Calculations at a general, convex quadrilateral or quadrangle. The calculation is done by fragmenting the quadrilateral into triangles, which can be calculated with the according formulas. Enter the first three lengths a, b and c and the two angles between them, β and γ. Choose the number of decimal places and click Calculate. Please enter angles in degrees, here you can convert angle units.
Quadrilateral shape (a bottom, b right, c top, d left). If this quadrilateral is drawn non-convex, that is, if it is concave (has an indent) or is crossed, the upper calculation is not valid:
α = arccos( (a² + d² - f²) / 2ad )
δ = 360° - α - β - γ
p = a + b + c + d
A = √ 4e²f² - ( b² + d² - a² - c² )² / 4
Side length, diagonals and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the angles are in degrees.
A quadrilateral is convex if it has no inward-facing corners. The calculation of a general convex quadrilateral is done by decomposing it into two triangles by one of the two diagonals. There are numerous special forms of convex quadrilaterals. In a trapezoid, two opposite sides are parallel; in a parallelogram, both pairs of sides are parallel, and they are of the same length. In a kite, two adjacent sides are the same length. The rhombus combines parallelogram and kite with four equal sides. The rectangle has four right angles and is also a parallelogram. Finally, the square combines all of the previous special cases with four equal sides and right angles. The tangential quadrilateral, which has an inscribed circle, and the cyclic quadrilateral, which has a circumcircle, are more difficult to recognize.
The opposite of convex is concave, this term describes quadrilaterals with one or two corners facing inwards. The concave quadrilateral includes the arrowhead quadrilateral, but also the crossed rectangle and the antiparallelogram.