Rhombus Area Calculator

What do you know?

Choose the two measurements you already have; the calculator solves the rest.

Diagonals (d₁ and d₂)

Base and height

Side and angle

Enter the two diagonals to get the area, or enter the area and one diagonal to find the other. Leave the field you want blank.

Diagonal 1 (d₁)

Diagonal 2 (d₂)

Area (A)

Please input values into the fields

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This rhombus area calculator allows you to calculate the area of a rhombus as well as all other associated values. Simply input any known information such as two diagonals, one side and height or one side and an angle and the tool will calculate the rest.

Since a rhombus is defined by two arbitrary measurements, usually no more than two values are required. Select a method, enter the values, and the area will be prominently displayed, along with the perimeter, side length, height, diagonals, and both interior angles.

What is a rhombus?

A rhombus is a quadrilateral with all four sides equal in length. It is a special kind of parallelogram since opposite sides are parallel and opposite angles are congruent. Also it is a kite, because two pairs of adjacent sides are congruent.

A rhombus is also called a diamond or lozenge. The symbol for the suit diamonds in playing cards is a rhombus with its point facing down. The two diagonals are perpendicular to each other and bisect each other. This property is crucial for some of the following formulas.

Three formulas for calculating the area of a rhombus.

There are three common ways to calculate the area of a rhombus and this calculator has support for all of them - choose the one which best suits your available measurements.

If you know both diagonals, multiply them together and divide by two.

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

If the length of one side (the base) and the perpendicular height are known, then multiply these two values together to find the area. This is the same as with any parallelogram.

A = a \times h

If you know the length of one side and any interior angle, square the side length and multiply it by the sine of the angle.

A = a^2 \times \sin(\theta)

You can use either of the two angles in the last equation. In a rhombus, the sum of any two adjacent angles is constant and equals 180 degrees. Also, the sine of an angle and its complement are equal, so sin 30 degrees = sin 150 degrees.

Extent, side length, height, diagonals.

Since all sides are of equal length, the perimeter is four times the side length.

P = 4a

The two diagonals divide the rhombus into four congruent right triangles. The legs of each triangle are half the lengths of the diagonals. Since the side length is the hypotenuse, we can use the Pythagorean theorem directly to calculate the side length.

a = \frac{1}{2}\sqrt{d_1^2 + d_2^2}

The height is the result of dividing the area by the side length and also corresponds to the product of the side length and sine of the angle. This calculator performs calculations in all directions so you can start with any two out of three inputs to display the side length, height, perimeter, both diagonals and both angles.

Application of the calculation tool:

Choose a method and enter any two of the three fields leaving the third field blank, then the calculator will calculate the blank field and show all attributes. Here are some typical input methods:

You choose	You enter	You get
Diagonals	The two diagonals	Area, side, height, perimeter, angles
Diagonals	Area and one diagonal	The other diagonal and the rest
Base and height	A side and the height	Area, perimeter, diagonals, angles
Side and angle	A side and an angle	Area, height, perimeter, diagonals

Examples of calculations with diagonals.

Consider a rhombus with diagonal lengths of 6 centimeters and 10 centimeters. Multiply the two values together, then divide by two.

A = \frac{6 \times 10}{2} = 30 \ \text{cm}^2

According to the Pythagorean theorem, the length of each side of this rhombus is about 5.83 cm, its perimeter is about 23.3 cm, its height is about 5.15 cm and its two internal angles are approximately 61.9 degrees and 118.1 degrees respectively. If you enter 6 and 10 in the fields for diagonals, these results will be shown at the same time.

Example calculation with one side and one angle:

Consider a rhomboid with sides of length 10 inches and an angle measuring 30 degrees. Square the side length, then multiply it by the sine of the angle.

A = 10^2 \times \sin(30^\circ) = 100 \times 0.5 = 50 \ \text{in}^2

The height is the result of multiplying 10 by sin(30) degrees, which is 5 inches. The perimeter is 40 inches and the diagonals are approximately 19.32 inches and 5.18 inches respectively. Switch to the "side length and angle" method, enter 10 and 30, and read off the remaining values from the results.

Calculation based on area.

You can work out the values in reverse with any of these methods. With the diagonal method, you input area and one diagonal, leave the other blank, and solve for it. For example, if the area is 40 square feet and one diagonal is 8 feet, then the other diagonal is 10 feet, because 10 multiplied by 8 divided by 2 equals 40.

The side length and angle method allows you to input either area and side length to calculate the angle or area and angle to calculate the side length. You only need to input two values since a quadrilateral is always uniquely determined when given two measurements.

Key points about rhombus:

Property	Value
Number of sides	4, all equal
Opposite sides	Parallel
Opposite angles	Equal
Neighbouring angles	Add up to 180 degrees
Sum of interior angles	360 degrees
Diagonals	Perpendicular, and bisect each other
Lines of symmetry	2, along the diagonals

Is a square a rhombus?

Yes. A square is a rhombus with all angles being right angles which means that the two diagonals are of equal length. All squares are rhombuses but only in this particular case is a rhombus a square. If you input two equal diagonal lengths, then the calculator will indicate that it is a square.

A rhombus is always a parallelogram because it has two sets of parallel sides and it is also a kite. However, a parallelogram is only a rhombus when all four sides are the same length.

Units for area of a rhombus

Area is measured in square units. If the length of a side or diagonal is given in centimeters, then the area will be in square centimeters. The same goes for feet and square feet. By switching the unit next to each field, the calculator converts all results. So you can input a rhombus with inch measurements and read off the area directly in square centimeters without having to convert yourself.

Angles can be shown in degrees, radians or gradians. The choice of angle representation has no effect on the calculated area since the calculation tool first converts the angle and then calculates the sine.

Applications of the rhombus area

The area of a rhombus is used in tiling and flooring where rhombus tiles are laid out in patterns. It can also be found in quilting art and stained glass work where rhombus panes of glass are combined. Technicians use this shape in joining techniques and grid structures, and it can also be found on road signs, playing cards, and jewelry pieces.

If the area is known, you can calculate how many rhombus tiles are needed to completely cover a floor, or the amount of glass or fabric for rhombus-shaped panes or strips, and also the material required for rhombus sections or panels. The length of sides and perimeter will help determine how much framing material or trim is needed.

Frequently asked questions

How to calculate area of rhombus with diagonals?

Multiply the two diagonals and divide by two. This means that A = (d1 * d2) / 2. If the diagonals are 6 and 10, then the area is 6*10/2, or 30 square units. In this calculator, select the method for diagonals and enter both diagonals.

How to calculate area of rhombus given side and angle?

Square the side length and multiply it by the sine of any interior angle. The formula is A = a² * sin(angle). If the side length is 10 and the angle is 30 degrees, then the area is 100 times 0.5, which is 50 square units. Any angle can be used because adjacent angles in a rhombus are supplementary.

What is the area of a rhombus with diagonals of length 8 and 10?

The area is 40 square units. Multiplying the two diagonals together, 8 times 10, gives us 80, and dividing that by 2 gives us 40. If the unit of the diagonals was feet, then the area would be 40 square feet.

How to calculate the height and side length of a rhombus?

The perimeter is four times the length of a side and the length of a side is half the square root of the sum of the squares of both diagonals. The height is either the value obtained by dividing the area by the length of a side or the product of the length of a side and the sine of an angle. Regardless of which two measurements are entered, this calculator will automatically display the length of a side, the height and the perimeter.

Is a square a rhombus?

Yes. A square is a rhombus with four right angles and congruent diagonals. All squares are rhombuses, but only rhombuses with 90-degree angles are squares. A rhombus is also a parallelogram and a kite.

Can you calculate the area of a rhombus using other values?

Yes, that's possible. Enter the area and another measurement and leave the unknown values blank. With the method using diagonals you can calculate one diagonal from the area and another diagonal. With the method using side lengths and angles you can either calculate an angle from the area and a side length or a side length from the area and an angle.

Related calculators

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Triangle Area Calculator (3 Sides)Find the area of a triangle from its three side lengths with Heron's formula, or enter the area with two sides to solve for the third. Also gives the angles, heights, medians, and inscribed and circumscribed circles.

Trapezoid Area CalculatorFind the area of a trapezoid from its two bases and height, or enter the area to solve for a missing base or the height. Also gives the median, perimeter, legs, base angles, and diagonal.

ABC Triangle CalculatorRight-triangle solver: enter any two measurements - two sides, a side and an acute angle, or the area with one side - and it finds the missing sides, both acute angles, the area, perimeter, height to the hypotenuse, circumradius, and inradius, with a built-in Pythagorean-triple check.

Area of a Triangle (SAS) CalculatorFind the area of a triangle from two sides and the included angle (SAS) with A = 1/2 a b sin(C). Also finds the missing third side, all three angles, the perimeter, heights, medians, and circles.

Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia: Rhombus
Definition and properties of the rhombus, its diagonals and angles, and its relationship to the parallelogram, kite, and square.
Math is Fun: Rhombus
Plain-language description of the rhombus, its area formulas, and its properties.
Math is Fun: Area of Plane Shapes
Area formulas for the rhombus and other basic shapes, with unit-square explanations.