Online calculator and formulas for calculating a rhombus
Two parameters are inputted for calculating the rhombus.
If invalid arguments are entered, e.g. height greater than side length, a error message issued.
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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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