Math
Rhombus Calculator
The rhombus calculator takes whichever pair you know — side and angle, both diagonals, or side and height — and returns the full shape: area, perimeter, diagonals, height, the radius of the inscribed circle, and both interior angles.
All four sides are equal.
Either interior angle; its neighbor is 180° minus this.
Pick the unit your measurements use. Area is reported in square units and volume in cubic units.
Try an example
Result
Area
—
- Perimeter
- —
- Diagonals (long, short)
- —
- Height
- —
- Angles
- —
- Inscribed circle radius
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the rhombus calculator solves
The rhombus calculator takes whichever pair you know — side and angle, both diagonals, or side and height — and returns the full shape: area, perimeter, diagonals, height, the radius of the inscribed circle, and both interior angles.
Formula
How to use it
- Pick the pair of measurements you have: side and angle, both diagonals, or side and height.
- Enter them in one unit and choose that unit.
- Read the area, perimeter, diagonals, height, inradius, and both angles.
How to read the answer
A rhombus has four equal sides, so the perimeter is simply 4s. Its diagonals cross at right angles and bisect each other, which is why the area is half their product and why each half-diagonal pair forms a right triangle with the side. The acute angle sits opposite the short diagonal.
Common mistakes and edge cases
- Using side × side for the area — that only works for a square. A rhombus needs the height or the angle: A = s²·sin θ.
- Entering half-diagonals instead of full diagonals in the diagonals mode.
- A height greater than the side is impossible; equal to the side means a square.
- Angles of 0° or 180° collapse the shape and are rejected.
Worked examples
Side 10, angle 60°
Area
86.6025
Diagonals 16 and 12 (side 10)
Area
96
Side 10, height 8
Area
80
Side 6, angle 90° (a square)
Area
36
Decimal diagonals 7.5 and 4.2
Area
15.75
Height larger than side (impossible)
Area
Error
Angle 0° (degenerate)
Area
Error
Frequently asked questions
How do I find the area of a rhombus from its diagonals?+
Multiply the diagonals and halve: A = (p·q)/2. Diagonals 16 and 12 give area 96.
How do I find the side of a rhombus from the diagonals?+
The half-diagonals form a right triangle with the side: s = sqrt((p/2)² + (q/2)²). For 16 and 12, s = sqrt(64 + 36) = 10.
What are the angles of a rhombus?+
Opposite angles are equal and adjacent angles add to 180°. From the diagonals, the acute angle is 2·arctan(q/p) where q is the shorter diagonal.
Is a rhombus a parallelogram?+
Yes. A rhombus is a parallelogram with all four sides equal; a square is a rhombus with right angles.
What is the height of a rhombus?+
The perpendicular distance between two parallel sides: h = s·sin θ. It equals the area divided by the side, and it is the diameter of the inscribed circle.
Do the diagonals of a rhombus bisect the angles?+
Yes — each diagonal splits the two angles it connects into equal halves, and the diagonals meet at 90°. That is what makes the half-diagonal triangles right triangles.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026