Rhombus Area Calculator — Diagonals, Base × Height, or Side & Angle
Find the area and perimeter of a rhombus using any of three methods: the two diagonals, base × height, or side length with an interior angle. All four sides of a rhombus are equal, so the perimeter is simply 4 × side.
Input method
Area of the rhombus in square units
- 1
Multiply diagonals
8 × 6 = 48 - 2
Area = d₁ × d₂ ÷ 2
48 ÷ 2 = 24The diagonals of a rhombus bisect each other at 90°, so area = half their product.
How does this calculator work?
A rhombus has four equal sides. Area = (d₁ × d₂) / 2 (from diagonals), or base × height, or s² × sin(θ). Perimeter = 4s. Side from diagonals: s = √((d₁/2)² + (d₂/2)²). Diagonals bisect each other at 90°.
Formula
How this is calculated
A rhombus is a parallelogram with all four sides equal. Its area can be computed in three equivalent ways, depending on which measurements you know. When the diagonals are given: Area = (d₁ × d₂) / 2 — the diagonals of a rhombus bisect each other at right angles, so the four right triangles they create tile the shape exactly. When base and perpendicular height are known: Area = base × height, the same as any parallelogram. When only a side and an interior angle are known: Area = s² × sin(θ), derived from the cross-product of two adjacent side vectors.
The perimeter is always 4 × side, regardless of angles. The side length can be recovered from the diagonals using the Pythagorean theorem: side = √((d₁/2)² + (d₂/2)²), because the diagonals bisect each other at right angles, forming four right triangles. The angles come in two supplementary pairs: if one angle is θ, the opposite angle is also θ and the adjacent angles are 180° − θ.
A square is a special rhombus (θ = 90°, d₁ = d₂). A rhombus with θ ≠ 90° has unequal diagonals. The shape is sometimes called a diamond in casual usage, particularly when oriented with a vertex at the top.
Frequently asked questions
Area = (d₁ × d₂) / 2, where d₁ and d₂ are the lengths of the two diagonals. This works because the diagonals of a rhombus are perpendicular bisectors of each other, dividing the shape into four congruent right triangles whose total area equals half the product of the diagonals.
Each half-diagonal forms a right-angle pair at the centre. By the Pythagorean theorem, side = √((d₁/2)² + (d₂/2)²). For example, diagonals of 8 and 6 give side = √(16 + 9) = √25 = 5.
Yes. A square satisfies all properties of a rhombus (four equal sides) plus it has four right angles (90°). Equivalently, it is the special case where both diagonals are equal (d₁ = d₂) and the interior angle is exactly 90°. Every square is a rhombus, but not every rhombus is a square.
Also known as
TG we-Calculate Editorial Team. (2026). Rhombus Area Calculator — Diagonals, Base × Height, or Side & Angle [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rhombus-area-calculator
TG we-Calculate Editorial Team. "Rhombus Area Calculator — Diagonals, Base × Height, or Side & Angle." TG we-Calculate. 2026. https://we-calculate.com/calculator/rhombus-area-calculator.
TG we-Calculate Editorial Team, "Rhombus Area Calculator — Diagonals, Base × Height, or Side & Angle," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rhombus-area-calculator
@misc{wecalculate_rhombus_area_calculator, title = {Rhombus Area Calculator — Diagonals, Base × Height, or Side & Angle}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rhombus-area-calculator}}, year = {2026}, note = {TG we-Calculate} }
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