Perimeter of Parallelogram Calculator
Enter two sides, the base, height and angle, or one side and both diagonals to find the perimeter.
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Perimeter of Parallelogram Calculator
Our Perimeter of Parallelogram Calculator finds the distance around a parallelogram. Know two neighbouring sides? It doubles their sum. Only know the base, the height and an angle, or one side and both diagonals? It finds the missing side first. It also shows the working, a drawing to scale and the angles.
Quick answer
The perimeter of a parallelogram is P = 2 × (a + b), twice the sum of two neighbouring sides: 2 × (12 + 8) = 40 cm.
- From base, height and angle: b = h ÷ sin θ, then P = 2 × (a + b)
- From one side and the diagonals: b = √((d₁² + d₂²) ÷ 2 − a²)
- The angle does not matter: sides 12 and 8 give 40 at any angle
- Units: a perimeter is a length (cm, m, ft), never cm²
What Is the Perimeter of a Parallelogram?
A parallelogram is a four-sided shape whose opposite sides are parallel and equal in length. Its perimeter is the total distance around its edge. Because the sides come in two equal pairs, you only need two neighbouring sides, a and b, and the answer uses the same unit as the sides.
Perimeter of a Parallelogram Formula
P = 2a + 2b
- Measure two sides that meet. Call them a (the base) and b (the slanted side).
- Use one unit. Convert first if one side is in m and the other in cm.
- Add them. 12 + 8 = 20. This is the half perimeter.
- Double it. 2 × 20 = 40, written as 40 cm, not 40 cm².
Parallelogram Perimeter Examples
| Sides a and b | Perimeter |
|---|---|
| 12 and 8 cm | 40 cm |
| 7.5 and 4 cm | 23 cm |
| 15 and 9 m | 48 m |
| 10 and 3.5 ft | 27 ft |
| 6 and 6 in | 24 in |
| 2.4 and 1.6 m | 8 m |
Perimeter From the Base, Height and Angle
The height h is measured at a right angle to the base, so it is shorter than the slanted side b. If you also know the angle θ between the sides, the slanted side is the height divided by sin θ.
P = 2 × (a + h ÷ sin θ)
The base and height alone are not enough: a base of 10 and a height of 4 fit a slanted side of 4, 5, 8 or any longer length, and each gives a different perimeter.
Perimeter From a Side and the Diagonals
The diagonals of a parallelogram follow the parallelogram law: the squares of the diagonals add up to the squares of all four sides. With one side and both diagonals, you can solve for the other side.
b = √((d₁² + d₂²) ÷ 2 − a²)
Side a must be longer than half the difference of the diagonals and shorter than half their sum, otherwise the diagonals cannot meet it.
Rectangles, Rhombuses and Squares
These are all parallelograms, so P = 2 × (a + b) still works. The angle between the sides changes the area but not the perimeter: sides of 12 and 8 give 40 whether the corners are 90° (area 96) or 60° (area about 83.14).
- Rectangle
- All angles 90°: P = 2 × (length + width).
- Rhombus
- All four sides equal: P = 4a.
- Square
- Equal sides and 90° angles: P = 4a.
Missing Side From the Perimeter
Halve the perimeter to get a + b, then subtract the side you know.
50 ÷ 2 − 15 = 10 cm
Common Mistakes
- Using the height as a side: 2 × (base + height) is only right for a rectangle. Use the slanted side.
- Adding only two sides: a + b is half the perimeter. Double it.
- Adding the diagonals: the diagonals run inside the shape and are not part of the perimeter.
- Mixed units: 1 m and 40 cm give 2 × 1.4 = 2.8 m, not 82.
- Square units: a perimeter is cm or m, not cm² or m².
Key Terms
- Perimeter
- The distance around the parallelogram, P = 2 × (a + b).
- Base
- The side a that the shape stands on.
- Side b
- The slanted side that meets the base.
- Height
- The distance between the base and the opposite side, at a right angle.
- Diagonals
- The lines d₁ and d₂ joining opposite corners.
How to Use the Perimeter of Parallelogram Calculator
- Choose what you know. Pick Two sides for the side lengths a and b, Height & angle for the base, height and angle, or Side & diagonals for one side and both diagonals.
- Enter the values. Type the lengths. Decimals and fractions such as 3/4 work. Choose a unit if you want one (mm, cm, m, km, in, ft, yd or mi), and ° or rad for the angle.
- Read and copy the result. The perimeter appears as you type, with a drawing to scale and the working. Press Copy to copy it, or Clear or Esc to start again.
Example: a slanted garden bed has 15 m and 9 m sides. Keep Two sides, enter 15 and 9 and choose m. The perimeter is 48 m, so you need 48 m of edging.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you find the perimeter of a parallelogram?
Add two neighbouring sides and double the sum: P = 2 × (a + b). Opposite sides are equal, so sides of 12 cm and 8 cm give 2 × 20 = 40 cm.
Can you find the perimeter of a parallelogram from the base and height?
Not from those two alone, because the height is not a side. You also need the angle θ between the sides: the slanted side is b = h ÷ sin θ. A base of 10, height of 4 and angle of 30° give b = 8 and P = 2 × (10 + 8) = 36.
How do you find the perimeter of a parallelogram from its diagonals?
You need one side as well. The diagonals satisfy d₁² + d₂² = 2(a² + b²), so b = √((d₁² + d₂²) ÷ 2 − a²). Side 10 with diagonals 13 and 9 gives b = 5 and P = 30.
Does the angle change the perimeter of a parallelogram?
No. Leaning the shape over keeps the side lengths, so the perimeter stays the same. Sides of 12 and 8 give 40 at 90° or 60°. Only the area changes, from 96 to about 83.14.
How do you find a missing side from the perimeter?
Halve the perimeter and subtract the known side: b = P ÷ 2 − a. A perimeter of 50 cm with a 15 cm side gives b = 25 − 15 = 10 cm.
Is the perimeter of a rhombus or rectangle found the same way?
Yes. Both are parallelograms, so P = 2 × (a + b) works. For a rhombus (and a square) all sides are equal, so it becomes P = 4a: a 6 in rhombus has a 24 in perimeter.
Is the Perimeter of Parallelogram Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Perimeter of Parallelogram Calculator to find the perimeter of any parallelogram from two sides, from the base, height and angle, or from one side and the diagonals.