Kite Calculator – Diagonals, Area, Perimeter & Angles

Complete analysis of kite geometry from diagonal lengths. (see formulas below)
Kite ABCD with diagonals AC (vertical axis) and BD (horizontal) crossing at O, top vertex A, bottom vertex C, sides a,b,c,d and angles α,β,γ marked

Kite ABCD: \(AC = e\), \(BD = f\), \(AO = g\) (with \(g < e\))

Given diagonal \(AC = e\), diagonal \(BD = f\) and the distance \(AO = g\) (from top vertex A to the crossing point O on BD), this tool computes all sides, perimeter, area and interior angles.

Enter known lengths (positive numbers)

Kite Measurements

— units
— units
— units²
— units
— degrees
— degrees
— degrees

Formulas Used

\[ \begin{aligned} \text{Area} &= \tfrac{1}{2} f e\\\\ a &= \sqrt{\left(\tfrac{f}{2}\right)^2 + (e-g)^2}\\\\ d &= \sqrt{\left(\tfrac{f}{2}\right)^2 + g^2}\\\\ \text{Perimeter} &= 2a + 2d\\\\ \alpha &= 2\arctan\!\left(\tfrac{f}{2g}\right) \times \tfrac{180}{\pi}\\\\ \gamma &= 2\arctan\!\left(\tfrac{f}{2(e-g)}\right) \times \tfrac{180}{\pi}\\\\ \beta &= 180^\circ - \tfrac{\alpha}{2} - \tfrac{\gamma}{2}\\ \end{aligned} \]

Angles: \(\alpha\) at vertex B, \(\beta\) at vertices C and A, \(\gamma\) at vertex D. Sides: \(a = AB = BC\), \(d = AD = DC\).