Parallelogram Area & Perimeter Calculator
Get the area, perimeter and diagonals of a parallelogram from its base, height and slant side.
How it works
Area = base · height · Perimeter = 2(base + side) · Base angle = atan2(height, √(side² − height²))
A parallelogram’s area uses its perpendicular height, not the slant side — the area equals base times the vertical distance between the two parallel base lines. The perimeter, however, uses the actual slant side, since that is the length you would walk along the edge. Because the perpendicular height is the side length times the sine of the base angle, the height can never exceed the slant side.
Worked example
With base 6, perpendicular height 4 and slant side 5: area = 6 · 4 = 24 units²; perimeter = 2(6 + 5) = 22 units. The horizontal offset is √(5² − 4²) = 3, so the base angle is atan2(4, 3) ≈ 53.13°.
Sources: Parallelogram — Wolfram MathWorld
Frequently asked questions
Why does the area use the height, not the slant side?
Area equals base times perpendicular height. Multiplying by the slant side instead would overstate the area, because the slant side is longer than the vertical distance it spans (unless the shape is a rectangle).
What is the difference from the standard parallelogram area calculator?
This version also returns the perimeter and the interior base angle, so it needs the slant side length in addition to the base and height.
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This calculator is for educational purposes. Double-check important results before acting on them.