Parallelogram Area Calculator
Base times height — or side and angle, if that is what you have.
Work out Parallelogram Area. Base times height — or side and angle, if that is what you have. Refuses impossible figures instead of printing NaN.
Leave at zero to use the side and angle instead.
Area
24
base 8 × height 3
Area is base times perpendicular height, exactly as for a rectangle — a parallelogram is a rectangle that has been pushed over, and pushing it over changes neither the base nor the height. If you have the slanted side and the angle instead, the height is side × sin(angle). At 90° the sine is 1 and the parallelogram is a rectangle. Using the slanted side as the height is the standard mistake and always overstates the area, by a factor of 1/sin(angle).
How the Parallelogram Area Calculator works
Enter a base and either the perpendicular height, or the slanted side with the angle between them. A parallelogram is a rectangle pushed over, and pushing it over changes neither the base nor the height — which is why the formula is the same.
Also known as: area of a parallelogram calculator · parallelogram perimeter calculator · base times height calculator · parallelogram with angle calculator
Frequently asked questions
What is the area of a parallelogram?
Base times perpendicular height, exactly as for a rectangle. If you have the slanted side and the angle instead, the height is side × sin(angle).
Why can I not use the slanted side as the height?
Because the height is a perpendicular distance and the slanted side is longer than it. Using the slant overstates the area by a factor of 1/sin(angle) — at 30° that is double.
What happens at 90°?
The parallelogram becomes a rectangle. The sine of 90° is 1, so side × sin(angle) is just the side, and the two formulas agree.
How is the perimeter calculated?
2 × (base + side). Opposite sides of a parallelogram are equal by definition, so only two lengths are needed.
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