2D Shape Master Calculator

Not everyone starts from the same known measurement — a circle cut from a template might come with its area already labeled, or a pipe might be specified by circumference. The Circle Input Type selector lets you supply whichever value you actually have, and the calculator solves back to a radius internally before computing everything else from that single common value.

It first recovers the interior angle from height and side using an inverse sine, then applies the law of cosines twice — once adding the cosine term for one diagonal, once subtracting it for the other. This is exact for a standard parallelogram, but because height alone can correspond to two different angles (acute or its obtuse supplement), an unusually shaped parallelogram could in principle solve to the wrong one of the two.

It combines two independent facts about the same triangle: how many sides are equal length (equilateral, isosceles, or scalene) and what its largest angle looks like (acute, right, or obtuse). A quilter or carpenter cutting triangular pieces can use this to sanity-check that entered measurements actually describe the shape they intended, since a typo in one side length often flips the classification unexpectedly.

Three side lengths only form a real triangle when each side is shorter than the sum of the other two — the triangle inequality. If your three numbers fail that test (for example, sides of 2, 3, and 10), no flat triangle can physically close, so the calculator reports zero area and flags the combination as invalid rather than returning a misleading result.

No — the Imperial/Metric toggle relabels which unit your typed-in numbers represent (feet versus meters) rather than converting the values themselves, since the dimension fields are shared across both. The output section separately reports area in multiple units (square feet, square meters, square inches, acres, hectares) so you can read off whichever unit you need without re-entering anything.