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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.

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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