Rhombus Calculator
Calculate area, perimeter, side lengths, and diagonals of any rhombus instantly
Calculation Results
Enter rhombus measurements to calculate all properties.
Side (a): units
Height (h): units
Diagonal 1 (d₁): units
Diagonal 2 (d₂): units
Area (A): square units
Perimeter (P): units
Angle (α): degrees
Angle (β): degrees
Rhombus Diagram
The Rhombus: A Special Parallelogram
A rhombus is a type of quadrilateral where all four sides are of equal length. It's a special case of a parallelogram where the diagonals bisect each other at right angles.
Key Properties of a Rhombus
- Side (a) – All four sides are equal in length.
- Diagonals (d₁, d₂) – Perpendicular bisectors that divide the rhombus into four right-angled triangles.
- Height (h) – The perpendicular distance between opposite sides.
- Area (A) – Can be calculated as base × height or (d₁ × d₂)/2.
- Perimeter (P) – The sum of all sides (4 × side length).
- Angles (α, β) – Opposite angles are equal, and adjacent angles are supplementary (sum to 180°).
Mathematical Equations of a Rhombus
- Area: A = a × h = (d₁ × d₂)/2
- Perimeter: P = 4a
- Side from diagonals: a = √((d₁/2)² + (d₂/2)²)
- Height from area: h = A/a
Why Are Rhombuses Important?
- Geometry & Mathematics - Fundamental shape in Euclidean geometry.
- Engineering - Used in structural designs and tiling patterns.
- Nature - Appears in crystal structures and certain mineral formations.
- Design & Art - Common in decorative patterns and logos.
Facts About Rhombuses
- A square is a special type of rhombus where all angles are 90°.
- The word "rhombus" comes from the Greek word "rhombos," meaning something that spins.
- All rhombuses are parallelograms, but not all parallelograms are rhombuses.
Rhombuses are elegant symmetrical shapes with unique properties that make them valuable in both theoretical mathematics and practical applications.
Side (a)
Diagonal 1 (d₁)
Diagonal 2 (d₂)
Angle (α)
Height (h)
Area (A)
Rhombus Formulas
- Area (A): A = a × h = (d₁ × d₂)/2
- Perimeter (P): P = 4a
- Side from diagonals: a = √((d₁/2)² + (d₂/2)²)
- Height from area: h = A/a
- Angle from diagonals:
Acute angle (α): α = 2 × tan−1(d₂ / d₁)Obtuse angle (β): β = 180° - α
How to Use the Rhombus Calculator
The Rhombus Calculator helps compute various properties based on input values. Here's how to use it:
1 Select What You Know
Choose the known values combination:
- Side and Height
- Diagonals
- Side and Angle
- Area and Perimeter
2 Enter the Values
Type in positive numeric values for your selected parameters.
Example: side = 5, height = 4
3 Click "Calculate"
The calculator will compute:
- All sides
- Diagonals
- Height
- Area
- Perimeter
- Angles
Example Use Cases
- Calculate the area of a rhombus-shaped plot of land.
- Determine the side length when you know the diagonals.
- Find the height needed for a rhombus-shaped sign with a given area.
Example Calculations
-
Example 1: a = 5 units, h = 4 units
- Area = 5 × 4 = 20 units²
- Perimeter = 4 × 5 = 20 units
- Diagonals ≈ 6.40 and 6.25 units
-
Example 2: d₁ = 8 cm, d₂ = 6 cm
- Area = (8 × 6)/2 = 24 cm²
- Side = √(4² + 3²) = 5 cm
- Perimeter = 4 × 5 = 20 cm
Frequently Asked Questions
In geometry, a rhombus is the precise term for an equilateral quadrilateral, while "diamond" is often used informally to describe a rhombus shape.
Yes! When all angles are 90°, the rhombus is actually a square - which is a special type of rhombus.
Height = Area ÷ Side length (h = A/a).
- Baseball diamonds (though technically squares)
- Kite designs
- Certain road signs
- Quartz crystal formations