How this calculator works
A rhombus has four equal sides. Its diagonals bisect each other at right angles, making four right triangles. Half-diagonals therefore recover the side, and half their product gives the area. Alternatively, treat the rhombus as a parallelogram with area side times perpendicular height. The table verifies the same area using those two methods and the sine formula. An area with one diagonal or height can be used in reverse.
Formula
A = d₁d₂/2 = ah = a² sin α; a = hypot(d₁/2, d₂/2); P = 4a; h ≤ a. Adjacent angles add to 180°.
Worked example
Diagonals 6 m and 8 m give side √(3² + 4²) = 5 m, area 24 m², height 24/5 = 4.8 m and perimeter 20 m. A side of 4 m with a 30° angle instead gives area 16 × 0.5 = 8 m².
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Frequently asked questions
Must I label the shorter diagonal first?
No. The calculator sorts the recovered diagonals for the output. Either diagonal can be the known one in reverse mode.
Why are two angles shown?
Adjacent angles are supplementary. A height alone cannot distinguish a chosen angle from its supplement, so the page reports the smaller and larger angles.
Can a square be entered?
Yes. Equal diagonals and height equal to the side describe a square, which is a special rhombus with two reported angles of 90°.