This all-in-one online Rhombus Area Calculator allows you to calculate the missing parameters of the rhombus, as well as its area and perimeter, if any two parameters of the rhombus are known.
What is Rhombus
In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length.
Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides.
Properties of Rhombus
One can easily prove that the rhombus is symmetric across each of its diagonals. And that any rhombus has the following properties:
• Opposite angles of a rhombus have equal measure;
• The two diagonals of a rhombus are perpendicular;
• The two diagonals of a rhombus bisect respective angles.
Thus, we see that every rhombus is a parallelogram. Therefore it has all of the properties of a parallelogram:
• Opposite sides are parallel;
• Adjacent angles are supplementary;
• Two diagonals bisect one another;
• Any line through the midpoint bisects the area;
• The sum of the squares of the sides equals to the sum of the squares of the diagonals.
Denoting the common side of a rhombus as \(a\) and the diagonals as \(p\) and \(q\), the last property we can formulate in the form:
$$4{a}^{2} = {p}^{2} + {q}^{2}.$$
Rhombus Area Formula
As for every parallelogram, the area \(S\) of a rhombus is the product of its base \(a\) and its height \(h\):
$$S = a\cdot h.$$
Area of a rhombus can also be expressed as half the product of the diagonals \(p\) and \(q\):
$$S = {\frac {p\cdot q}{2}}.$$
If we know the rhombus side \(p\) and any angle \(\alpha\) we can use the following formula for its area:
$$S = {a}^{2}\cdot sin(\alpha).$$
The rhombus perimeter \(P\) is expressed by the following trivial formula:
$$P = 4\cdot a.$$
These formulas are used in our Rhombus Area Calculator. With this calculator you can easily find all the parameters of a rhombus if any two of its parameters are known.
Note that we don’t specify units of measure in our calculator. We assume that area is measured in square units of length.
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Check out our other geometry calculators such as Ellipse Calculator or Triangle Calculator.