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.
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Solve for

Enter any two values of a rhombus.

side

a =

area

A =

perimeter

P =

long diagonal

d₁ =

short diagonal

d₂ =

height

h =

incircle radius

r =

angle

α =

angle

β =

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Rhombus formulas

Rhombus illustration showing sides, height, diagonals and incircle radius.

$$ A = \frac{d_1 \times d_2}{2} $$

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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