Parallelogram Calculator
Calculate area, perimeter, diagonals, and angles of any parallelogram
Perpendicular distance between the parallel sides
The slanted side (must be ≥ height)
Any interior angle of the parallelogram
The angle where the diagonals intersect
Parallelogram Properties
Area
Perimeter
Height
Interior Angle
°
Base (b)
Side (a)
Diagonal d₁
Diagonal d₂
Acute Angle
°
Opposite angles are equal
Obtuse Angle
°
Adjacent angles sum to 180°
Parallelogram Formulas
Area
A = b × h
Perimeter
P = 2(a + b)
Area (from angle)
A = a × b × sin(θ)
Parallelogram Law
d₁² + d₂² = 2(a² + b²)
Find this parallelogram calculator helpful?
Share it with students and math enthusiasts!
Related Calculators
Other calculators you might find useful.
Prime Number Calculator
Check if a number is prime, find prime factors, and generate prime sequences
WHIP Calculator
Calculate Walks plus Hits per Innings Pitched for baseball pitchers
Inverse Variation Calculator
Calculate inverse variation relationships where xy = k (constant)
Area Calculator
Calculate the area of rectangles, circles, triangles, and other 2D shapes instantly
Direct Variation Calculator
Calculate the constant of variation and solve direct variation equations (y = kx)
Pythagorean Theorem Calculator
Calculate any side of a right triangle using the Pythagorean theorem a² + b² = c²
About Parallelogram Calculator
What is a Parallelogram?
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides are equal in length, and opposite angles are equal. Adjacent angles are supplementary, meaning they add up to 180°.
Parallelograms are fundamental shapes in geometry and are commonly found in architecture, engineering, tile patterns, and everyday objects.
Types of Parallelograms
General Parallelogram
A parallelogram with no special properties beyond having two pairs of parallel sides. Adjacent sides can have different lengths.
Rectangle
A parallelogram where all angles are 90°. The diagonals are equal in length.
Rhombus
A parallelogram where all sides are equal in length. The diagonals bisect each other at right angles.
Square
A parallelogram that is both a rectangle and a rhombus—all sides equal and all angles 90°.
How to Use This Calculator
From Base & Height Mode
- Select Base & Height mode
- Enter the base length (a)
- Enter the height (h) — perpendicular distance between parallel sides
- Optionally enter the side length (b) for perimeter and diagonal calculations
- View all calculated properties instantly
From Sides & Angle Mode
- Select Sides & Angle mode
- Enter both side lengths (a and b)
- Enter an interior angle (in degrees)
- The calculator computes area, height, diagonals, and all other properties
From Diagonals Mode
- Select From Diagonals mode
- Enter both diagonal lengths (d₁ and d₂)
- Enter the angle between the diagonals
- The calculator derives area and other properties
Parallelogram Formulas
Core Formulas
| Property | Formula | Description |
|---|---|---|
| Area (base × height) | A = b × h | Base times perpendicular height |
| Area (sides × sin) | A = a × b × sin(θ) | Product of sides times sine of included angle |
| Perimeter | P = 2(a + b) | Sum of all four sides |
| Height | h = A / b | Area divided by base |
Diagonal Formulas
| Property | Formula |
|---|---|
| Diagonal d₁ | d₁ = √(a² + b² + 2ab·cos(θ)) |
| Diagonal d₂ | d₂ = √(a² + b² - 2ab·cos(θ)) |
| Diagonal relationship | d₁² + d₂² = 2(a² + b²) |
Angle Formulas
| Property | Formula |
|---|---|
| Adjacent angles | θ₁ + θ₂ = 180° |
| Opposite angles | Equal to each other |
Understanding Parallelogram Properties
The Parallelogram Law
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 a fundamental property that distinguishes parallelograms from other quadrilaterals.
Diagonals
In a parallelogram, the diagonals bisect each other (they cut each other in half at their intersection point). However, unlike in a rectangle, they are generally not equal in length.
Height vs. Side Length
The height (h) is the perpendicular distance between two parallel sides, not the length of the slanted side. For a parallelogram with sides a and b and angle θ: h = b × sin(θ)
Real-World Applications
Architecture & Construction
- Roof structures and support beams
- Window and door frame designs
- Tile and flooring patterns
- Bridge trusses
Engineering
- Mechanical linkages (parallelogram motion)
- Force vectors and resolution
- Structural analysis
Everyday Objects
- Erasers and boxes viewed at angles
- Laptop screen hinges
- Some table designs
- Pattern designs in textiles
Frequently Asked Questions
What's the difference between a parallelogram and a rhombus?
A rhombus is a special type of parallelogram where all four sides are equal in length. In a general parallelogram, only opposite sides are equal.
How do I find the area if I only know the sides?
You need to know at least one angle in addition to the sides. The area formula using sides is A = a × b × sin(θ), where θ is any interior angle.
Are the diagonals of a parallelogram equal?
Not in a general parallelogram. The diagonals are only equal in a rectangle (a special parallelogram with all 90° angles).
What is the height of a parallelogram?
The height is the perpendicular distance between two parallel sides. It's different from the side length unless the parallelogram is a rectangle.
Can I calculate area from just the diagonals?
Yes, if you also know the angle where the diagonals intersect. The area is A = ½ × d₁ × d₂ × sin(α), where α is the angle between the diagonals.
Important Notes
- The height must be measured perpendicular to the base, not along a side
- All angles in a parallelogram must be between 0° and 180° (exclusive)
- Opposite angles are always equal; adjacent angles always sum to 180°
- The diagonals bisect each other but are not perpendicular (unless it's a rhombus)
Note: This calculator provides mathematical results for geometric shapes. For engineering or construction projects, always consult with qualified professionals and verify measurements.