Parallelogram Area Calculator
Find the area and perimeter of a parallelogram.
Needed for perimeter
Results update as you type.
How it works
A parallelogram is a four-sided shape with two pairs of parallel sides, and this calculator finds its area from the base and height and, if you supply the side length, its perimeter. You enter the base and the perpendicular height, and optionally the length of the slanted side, and it returns the area and perimeter. The area formula is beautifully simple: base times height, exactly the same as a rectangle. This works because you can cut a triangle off one end of a parallelogram and move it to the other end to form a rectangle with the same base and height, proving the areas are equal. The crucial point is that the height is the perpendicular distance between the two parallel bases, measured straight across, not the length of the slanted side, which is longer. The perimeter simply adds up all four sides, which is twice the base plus twice the adjacent side. Parallelograms include rectangles, squares, and rhombuses as special cases, and they appear in engineering, physics for force diagrams, and design. Enter the base and height for the area, and add the side length to also get the perimeter.
Area = base × height; Perimeter = 2(base + side)
The area of a parallelogram equals its base times its perpendicular height, the same as a rectangle with the same base and height, because a parallelogram can be rearranged into one. The height must be measured straight across, perpendicular to the base, not along the slanted side. The perimeter is twice the sum of the base and the adjacent side length.
Source:Euclidean geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter base and height.
- 2
Adjust the options
Adjust side length (optional) if they apply — sensible defaults are already set.
- 3
Read your result
Area updates instantly as you type — no button to press.
Frequently asked questions
How do you find the area of a parallelogram?
Multiply the base by the perpendicular height. For a base of five and a height of three, the area is 15 square units. This is the same formula as a rectangle because a parallelogram can be rearranged into one with the same base and height, which is why their areas are identical.
What height do I use for the area?
Use the perpendicular height, the straight-across distance between the two parallel bases, not the length of the slanted side. The slanted side is longer and would overstate the area. If you only know the side and an angle, multiply the side by the sine of the angle to find the true perpendicular height first.
How do I find the perimeter?
The perimeter is twice the base plus twice the adjacent side length, since a parallelogram has two pairs of equal sides. You must supply the side length as well as the base for the perimeter, because the height alone does not determine the side. Leave the side blank if you only need the area.
Is a rectangle a parallelogram?
Yes. A rectangle is a special parallelogram in which all angles are 90 degrees. Squares and rhombuses are also special parallelograms. The base-times-height area formula applies to all of them, and for a rectangle the height equals the side because the sides are already perpendicular to the base.
Why is the area the same as a rectangle?
If you slice a right triangle off one end of a parallelogram and slide it to the other end, you form a rectangle with the identical base and height. No area is added or removed in this rearrangement, so the parallelogram and the rectangle have exactly the same area, which is why both use base times height.