Parallelogram Calculator

Calculate all properties of a parallelogram including area, perimeter, diagonals, and angles. Works with height or angle input.

Length of the base side

Length of the adjacent side

Height in same units, or angle in degrees

Area = base * height = a * h Perimeter = 2(a + b) Height = b * sin(θ) Diagonal₁ = sqrt(a^2 + b^2 + 2ab*cos(θ)) Diagonal₂ = sqrt(a^2 + b^2 - 2ab*cos(θ)) Where: a = base length b = side length h = height (perpendicular) θ = angle between sides
Example 1 (From Height): Base = 12 cm Side = 8 cm Height = 6 cm Area = 12 * 6 = 72 cm^2 Perimeter = 2(12 + 8) = 40 cm Angle = arcsin(6/8) = 48.59deg Diagonal₁ ≈ 17.09 cm Diagonal₂ ≈ 10.58 cm Example 2 (From Angle): Base = 10 ft Side = 6 ft Angle = 60deg Height = 6 * sin(60deg) = 5.20 ft Area = 10 * 5.20 = 51.96 ft^2 Perimeter = 2(10 + 6) = 32 ft

What is a parallelogram?

A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite sides are equal in length, and opposite angles are equal. Rectangles, rhombuses, and squares are all special types of parallelograms.

What is the formula for the area of a parallelogram?

The area of a parallelogram is: Area = base * height, where the height is the perpendicular distance between the base and its opposite side. For example, with base 10 cm and height 5 cm: Area = 10 * 5 = 50 cm^2. Note that height is not the same as the side length.

How do I calculate the perimeter of a parallelogram?

The perimeter is: Perimeter = 2(a + b) or 2a + 2b, where a and b are the lengths of adjacent sides. Since opposite sides are equal, you only need two measurements. For sides 10 cm and 6 cm: Perimeter = 2(10 + 6) = 32 cm.

What is the difference between base and side in a parallelogram?

The base is whichever side you choose as the reference (usually the bottom). The side is an adjacent edge. The height must be perpendicular to the base. You can choose either pair of parallel sides as the base, which gives different height values but the same area.

How do I find the height if I know the sides and angle?

If you know the side length (s) and the angle (θ) between the base and side, use: height = s * sin(θ). For example, with side 8 cm and angle 60deg: height = 8 * sin(60deg) = 8 * 0.866 = 6.93 cm.

What are the diagonals of a parallelogram?

A parallelogram has two diagonals that bisect each other (cross at their midpoints). The diagonals are generally not equal in length, except in rectangles and squares. They can be calculated using: d₁ = sqrt(a^2 + b^2 + 2ab*cos(θ)) and d₂ = sqrt(a^2 + b^2 - 2ab*cos(θ)).

What are the angle properties of a parallelogram?

In a parallelogram: opposite angles are equal, adjacent angles are supplementary (sum to 180deg), and all four angles sum to 360deg. If you know one angle, you automatically know all four angles.

What is the difference between a parallelogram and a rectangle?

A rectangle is a special parallelogram where all angles are 90deg. In a rectangle, the diagonals are equal in length, and the height equals the side length. All rectangles are parallelograms, but not all parallelograms are rectangles.

What are real-world applications of parallelogram calculations?

Parallelograms appear in: mechanical linkages and scissor lifts, architectural designs, parallelogram desks and tables, bridge truss systems, force diagrams in physics, tile patterns, and various engineering structures that need to maintain parallel sides.

Can I calculate a parallelogram with only the diagonals?

You need more information than just the diagonals. To fully define a parallelogram, you need: two sides and an angle, or one side, one diagonal, and an angle, or similar combinations. Diagonals alone give infinite possibilities.