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Rhombus Calculator

Enter any two values — diagonals, side, area, or an angle — and get the rest in real time. Useful for tilers, pattern designers, jewellers, and geometry students who need a clean answer with the working shown.

Dimensions

Updates as you type
Solve from
What do you know? ?
Unit
Values
Diagonal d1 ? —
cm
12550100
Diagonal d2 ? —
cm
12550100

Live diagram

Drag a vertex
s d₁ d₂ θ 180°−θ

Drag any vertex to reshape — inputs follow.

Formula

A = d1 × d2 2 , s = 1 2 √ ( d12 + d22 ) , P = 4s
A
Area of the rhombus
s
Side length (all four sides are equal)
P
Perimeter
d1, d2
Lengths of the two diagonals (always meet at 90°)
θ
Acute interior angle (the obtuse angle is 180° − θ)
Worked example — your numbers
  1. Half-diagonals: —
  2. Side s = ½√(d12 + d22) = —
  3. Area A = (d1 × d2) / 2 = —
  4. Perimeter P = 4s = —
  5. Acute angle θ = 2 · arctan(d1 / d2) = —
  6. Obtuse angle = 180° − θ = —

Because the diagonals of a rhombus always bisect each other at right angles, the shape is split into four congruent right triangles. That symmetry is why both the area formula and the side formula come out so cleanly. A square is the special case where d₁ = d₂ and both angles equal 90°.

Examples

How It Works

A rhombus is a parallelogram whose four sides are all the same length. That single rule has powerful consequences: opposite sides are parallel, opposite angles are equal, and — most useful for calculation — the two diagonals always cross at right angles and bisect each other.

The fastest formula for area uses the diagonals: A = (d₁ × d₂) / 2. Because the diagonals split the rhombus into four congruent right triangles, you can also recover the side from them with the Pythagorean theorem: s = ½√(d₁² + d₂²). Going the other way, if you know the side and one diagonal you can solve for the other: d₂ = 2√(s² − (d₁/2)²).

Knowing only the side isn't enough to fix a rhombus — it could be anything from a thin sliver to a perfect square. A second piece of information (a diagonal, an angle, or the area) closes that ambiguity. With side + acute angle θ, the area becomes A = s² × sin(θ), and the diagonals follow from the law of cosines.

A square is the special case where both diagonals are equal — the rhombus's two angles both become 90°. At the other extreme, very unequal diagonals produce a long, thin "diamond" shape with one acute and one obtuse angle that always sum to 180°.

Tips & Best Practices

A rhombus is fully defined by any two independent values — typically two diagonals, a side and a diagonal, a side and an angle, or the area and one diagonal.
Diagonals always meet at 90° and cut each other in half. That right angle is what lets you derive the side from half-diagonals using the Pythagorean theorem.
A square is a rhombus with equal diagonals — both angles become 90°. If you need a square, set d₁ = d₂.
The two angles of a rhombus always add up to 180°. Knowing one immediately gives you the other.
For tiling work, the perimeter (4 × side) tells you how much edging or grout line you need; for fabric or paper it tells you the cut length per shape.

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Frequently Asked Questions

Is a square a rhombus?

Yes. A square is the special case of a rhombus where the two diagonals are equal in length, which makes both pairs of angles 90°. Every square is a rhombus, but not every rhombus is a square.

The diagonals of a rhombus bisect each other at right angles, so each side is the hypotenuse of a right triangle with legs d₁/2 and d₂/2. The formula is s = ½√(d₁² + d₂²). For example, a rhombus with diagonals 10 and 8 has side ½√(100+64) = ½√164 ≈ 6.40.

No — the side alone fixes the perimeter (4s) but the rhombus can still be squashed into infinitely many shapes. You need a second value: a diagonal, an angle, or the area. This calculator switches modes so you can enter whichever pair you have.

A kite has two pairs of equal adjacent sides; a rhombus has all four sides equal. Both have perpendicular diagonals, but only the rhombus has diagonals that bisect each other. Visually, a kite is asymmetric top-to-bottom, while a rhombus has full point symmetry.

If you know the diagonals, the acute angle satisfies tan(θ/2) = (d₁/2) / (d₂/2). The obtuse angle is simply 180° − θ. If you know the side and area instead, sin(θ) = A / s².

Because all four sides are equal, the diagonals split the rhombus into four congruent right triangles by symmetry. The right angle at the centre is what makes ½ × d₁ × d₂ such a clean area formula.