Rhombus Calculator
This rhombus calculator finds every measure from two suitable inputs: side and angle, both diagonals, or area and side. Example: a side of 5 and an angle of 60° give diagonals of 8.66 and 5, an area of 21.65 and a perimeter of 20.
Example: What is given: Side and angle · Side a 5 · Angle between two sides 60 ° → Result: Side a = 5 · Area A = 21.6506 · Perimeter P = 20. Source: Wikipedia – Raute (Geometrie). Updated: .
How it is calculated
A rhombus has four equal sides, and its diagonals meet at right angles and bisect each other. That is why two suitable inputs are enough to find everything else. The calculator shows side, diagonals, angles, perimeter, area, height and incircle radius at a glance.
The key formulas
The area is A = e·f / 2 from the diagonals e and f, or A = a²·sin α from side and angle, or A = a·h from side and height. The perimeter is P = 4a. The side follows from the diagonals by the Pythagorean theorem: a = ½·√(e² + f²), because each side is the hypotenuse of a right triangle with legs e/2 and f/2. The acute angle is α = 2·arctan(f / e) and the obtuse one β = 180° − α. The incircle touches all four sides; its radius is r = A / (2a) = h / 2.
Example
With diagonals e = 10 and f = 6 the side is a = ½·√136 ≈ 5.83, the area A = 30, the perimeter P ≈ 23.32 and the acute angle α ≈ 61.93°. If instead the area 12.5 is given with side 5, then sin α = 12.5 / 25 and α = 30°.
- For “side and angle” the angle may be acute or obtuse; the rhombus is the same.
- For “side and diagonal” the diagonal must be shorter than 2a.
- The square appears at α = 90°, where both diagonals are equal.
Frequently asked questions
How do you calculate the area of a rhombus?
Most simply from the diagonals: A = e·f / 2. Alternatively from side and angle with A = a²·sin α, or from side and height with A = a·h.
How do you find the side of a rhombus from its diagonals?
With the Pythagorean theorem: a = ½·√(e² + f²). For e = 10 and f = 6 that gives a ≈ 5.83.
Is a square a rhombus?
Yes. A square is a rhombus with four right angles. Both diagonals are then equal and the rhombus formulas still apply.
Sources and legal basis
As of: · Editorial policy
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