About the Parallelogram Calculator
A parallelogram is a four-sided shape with two pairs of parallel sides. Rectangles, rhombuses and squares are special cases. Its area is the base times the perpendicular height, not the base times the slanted side, which is a common mistake. This calculator works out the area, perimeter, both heights, both diagonals and the second angle when you know two neighbouring sides and the angle between them. If you already have the base and height, switch modes and get the area straight away, plus the perimeter if you add the slanted side. All lengths use the same unit that you enter.
Updated October 2026
How to use the Parallelogram Calculator
- 1Choose whether you know two sides and an angle, or the base and height.
- 2Enter the sides and the angle between them, or the base and height.
- 3Read the area and perimeter.
- 4Check the diagonals, heights and the other angle.
- 5Copy the summary.
Worked example
A paving slab is shaped like a parallelogram with sides 60 cm and 40 cm meeting at 70 degrees. The height to the 60 cm side is 40 × sin(70°) = 37.6 cm, so the area is 60 × 37.6 = 2,256 square centimetres. The perimeter is 200 cm. The shorter diagonal is about 59.7 cm and the longer about 82.7 cm, which tells you the size of the smallest rectangle that can hold it.
Check your numbers against the shape. If the angle you enter is close to 90 degrees, the parallelogram is nearly a rectangle and its area approaches the product of the two sides. If the angle is small, the shape is squashed and the area drops sharply, even though the perimeter does not change at all. That is why a rack of tiles that has been pushed out of square covers less floor than the same tiles laid properly square.
In land measurement, plots shaped like parallelograms are common where roads meet at an angle. Surveyors give the two side lengths and the angle between them, and the area follows from the sine formula. The diagonals then help to check the plot by measuring across it, since two parallelograms with the same sides but different angles have different diagonals even though their perimeters match exactly.
Special cases
- Rectangle: all angles 90 degrees.
- Rhombus: all four sides equal.
- Square: a rhombus with right angles.
- The area is unchanged if the top side slides along while the base and height stay the same.
- Two congruent triangles make a parallelogram.
Common mistakes
Do not multiply the base by the slanted side: that overstates the area unless the shape is a rectangle. Use the perpendicular height or the sine of the angle. When entering an angle, use the one between the two sides you gave, and remember that both the angle and its supplement describe the same shape from different corners.
Related tools
The Rhombus Calculator handles the equal-sided case, the Trapezoid Calculator covers shapes with one pair of parallel sides, the Triangle Calculator finds half a parallelogram and the Area Calculator handles other shapes.
Features
- Two modes of input
- Area, perimeter and both heights
- Short and long diagonals
- The other angle
- Checks for impossible angles
- Any unit
Frequently asked questions
What is the area of a parallelogram?
Base times perpendicular height. With sides a and b and angle θ between them, it equals a × b × sin(θ). For sides 8 and 5 at 60 degrees the area is 8 × 5 × 0.866 = 34.64.
What is the perimeter?
Twice the sum of the two different side lengths: 2 × (a + b). Opposite sides of a parallelogram are equal.
How do I find the diagonals?
Use the law of cosines. The shorter diagonal is the square root of a² + b² − 2ab·cos(θ), and the longer is the square root of a² + b² + 2ab·cos(θ), where θ is the acute angle between the sides.
What are the angles in a parallelogram?
Opposite angles are equal and neighbouring angles add up to 180 degrees. If one angle is 60 degrees, the next is 120.
What is the difference between a parallelogram and a rectangle?
A rectangle is a parallelogram with four right angles. In a general parallelogram the sides lean over, and the height is shorter than the slanted side.
Do the diagonals bisect each other?
Yes. In every parallelogram, the diagonals cut each other in half where they cross, which is a handy property for proofs and construction.