and beams.
- Mathematics - A key figure in vector geometry and linear algebra.
- Art & Design - Frequently used in tiling patterns and perspective drawing.
Facts About Parallelograms
- The word "parallelogram" comes from the Greek "parallelogrammon", meaning "bounded by parallel lines".
- A square, rectangle, and rhombus are all special types of parallelograms.
- The diagonals of a parallelogram always bisect each other.
Parallelograms blend simplicity with versatility. Their symmetrical structure and mathematical properties make them vital in geometry, physics, design, and more.
Parallelogram Formulas
- Area (A): A = b × h
- Area (A): Using two adjacent sides and included angle:
A = ab · sin(θ) - Perimeter (P): P = 2(a + b)
- Height (h): h = A / b
- Base (b): b = A / h
- Diagonal (d₁/d₂): d = √(a² + b² ± 2ab cosθ)
Base (b)
Height (h)
Area (A)
Diagonal
How to Use the Parallelogram Calculator
This Parallelogram Calculator helps compute area, perimeter, height, or side lengths depending on the known values.
1 Select the Input Type
Choose what you know:
- Base and height
- Area and base
- Area and Height
- Perimeter and Base
- Base, Side & included Angle (θ)
Example: If you know base = 10 and height = 5, choose those inputs.
2 Enter the Known Value(s)
Enter numeric values in the fields.
- Use only positive values.
- Use decimals if needed (e.g., 7.5).
Example: Base = 8, Height = 4
3 Click "Calculate"
The calculator will display:
- Area
- Perimeter
- Diagonal (if angle is given)
Example Use Cases
- Calculating floor space in slanted structures like attics.
- Determining beam length in roof trusses.
- Finding the angle between sides using diagonals.
Example Calculations
-
Example 1: Base = 10 units, Height = 6 units
- Area = 60 units²
- Perimeter = (2 × (10 + 6)) = 32 units
-
Example 2: Area = 72 units², Base = 12 units
- Height = 6 units
- Perimeter requires side info
-
Example 3: Sides a = 8, b = 6, θ = 60°
- Diagonal ≈ 11.66 units (using cosine formula)
Frequently Asked Questions
Use the formula:
A = b × h
No. While all rectangles are parallelograms, not all parallelograms have right angles, which is required for rectangles.
Yes, the diagonals always bisect each other but are not generally equal in length.
- Physics: Force diagrams
- Engineering: Parallelogram linkages
- Design: Tiling, weaving patterns
- Graphics: 3D transformations and perspective