Parallelogram (Rhomboid) Calculator

This function calculates the properties of a parallelogram for a given side a and b and the angle α in degrees or radians. To calculate the parallelogram, enter the known parameters, select the angle unit degrees or radians. Then click the 'Calculate' button.

Formulas for calculating a parallelogram

Area (A)

\(\displaystyle A = b · h_a\)       \(\displaystyle =a · h_b\)       \(\displaystyle =a · b· sin(α)\)

Length (l)

\(\displaystyle a = \frac{A}{h_b}\)       \(\displaystyle = \frac{A}{b · sin(α)}\)       \(\displaystyle = \frac{A }{ b · sin(β)}\)

Width (b)

\(\displaystyle b = \frac{A}{h_a}\)       \(\displaystyle = \frac{A}{a · sin(α)}\)       \(\displaystyle = \frac{A }{ a · sin(β)}\)

Height (h_a)

\(\displaystyle h_a = \frac{A}{b}\)       \(\displaystyle = sin(α) · a\)       \(\displaystyle = sin(β) · a\)

Height (h_b)

\(\displaystyle h_b = \frac{A}{a}\)       \(\displaystyle = sin(α) ·b\)       \(\displaystyle = sin(β) ·b\)

Perimeter (P)

\(\displaystyle P = 2 ·(a + b)\)       \(\displaystyle = 2 · \frac{h_a}{sin(α)} + (2 · b)\)

Diagonal (e)

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

Diagonal (f)

\(\displaystyle f = \sqrt{a^2 + b^2; - 2 · a · b · cos(α)}\)

Angle (α)

\(\displaystyle α = asin\left(\frac{A}{a · b}\right)\)