About the Rhombus Calculator
A rhombus is a quadrilateral with four equal sides — a “diamond” or a pushed-over square. Its diagonals cross at right angles and bisect each other, which makes it easy to solve completely from just two measurements. This rhombus calculator accepts any of five common pairs: both diagonals, side and angle, side and height, side and one diagonal, or area and side.
From that pair it returns the area, perimeter, side length, both diagonals, the height (distance between opposite sides), the radius of the inscribed circle and the acute and obtuse interior angles. It suits geometry homework, tiling and quilting patterns made of diamonds, kite and lattice designs, and checking a CAD sketch.
Use any length unit consistently; the area comes out in the matching square unit and angles are in degrees. A square is the special case where both diagonals are equal and every angle is 90°.
With the default inputs, the area is 24 sq units. Change any value above to recalculate instantly.
How to use the rhombus calculator
- 1Choose which two measurements you know.
- 2Enter the values in any consistent unit (angles in degrees).
- 3Read the area and perimeter.
- 4Check the diagonals, height, inradius and both interior angles.
Formula and method
The diagonals of a rhombus are perpendicular bisectors of each other, so they split it into four congruent right triangles with legs p/2 and q/2 and hypotenuse a. That gives the side a = √(p² + q²)/2 and the area pq/2. The area can also be written a² sin α or base × height, a·h.
Whatever pair you enter, the calculator first finds the side a and the acute angle α (for example α = arcsin(h/a) from side and height, or arcsin(A/a²) from area and side), then derives everything else: the short diagonal 2a sin(α/2), the long diagonal 2a cos(α/2), the obtuse angle 180° − α, the perimeter 4a and the inradius h/2 (a rhombus always has an inscribed circle touching all four sides).
- a
- Side length
- p, q
- Diagonals
- α
- Acute interior angle
- h
- Height (distance between opposite sides)
- A
- Area
Worked examples
Diagonals of 6 and 8
Half-diagonals 3 and 4 form a 3-4-5 right triangle, so each side is 5 and the perimeter is 20. Area = 6 × 8 ÷ 2 = 24 and the height is 24 ÷ 5 = 4.8.
Side 10 with a 60° angle
Area = 10² × sin 60° ≈ 86.60. A 60° rhombus is two equilateral triangles, so the short diagonal equals the side (10) and the long diagonal is 10√3 ≈ 17.32.
Side 13 and one diagonal of 10
Half the known diagonal (5) and the side (13) make a 5-12-13 triangle, so the other half-diagonal is 12 and the full diagonal is 24. Area = 10 × 24 ÷ 2 = 120.
Area 50 with side 10
sin α = 50 ÷ 100 = 0.5, so the acute angle is 30° and the height is 50 ÷ 10 = 5. The diagonals are 20 sin 15° ≈ 5.18 and 20 cos 15° ≈ 19.32.
Frequently asked questions
How do you find the area of a rhombus?+
Multiply the diagonals and halve the result: A = pq/2. Alternatively use side × height, or side² × sin of any interior angle. Diagonals 6 and 8 give an area of 24.
How do you find the side of a rhombus from its diagonals?+
The half-diagonals are the legs of a right triangle whose hypotenuse is the side, so a = √(p² + q²) ÷ 2. Diagonals 10 and 24 give a side of 13.
Are the diagonals of a rhombus equal?+
Only when the rhombus is a square. In general they are different lengths, but they always bisect each other at right angles and bisect the interior angles.
What is the difference between a rhombus and a square?+
Both have four equal sides, but a square also has four 90° angles. Every square is a rhombus; a rhombus is a square only if one angle is 90°.
What is the perimeter of a rhombus?+
Since all four sides are equal, P = 4a. If you only know the diagonals, use P = 2√(p² + q²); diagonals 6 and 8 give a perimeter of 20.