Rhombus Calculator

Calculate rhombus area, perimeter, diagonals, angles, height, and other properties. Solve for any rhombus parameter with step-by-step solutions.

Side & Angle
Diagonals
Side & Diagonal
Area & Perimeter
Side & Height

Given: Side length (a) and one angle (θ)

Formulas: Area = a² × sin(θ), Perimeter = 4a, Diagonals: p = 2a × cos(θ/2), q = 2a × sin(θ/2)

units
degrees
Acute angle (0° < θ < 90°) or obtuse angle (90° < θ < 180°)
Rhombus Calculation Results
Side Length
10.00
units
Perimeter
40.00
units
Area
86.60
sq units
Height
8.66
units
Diagonal p
17.32
units
Diagonal q
10.00
units
Acute Angle
60.00
degrees
Obtuse Angle
120.00
degrees
60.0°
Acute Angle
120.0°
Obtuse Angle

Rhombus Properties and Formulas

A rhombus is a quadrilateral with all sides equal in length. It is a special type of parallelogram where all sides are equal, and its diagonals are perpendicular bisectors of each other.

Key Properties of a Rhombus:

  • All sides are equal in length (a = b = c = d)
  • Opposite sides are parallel
  • Opposite angles are equal (∠A = ∠C, ∠B = ∠D)
  • Adjacent angles are supplementary (∠A + ∠B = 180°)
  • Diagonals bisect each other at right angles (90°)
  • Diagonals bisect the interior angles

Rhombus Formulas

Property Formula Description
Perimeter (P) P = 4a Four times the side length
Area (A) using side & angle A = a² × sin(θ) Side squared times sine of any angle
Area using diagonals A = (p × q) / 2 Half the product of diagonals
Area using side & height A = a × h Base times height
Diagonal p p = a × √(2 + 2 cos θ) From side and acute angle
Diagonal q q = a × √(2 - 2 cos θ) From side and acute angle
Side from diagonals a = √(p² + q²) / 2 Half the square root of sum of squares of diagonals
Height (h) h = a × sin(θ) Side times sine of angle

Comparison with Other Quadrilaterals

Square

All sides equal, all angles 90°

Rhombus

All sides equal, angles not necessarily 90°

Rectangle

Opposite sides equal, all angles 90°

Parallelogram

Opposite sides equal and parallel

Applications of Rhombus Geometry

  • Architecture: Diamond-shaped tiles and patterns
  • Engineering: Structural components with equal strength in all directions
  • Design: Kite designs and logos
  • Mathematics: Basis for understanding parallelograms and quadrilaterals
  • Crystallography: Rhombic crystal structures

Calculator Features:

  • Five different calculation modes for maximum flexibility
  • Step-by-step solutions showing how each property is calculated
  • Interactive visualization of the rhombus with labeled dimensions
  • Angle visualization with acute and obtuse angles displayed
  • Comprehensive results including all rhombus properties

Frequently Asked Questions

A square is a special type of rhombus where all angles are 90°. All squares are rhombuses, but not all rhombuses are squares. A rhombus has all sides equal but its angles are not necessarily 90°.

No, the diagonals of a rhombus are generally not equal. They are equal only in the special case of a square. However, the diagonals of a rhombus always bisect each other at right angles (90°).

If you only know the side length of a rhombus, you cannot determine its area without additional information. You need at least one angle or the length of at least one diagonal to calculate the area.

Yes, if a rhombus has a right angle, then all its angles are right angles, which makes it a square. So a square is a special case of a rhombus with right angles.

The diagonals of a rhombus (p and q) and the side length (a) are related by the formula: 4a² = p² + q². This is derived from the Pythagorean theorem applied to the four right triangles formed by the diagonals.