A kite is a four-sided shape with two pairs of adjacent equal sides — think of the classic diamond-shaped toy it's named after. This calculator finds its area and perimeter from whichever pair of measurements you already have: the two diagonals, or the two distinct side lengths with the angle between them.
How the Kite Calculator works
A kite's two diagonals always intersect at a right angle, with one diagonal (the axis of symmetry) bisecting the other. That perpendicularity is what makes A = ½·d₁·d₂ exact for every kite, the same formula used for a rhombus. When you instead know the two distinct side lengths a and b and the angle θ between them, the axis of symmetry splits the kite into two congruent triangles, giving A = a·b·sinθ as an equivalent path to the same area.
Inputs and what they mean
In Diagonals mode, both diagonal lengths must be positive numbers — the calculator doesn't need to know how one diagonal splits the other, since the area formula only depends on their full lengths. In Sides + Angle mode, a and b are the lengths of the two distinct side pairs, and θ is the angle between them, entered in degrees between 0° and 180°. Unlike diagonals, knowing the sides and angle also lets the calculator compute the perimeter.
Limits and edge cases
Perimeter cannot be derived from diagonals alone: a kite's diagonals fix the overall size and the right-angle intersection, but not exactly where along the longer diagonal the two triangles meet, so many different side-length combinations can produce the same pair of diagonals. If you only know the diagonals, switch to Sides + Angle mode (or measure the sides directly) to get the perimeter. An angle of exactly 0° or 180° describes a degenerate kite with no area, so those inputs are rejected.
Use finite values with magnitude at most 1e50. Expressions support pi, sqrt(), fractions and arithmetic. Angles are limited to 1e12 degrees. Units are mathematical; geometry alone does not establish physical safety. Read the linked values, named formulas, diagram coordinate table and any branch or parameter comparison.