Rhombus Calculation
Online calculator and formulas for calculating a rhombus
Two parameters are inputted for calculating the rhombus.
- As the first argument, the side length a or the perimeter P may be entered.
- As a second argument, you can choose between the height h, the area A, or the angles α and β.
If invalid arguments are entered, e.g. height greater than side length, a error message issued.
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Description of a diamond
In geometry, a diamond or rhombus is a flat square with four sides of equal length. Opposite sides are parallel and opposite angles are equal. Here you will find a number of formulas for calculating rhombuses.
Formulas
Area (A)
\(A = a · h\) \(\displaystyle = \frac{e · f}{2}\) \(\displaystyle =a^2 · sin(α)\)
Length (a)
\(\displaystyle a = \frac{A}{h}\) \(\displaystyle = \sqrt{\left(\frac{e}{2}\right)^2 + \left(\frac{f}{2}\right)^2}\) \(\displaystyle =\frac{h}{sin(α)}\) \(\displaystyle =\frac{h}{sin(β)}\)
Height (h)
\(\displaystyle h = \frac{A}{a}\) \(\displaystyle = sin(α) · a\) \(\displaystyle = sin(β) · a\)
Perimeter (P)
\(\displaystyle P = 4 · a\) \(\displaystyle = 4 · \frac{h}{sin(α)}\) \(\displaystyle = 4 · \frac{h}{sin(β)}\)
Diagonal (e)
\(\displaystyle e =\frac{ h }{ sin(α/2)}\) \(\displaystyle e = a ·\frac{ sin(β)}{ sin(α/2)}\) \(\displaystyle e = 2 · a · cos\left(\frac{α}{2}\right)\)
Diagonal (f)
\(\displaystyle f =\frac{ h }{ sin(β/2)}\) \(\displaystyle f = a ·\frac{ sin(α)}{ sin(β/2)}\) \(\displaystyle f = 2 · a · cos\left(\frac{β}{2}\right)\)
Angle (β)
\(\displaystyle β =\frac{asin( h) }{a}\)
Square • Rectangle • Golden Rectangle • Rectangle to Square • Rhombus, given varios parameter • Rhombus , given diagonal e, f • Parallelogram, given 2 sides and angle • Parallelogram area, given side and height • Trapezoid • Cyclic Quadrilateral • General Quadrilateral • Concave Quadrilateral • Arrowhead Quadrilateral • Crossed Square • Frame • Kite, given 2 diagonal and distance • Kite Area, given 2 diagonal • Half Square Kite • Right Kite"
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