Area of a Rhombus Calculator

Enter both diagonals — or side and angle — to get area, perimeter, and step-by-step working instantly.

Unit:
Diagonal 1 (d₁)
cm
Diagonal 2 (d₂)
cm

Enter both diagonals to calculate area, side length, and perimeter.

Diagram

Rhombus Area Formulas

From Diagonals

A = (d₁ × d₂) / 2

Multiply both diagonals together and halve the result.

From Side & Angle

A = s² × sin(θ)

θ is any interior angle of the rhombus.

Perimeter

P = 4 × s

All four sides of a rhombus are equal.

Side from Diagonals

s = √(d₁² + d₂²) / 2

From Pythagoras applied to the half-diagonals.

What Is a Rhombus?

A rhombus is a quadrilateral with all four sides equal in length. It is a special case of a parallelogram. While it looks like a "squashed square" or diamond shape, its defining property is equal side lengths — not equal angles.

The diagonals of a rhombus are special: they always bisect each other at right angles (90°). This property is what makes the area formula so elegant — each diagonal splits the rhombus into two pairs of congruent right triangles.

A = d₁d₂/2
Area from diagonals — the primary formula
P = 4s
All four sides are equal — perimeter is simply 4 times any side
90°
Diagonals always cross at right angles

How to Calculate the Area of a Rhombus

  1. 1

    Measure both diagonals

    The diagonals are the two lines connecting opposite vertices. Label them d₁ (horizontal) and d₂ (vertical).

  2. 2

    Apply A = (d₁ × d₂) / 2

    Multiply the two diagonals and divide by 2. This formula works because the rhombus can be thought of as two triangles with base d₁ and height d₂/2 each.

  3. 3

    Find side and perimeter

    Side s = √(d₁² + d₂²) / 2 using the Pythagorean theorem on the half-diagonals. Then P = 4s.

Worked Example — Rhombus kite with diagonals 10 cm and 6 cm

Given: d₁ = 10 cm, d₂ = 6 cm
Formula: A = (d₁ × d₂) / 2
Step 1: A = (10 × 6) / 2 = 60 / 2
Area: A = 30 cm²
Side: s = √(10² + 6²) / 2 = √136 / 2 ≈ 5.83 cm
Perimeter:P = 4 × 5.83 ≈ 23.32 cm

Real-World Applications

💎

Jewelry

Diamond shapes in rings, pendants, and earrings are often rhombus-shaped. Area calculation helps determine material needed.

🪁

Recreation

Kite shapes, diamond kites, and rhombus-shaped flags use this formula for fabric and material estimation.

🏗️

Construction

Diamond paving patterns, road warning signs, and decorative tiles often use rhombus shapes.

🎨

Design

Playing card diamond suits, decorative patterns, and logos frequently use rhombus geometry.

📐

Mathematics

The rhombus is a special case of a parallelogram and is central to geometry study. Understanding it builds intuition for vector algebra.

Common Rhombus Measurements

Object d₁ d₂ Area Side Perimeter
Diamond tile 20 cm 16 cm 160 cm² 12.81 cm 51.24 cm
Kite shape 30 cm 20 cm 300 cm² 18.03 cm 72.11 cm
Road diamond 1.2 m 0.8 m 0.48 m² 0.72 m 2.88 m
Playing card 8 cm 6 cm 24 cm² 5.0 cm 20.0 cm
Fabric panel 50 cm 40 cm 1000 cm² 32.02 cm 128.06 cm

Frequently Asked Questions

What is the area formula for a rhombus?
A = (d₁ × d₂) / 2 where d₁ and d₂ are the two diagonals. For example, diagonals 10 cm and 6 cm give A = (10 × 6)/2 = 30 cm².
How are a rhombus and square related?
A square is a special rhombus where all angles are 90°. In a square, both diagonals are equal: d₁ = d₂ = s√2. The area formula gives A = (s√2)²/2 = 2s²/2 = s², which matches the standard square formula.
Do the diagonals of a rhombus bisect each other?
Yes — at right angles (90°). Each diagonal is cut exactly in half by the other at the centre of the rhombus. This means the four triangles formed are all right triangles with legs d₁/2 and d₂/2.
How do you find side length from diagonals?
Use Pythagoras on the half-diagonals: s = √((d₁/2)² + (d₂/2)²) = √(d₁² + d₂²) / 2. For d₁ = 10, d₂ = 6: s = √(100+36)/2 = √136/2 ≈ 5.83 cm.
What is the perimeter of a rhombus?
P = 4s since all sides are equal. Once you know the side from diagonals (s = √(d₁² + d₂²)/2), the perimeter is simply 4 times that value.

Related Area Calculators

Circle Semicircle Square Rectangle Parallelogram Trapezium Scalene Triangle Right Triangle Equilateral Triangle Isosceles Triangle Regular Hexagon Sector & Segment