How is the area of a parallelogram calculated?

Area = base × side × sin(angle), which equals base × height. The height is the side length times the sine of the included angle.

How are the two diagonals found?

They come from the law of cosines: d₁ = √(a² + b² − 2ab·cos(angle)) and d₂ = √(a² + b² + 2ab·cos(angle)), where a is the side and b is the base.

What is the perimeter of a parallelogram?

The perimeter is 2 × (base + side), because opposite sides are equal in length. The angle does not affect the perimeter, only the area and the diagonals.

Why does the height depend on the angle?

The height is the perpendicular distance between the base and its opposite side. It equals the side length times sin(angle), so a flatter parallelogram (smaller angle) has a shorter height and less area.

What happens at a 90-degree angle?

At 90° the parallelogram becomes a rectangle: the height equals the side, the area equals base × side, and both diagonals are equal at √(a² + b²).

Which angle should I enter?

Enter the interior angle between the base and the adjacent side, in degrees. The opposite angle is the same, and the other two interior angles are its supplement (180° minus your value).

Is any data uploaded?

No — all calculations happen in your browser and nothing leaves your device.

Parallelogram Calculator

Parallelogram calculator

A parallelogram is a four-sided shape with two pairs of parallel, equal sides. Enter the base, the adjacent side and the included angle between them, and this tool returns the area, the height, the perimeter and both diagonals. It is useful for geometry homework, drafting and any layout where you know two sides and the angle between them.

How it works

With base b, side a and included angle θ (converted to radians), the tool computes:

area      = b × a × sin(θ)
height    = a × sin(θ)          (perpendicular height onto the base)
perimeter = 2 × (b + a)
d1        = √(a² + b² − 2ab·cos(θ))
d2        = √(a² + b² + 2ab·cos(θ))

The two diagonals use supplementary angles, which is why one has a minus and the other a plus in front of the cosine term.

Example

Base 10, side 6, angle 60°:

Height: 6 × sin(60°) = 6 × 0.8660 = 5.196
Area: 10 × 6 × sin(60°) = 51.96
Perimeter: 2 × (10 + 6) = 32
d1: √(36 + 100 − 120·cos60°) = √(136 − 60) = √76 ≈ 8.718
d2: √(36 + 100 + 60) = √196 = 14.0

Everything is computed locally in your browser — nothing is uploaded.