Parallelogram Calculator

A parallelogram is a four-sided shape with two pairs of parallel sides of equal length. This calculator finds its area from the base and perpendicular height, and its perimeter from the base and slanted side. Because the area depends on the perpendicular height rather than the slanted side, a parallelogram and a rectangle with the same base and height share the same area.

Formula

Area = base × height; Perimeter = 2 × (base + side)

base

Length of the base side

side

Length of the slanted (non-base) side

height

Perpendicular distance between the base and its opposite side

How it works

1. Enter the base length, the slanted side length, and the perpendicular height (the straight-line distance between the base and its opposite side, not the length of the slanted side).
2. The area is computed as base multiplied by height, and the perimeter as twice the sum of the base and the side. Both results are rounded to three decimal places.

Worked example

Frequently asked questions

Why does the area use the height instead of the slanted side?

Area equals base times the perpendicular height because that height measures how far apart the two parallel bases are. The slanted side is longer than the height, so using it would overstate the area; it is only needed for the perimeter.

How do I find the height if I only know the side and an angle?

If you know the slanted side and the interior angle it makes with the base, the perpendicular height equals the side multiplied by the sine of that angle. Compute that value first, then enter it as the height here.

Does this calculator find the diagonals of the parallelogram?

No. This tool reports only the area and the perimeter. Diagonal lengths require the angle between the sides, which is not one of the inputs used by this calculator.

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