Parallelogram Perimeter Calculator

Enter two adjacent side lengths and the included angle to get the perimeter (P = 2(a+b)), area, and both diagonals.

Quick Facts

Perimeter formula
P = 2(a + b)
Sum of two adjacent sides, doubled — opposite sides of a parallelogram are equal.
Area formula
A = a × b × sin(θ)
θ is the angle between sides a and b; equivalent to base × height.
Diagonals (law of cosines)
d = √(a² + b² ± 2ab·cos θ)
The two diagonals use the angle and its supplement.

Your Results

Calculated
Perimeter
-
P = 2(a + b)
Area
-
A = a × b × sin(θ)
Diagonal 1
-
√(a² + b² − 2ab·cos θ)
Diagonal 2
-
√(a² + b² + 2ab·cos θ)

Ready

Enter two adjacent side lengths, the unit, and (optionally) the included angle, then press Calculate.

Formula and Method for the Perimeter of a Parallelogram

A parallelogram is a four-sided polygon with two pairs of parallel, equal-length sides. Because opposite sides are always equal, the perimeter is simply twice the sum of two adjacent sides: P = 2(a + b), where a and b are the lengths of a pair of adjacent sides. This calculator also uses the included angle between those sides to derive the area and both diagonals.

How the calculation works

Enter the two adjacent side lengths (a and b) and choose the unit they are measured in. The calculator adds them and doubles the sum to get the perimeter: P = 2(a + b) — this alone does not require an angle. If you also provide the included angle θ between sides a and b, the tool computes the area as A = a·b·sin(θ), and the two diagonals using the law of cosines: d1 = √(a² + b² − 2ab·cos θ) and d2 = √(a² + b² + 2ab·cos θ), since the two diagonals split the parallelogram into triangles using θ and its supplement (180° − θ).

Common mistakes

  • Using all four sides instead of two: because opposite sides are equal, you only need one pair of adjacent sides — entering a side twice or adding all four measured sides double-counts.
  • Confusing the angle with a right angle: unlike a rectangle, a parallelogram's included angle is not assumed to be 90° — enter the actual angle between the two sides you measured, or leave area/diagonals unused if you only need the perimeter.
  • Mixing units: keep both side lengths in the same unit — convert inches to feet, or centimeters to meters, before entering the values.

Real-world applications

  • Fencing, edging, and trim projects use the perimeter to determine how much linear material is needed around a parallelogram-shaped plot or panel.
  • Land surveying and CAD drafting use the side-angle-side data (two sides plus the included angle) to fully define a parallelogram-shaped parcel or component.
  • Structural and mechanical design use the diagonal lengths to check bracing, cross-supports, or the rigidity of a hinged parallelogram linkage.
  • Textile and sheet-material cutting use the area to estimate how much material a parallelogram-shaped panel requires.

Frequently Asked Questions

What is the formula for the perimeter of a parallelogram?
The perimeter equals twice the sum of two adjacent sides: P = 2(a + b), where a and b are the lengths of a pair of adjacent sides. For example, sides of 8 ft and 5 ft give a perimeter of 2(8 + 5) = 26 ft.
Do I need the angle to find the perimeter?
No — the perimeter only depends on the two side lengths, P = 2(a + b). The angle between the sides is only needed if you also want the area (A = ab·sin(θ)) or the diagonal lengths.
How do you find the diagonals of a parallelogram?
Using the law of cosines with adjacent sides a and b and the included angle θ: the diagonal opposite the angle is d1 = √(a² + b² − 2ab·cos θ), and the other diagonal uses the supplementary angle, d2 = √(a² + b² + 2ab·cos θ).
How is the area of a parallelogram calculated from its sides?
When you know two adjacent sides a and b and the included angle θ, area is A = a·b·sin(θ). This is equivalent to the more common base × height formula, since height = b·sin(θ) when b is the side adjacent to the base a.

Related calculators