Area of a rhombus

Three different ways to calculate the area of a rhombus are given below, with a formula for each.
Try this Drag the orange dots on each vertex to reshape the rhombus. The area will be continuously calculated using the "base times height" method.

A rhombus is actually just a special type of parallelogram. Many of the area calculations can be applied to them also. Choose a formula based on the values you know to begin with.

1. The "base times height" method

First pick one side to be the base. Any one will do, they are all the same length. Then determine the altitude - the perpendicular distance from the chosen base to the opposite side. The area is the product of these two, or, as a formula: where
b is the length of the base
a is the altitude (height).

Use the calculator below to calculate the area of the rhombus given the base (side) length and altitude (perpendicular height).

Enter any two values and the missing one will be calculated. For example, enter the area and base length, and the height needed to get that area is calculated.

Base clear
Height clear
Area clear

2. The "diagonals" method

Another simple formula for the area of a rhombus when you know the lengths of the diagonals. The area is half the product of the diagonals. As a formula: where
d1 is the length of a diagonal
d2 is the length of the other diagonal

3. Using trigonometry

If you are familiar with trigonometry, there is a handy formula when you know the length of a side and any angle: where
s is the length of any side
a is any interior angle
sin  is the sine function
(see Trigonometry Overview)

It may seem odd at first that you can use any angle since they are not all equal. But the angles are either equal or supplementary, and supplementary angles have the same sine.

Other polygon topics


Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons