Rhombus Area Calculator

Calculate area and perimeter of a rhombus

Diagonal 1 (d₁)

Diagonal 2 (d₂)

Side length (s)

How to Use This Rhombus Area Calculator

Enter the diagonal lengths

Input the lengths of both diagonals (d1 and d2). These are the lines connecting opposite corners of the rhombus.

Enter the side length

Input the length of one side. All four sides of a rhombus are equal, so you only need one measurement.

Click Calculate

The calculator computes the area using A = (d1 x d2) / 2 and the perimeter using P = 4 x side length.

Rhombus Properties Reference

Property	Formula	Example
Area	(d1 x d2) / 2	(10 x 8) / 2 = 40
Perimeter	4 x s	4 x 6 = 24
Side from diagonals	s = sqrt((d1/2)² + (d2/2)²)	sqrt(25 + 16) = 6.4
Area from side & height	s x h	6 x 5 = 30
Area from side & angle	s² x sin(θ)	36 x sin(60°) = 31.2

Understanding Rhombuses

A rhombus is a quadrilateral with four equal sides. It's a special type of parallelogram where all sides have the same length. You might know it as a "diamond" shape — though mathematically, a diamond is just a rhombus oriented with its diagonals vertical and horizontal.

The diagonals of a rhombus have two important properties: they bisect each other at right angles (90°), and they bisect the corner angles. This means the diagonals split the rhombus into four congruent right triangles. This property is why the area formula uses diagonals — you're essentially calculating the area of those four triangles.

A square is a special case of a rhombus where all angles are 90°. All squares are rhombuses, but not all rhombuses are squares. The rhombus is more flexible — it can be squashed or stretched while keeping all four sides equal.

Key insight: The area formula A = (d1 x d2) / 2 works because the diagonals create four right triangles. Each triangle has area (d1/2 x d2/2) / 2, and four of them give (d1 x d2) / 2.

Rhombus vs Other Quadrilaterals

Rhombus vs Square

Both have four equal sides. A square also has four 90° angles and equal diagonals. A rhombus has opposite angles equal but not necessarily 90°, and its diagonals are usually different lengths.

Rhombus vs Rectangle

Rectangles have four 90° angles but opposite sides equal (not all four). A rhombus has all sides equal but angles aren't necessarily 90°. A square is both a rhombus and a rectangle.

Rhombus vs Parallelogram

All rhombuses are parallelograms (opposite sides parallel), but not all parallelograms are rhombuses. A parallelogram only requires opposite sides to be equal, not all four sides.

Rhombus vs Kite

A kite has two pairs of adjacent equal sides. A rhombus has all four sides equal. Both have perpendicular diagonals, but only the rhombus has diagonals that bisect each other.

Frequently Asked Questions

What if I only know the side length?

You need more information — either the height, one angle, or one diagonal. With just the side length, there are infinitely many rhombuses possible (think of a square being squashed flatter and flatter while keeping the same side length).

How do I find the diagonals if I know the side and angle?

Use trigonometry: d1 = 2 x s x cos(θ/2) and d2 = 2 x s x sin(θ/2), where θ is any corner angle. The diagonals bisect the angles, so you use half the angle in the formulas.

Is a rhombus always a parallelogram?

Yes. By definition, a rhombus has opposite sides parallel (that's what makes all four sides equal possible). Every rhombus is a parallelogram, but the reverse isn't true.

Can a rhombus have right angles?

Yes — if all four angles are 90°, it's a square. A square is a rhombus with right angles. If only some angles are 90°, it's not a valid rhombus (opposite angles must be equal).

What units should I use?

Any consistent units work. If diagonals are in centimeters, area is in square centimeters. If sides are in meters, perimeter is in meters. The calculator doesn't assume units — just be consistent.

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