Formulas, without the guesswork.
Choose a relationship from the measurements you know. The variable names below belong to each calculator; a letter can have a different role in another method. π is evaluated using the browser’s full numerical constant, rather than replacing it with 3.14.
Perpendicular diagonals
Inputs: Symmetry diagonal p (length units); Crossing diagonal q (length units).
Adjacent side lengths and crossing diagonal
Inputs: Side pair a (length units); Side pair b (length units); Crossing diagonal d (length units).
Area to missing diagonal
Inputs: Area A (square units); Known diagonal p (length units).
Symmetry diagonal segments and crossing diagonal
Inputs: Upper segment p (length units); Lower segment q (length units); Crossing diagonal d (length units).
Reading the notation
√ means a square root, ∛ means a cube root, and a superscript ² or ³ means a square or cube. Sine, cosine and tangent use angles converted from entered degrees. Where an inverse trigonometric function is used, its displayed angle is converted back to degrees. The ellipse perimeter is approximate; other formula labels describe the ideal mathematical model.
The symmetry diagonal does not usually get bisected. These tools assume a convex kite, not a dart.
Reference reading: Kite at Wolfram MathWorld.