Parallelogram Calculator
Calculate area, perimeter, diagonals, and more from any known values
Parallelogram Calculator
How to Use the Parallelogram Calculator
- Select Input Method: Choose how you want to define the parallelogram - by base and height, base/side/angle, or diagonals
- Enter Values: Input the known measurements
- View Results: All properties are calculated automatically including area, perimeter, diagonals, and angles
- Copy Values: Click the copy button next to any result
Understanding Parallelograms
A parallelogram is a quadrilateral with two pairs of parallel sides. It is one of the most fundamental shapes in geometry, with many practical applications in architecture, engineering, and design.
Key Properties:
- Opposite sides are equal: If sides are a and b, then the parallelogram has two sides of length a and two of length b
- Opposite sides are parallel: This is the defining property
- Opposite angles are equal: Angles at opposite corners are congruent
- Adjacent angles are supplementary: Any two adjacent angles sum to 180°
- Diagonals bisect each other: They meet at their midpoints but are not necessarily equal
Special Cases:
- Rectangle: A parallelogram with all 90° angles
- Rhombus: A parallelogram with all sides equal
- Square: A parallelogram that is both a rectangle and a rhombus
Parallelogram Formulas
Area Formulas
Other Formulas
Practical Applications
Architecture & Construction
- Roof pitch calculations
- Sloped surface area estimation
- Window and door frames
- Decorative patterns and tiles
Engineering
- Force vector analysis
- Mechanical linkages
- Structural stability
- Bridge design components
Art & Design
- Perspective drawing
- Pattern and textile design
- Graphic design layouts
- 3D modeling projections
Physics & Math
- Vector addition (parallelogram rule)
- Area transformations
- Coordinate geometry
- Linear algebra concepts
Frequently Asked Questions
How do I find the area of a parallelogram?
The area of a parallelogram is calculated by multiplying the base by the perpendicular height: A = b × h. Alternatively, use A = b × a × sin(θ), where a is the side length and θ is the included angle.
What is the perimeter formula for a parallelogram?
The perimeter of a parallelogram is P = 2(a + b), where a and b are the lengths of the two different sides. Since opposite sides are equal, you simply add two adjacent sides and multiply by 2.
How do I calculate the diagonals of a parallelogram?
The diagonals can be calculated using the law of cosines: d₁ = √(a² + b² - 2ab·cos(θ)) and d₂ = √(a² + b² + 2ab·cos(θ)), where a and b are the sides and θ is one of the angles.
What is the parallelogram law?
The parallelogram law states that the sum of the squares of the diagonals equals twice the sum of the squares of the sides: d₁² + d₂² = 2(a² + b²). This is useful for checking calculations or finding missing values.
What are the properties of a parallelogram?
A parallelogram has: (1) opposite sides that are equal and parallel, (2) opposite angles that are equal, (3) adjacent angles that are supplementary (sum to 180°), and (4) diagonals that bisect each other but are not necessarily equal.