Quadrilateral properties calculator and formulas

This function calculates various properties of a general quadrilateral.

To calculate, enter the lengths of 3 sides and the two angles that connect these sides. Then click on the 'Calculate' button.

Quadrilateral calculator

Input

Side length a

Side length b

Side length c

Angle β

Angle γ

Decimal places

Results

Side length d

Diagonal e

Diagonal f

Area A

Perimeter P

Angle α

Angle δ

Formulas of a quadrilateral

Diagonal e

\(\displaystyle e =\sqrt{a^2+b^2-2ab·cos(β)} \)

Diagonal f

\(\displaystyle f =\sqrt{b^2+c^2-2bc·cos(γ)} \)

Area A

\(\displaystyle A=\frac{\sqrt{4e^2f^2-(b^2+d^2-a^2-c^2)^2}}{4}\)

Perimeter P

\(\displaystyle P=a+b+c+d\)

Angle α

\(\displaystyle α=arccos\left(\frac{a^2+d^2-f^2}{2ad} \right)\)

Angle δ

\(\displaystyle δ=360°-α-β-γ\)

Side length d

\(\displaystyle d=\sqrt{c^2+e^2-2ce·cos(γ_2)}\)

\(\displaystyle γ_2=γ-γ_1\)

\(\displaystyle γ_1=arcos\left(\frac{b^2+e^2-a^2}{2be}\right)\)

Quadrilateral calculator