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Parallelogram Calculator

Find the area and perimeter of a parallelogram.

Result

60.00 units²
38.00 units

How it is calculated

A parallelogram has two pairs of parallel sides. The tool uses area = base × height and perimeter = 2 × (base + side). The base and the slanted side are two neighbouring sides, and the height is the perpendicular distance between the base and the opposite side, not the length of the slanted side. All three values must be above zero and use the same length unit. The results are given to two decimals and labelled generically as units and units², so read them as metres and m², centimetres and cm², and so on. The tool does not check that the height can fit the side you entered (the height can never exceed the slanted side).

Worked example

Take a parallelogram with base 12, perpendicular height 5 and slanted side 7. Area: 12 × 5 = 60, shown as 60.00 units². Perimeter: add base and side, 12 + 7 = 19, then double it, 2 × 19 = 38, shown as 38.00 units. Notice that the area uses the height 5, while the perimeter uses the slanted side 7.

Try this example →

Common mistakes

  • Entering the slanted side as the height. Area needs the perpendicular height, which is always shorter than the slanted side unless the shape is a rectangle.
  • Multiplying the two neighbouring sides for the area. That only works for a rectangle; a slanted parallelogram has less area.
  • Mixing units, such as base in metres and height in centimetres, which gives a meaningless area.
  • Entering a height larger than the slanted side. This cannot occur in a real parallelogram and signals a measuring error.
  • Forgetting that the perimeter has two copies of each side. Adding only base and side gives half the perimeter.

About this calculator

A parallelogram's area is base times height (A = b·h), the perpendicular distance between the two parallel base sides — the same principle behind the rectangle formula, since any parallelogram can be reshaped into a rectangle of equal area by shifting a triangular slice from one end to the other. Its perimeter is simply the sum of all four sides, 2(a+b), since opposite sides are equal in length.

This shape and its area formula show up constantly in geometry and trigonometry courses, but also in real design work: architects and engineers compute parallelogram areas for skewed roof panels, floor tiles, and structural bracing, while land surveyors use the same base-times-height logic to estimate irregular plot areas. Graphic designers and woodworkers use it when laying out diamond or rhombus patterns that are just parallelograms with equal sides.

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