About the Rhombus Calculator
A rhombus is a four-sided shape with all sides the same length, like a diamond on a playing card. Its diagonals cross at right angles and cut each other in half, which makes it easy to calculate from just a few measurements. This calculator finds the area, side, perimeter, both angles and the radius of the largest circle that fits inside, starting from any of three sets of data: the two diagonals, one side and one angle, or one side and one diagonal. It tells you when a combination is impossible, for example a diagonal longer than twice the side.
Updated October 2026
How to use the Rhombus Calculator
- 1Choose what you know: both diagonals, a side and an angle, or a side and a diagonal.
- 2Enter the values.
- 3Read the area and perimeter.
- 4Check the side, diagonals and both angles.
- 5Use the inscribed circle radius for fitting a round object.
Worked example
A kite-shaped tile is actually a rhombus with diagonals of 30 cm and 40 cm. Each side is the square root of 15² + 20², which is exactly 25 cm. The area is 30 × 40 ÷ 2 = 600 square centimetres, the perimeter is 100 cm and the acute angle is 2 × arctan(30 ÷ 40) = 73.74 degrees. The inscribed circle has a radius of 600 ÷ 50 = 12 cm.
In practice you may only be able to measure one diagonal and one side, for example the long span of a diamond-shaped window frame and its edge. The calculator handles that case and checks that the data are possible. If the side-and-diagonal combination fails, the diagonal is too long for that side. Measure again, or use the two-diagonal mode, which always works because any two positive diagonals make a valid rhombus.
Since a rhombus is a parallelogram, you can also use it to see how area changes when the shape is pushed over. Keeping the side fixed at 10 units, a square has an area of 100, but a rhombus with a 60 degree angle has only 86.6 and one with a 30 degree angle has only 50. The perimeter stays at 40 the whole time, which shows why measuring only the outline of a frame can tell you very little about the area it encloses.
Properties
- All four sides are equal.
- Diagonals are perpendicular bisectors of each other.
- Diagonals bisect the angles at the corners.
- Opposite angles are equal.
- It is a special parallelogram.
Uses
Rhombuses appear in tile patterns, windows, bridge trusses, jewellery settings and road signs. In engineering, a scissor jack is a rhombus whose diagonals change as the jack is wound, and the area formula shows how the lifting height relates to the width.
Related tools
The Parallelogram Calculator is the general case, the Triangle Calculator splits a rhombus into halves, the Pythagorean Theorem Calculator finds a side from half-diagonals and the Circle Calculator handles the inscribed circle.
Features
- Three ways to start
- Area, side, perimeter and angles
- Both diagonals
- Inscribed circle radius
- Checks for impossible shapes
- Any unit
Frequently asked questions
What is the area of a rhombus?
Half the product of its diagonals: p × q ÷ 2. With diagonals of 10 and 24 the area is 120. It also equals the base times the height, or the side squared times the sine of an angle.
How do I find the side from the diagonals?
The diagonals form four right triangles, each with legs of p/2 and q/2. The side is the hypotenuse: the square root of (p/2)² + (q/2)². For 10 and 24 that gives 13.
What are the angles of a rhombus?
Opposite angles are equal and neighbouring angles add up to 180 degrees. The acute angle is 2 × arctan(shorter diagonal ÷ longer diagonal).
Is a square a rhombus?
Yes. A square is a rhombus whose angles are all 90 degrees, and so whose diagonals are equal. Every square is a rhombus, but not every rhombus is a square.
What is the inscribed circle?
The largest circle that fits inside the rhombus, touching all four sides. Its radius is twice the area divided by the perimeter, which is also half the height.
Why does the calculator say a diagonal is too long?
A diagonal can never be as long as twice the side, since the two sides meeting at the corner must be at least as long as half of it. If you get this message, check your measurements.