Rhombus Calculation

Online calculator and formulas for calculating a rhombus

Calculate parameters of 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.


Calculate rhombus

 Input
Decimal places
 Results
Length a
Height h
Area A
Perimeter P
Diagonal e
Diagonal f
Angle α
Angle β

Formulas for calculating a rhombus

Area \(A \)

\(A = a · h\)

\(\displaystyle A= \frac{e · f}{2}\)

\(A=a^2 · sin(α)\)


Length \(a \)

\(a = A / h\)

\(\displaystyle a = \sqrt{\left(\frac{e}{2}\right)^2 + \left(\frac{f}{2}\right)^2}\)


Height \(h \)

\(\displaystyle h = \frac{A}{a}\)

\(h = sin(α) · a\)

\(b = sin(β) · a\)


Perimeter \(P \)

\(P = 4 · a\)

\(\displaystyle P = 4 · \frac{h}{sin(α)}\)

\(\displaystyle P = 4 · \frac{h}{sin(β)}\)


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 \(β \)

\(\displaystyle β =\frac{asin( h) }{a}\)

 

 

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