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# Rhombus calculator

This calculator finds the unknown element of a rhombus given any two known dimensions. The calculator can determine side, area, long and short diagonal, perimeter, height, incircle radius, and interior angle. The calculator gives you a step-by-step solution on how to find the missing value.

Rhombus calculator
Enter any two elements of a rhombus and choose an element to find.
help ↓↓ examples ↓↓
Solve for
Enter any two values of a rhombus.
a =

A =

P =
d1 =

d2 =
h =

r =
α =

β =
working...
Rhombus formulas
 $$A = \frac{d_1 \times d_2}{2}$$ area
 $$A = \frac{a \times h}{2}$$ height
 $$P = 4 \times a$$ perimeter
 $$r = \frac{h}{2}$$ incircle radius
 $$h = a \times \sin\alpha$$ height
 $$\alpha + \beta = 90^o$$ sum of angles
 $$a^2 = \frac{d_1^2}{4} + \frac{d_2^2}{4}$$ side
 $$d_1^2 = 2a^2(1 - \cos\alpha)$$ short diagonal
 $$d_2^2 = 2a^2(1 - \cos\beta)$$ long diagonal
Examples
ex 1:
Calculate the perimeter of the rhombus if the diagonals are 16 and 12 centimeters long.
ex 2:
A rhombus has a circumference of 40 cm and a diagonal of 15cm. Determine its height.
ex 3:
A rhombus has a side length of 8 cm, and the angle between the two sides is 45 degrees. Find the radius of the inscribed circle of the rhombus.
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