# Rhombus Calculator

Calculate rhombus area, perimeter, diagonals, and angles. Enter diagonals, side and angle, or side and area. Free online rhombus calculator.

## What this calculates

Calculate the area, perimeter, diagonals, side length, and interior angles of a rhombus. Choose from three input methods depending on what measurements you have.

## Inputs

- **Calculate From** — options: Two Diagonals (d1, d2), Side & Angle, Side & Area — Choose what measurements you have.
- **Diagonal 1 (d₁)** — Length of the first diagonal. Used when calculating from diagonals.
- **Diagonal 2 (d₂)** — Length of the second diagonal. Used when calculating from diagonals.
- **Side Length (a)** — The length of one side. All four sides are equal in a rhombus.
- **Angle (degrees)** — One interior angle in degrees (for Side & Angle method).
- **Area** — The area of the rhombus (for Side & Area method).

## Outputs

- **Area** — The area of the rhombus.
- **Perimeter** — The perimeter (4 times the side length).
- **Side Length** — The length of each side.
- **Diagonal 1 (d₁)** — The length of the first diagonal.
- **Diagonal 2 (d₂)** — The length of the second diagonal.
- **Interior Angles** — formatted as text — The two pairs of opposite equal angles.

## Details

A rhombus is a quadrilateral with all four sides equal in length. It is a special case of a parallelogram where all sides are the same, and its diagonals bisect each other at right angles.

**Key Formulas:**

**Area (from diagonals):**
Area = (d1 x d2) / 2

**Area (from side and angle):**
Area = a² x sin(α)

**Perimeter:**
P = 4a (since all sides are equal)

**Side from diagonals:**
a = sqrt((d1/2)² + (d2/2)²)

**Diagonals from side and angle:**
d1 = 2a x sin(α/2), d2 = 2a x cos(α/2)

**Properties of a Rhombus:**

- All four sides are equal in length
- Opposite angles are equal
- Adjacent angles are supplementary (add up to 180°)
- Diagonals bisect each other at right angles (90°)
- Diagonals bisect the vertex angles
- A square is a special rhombus where all angles are 90°

**Example:**

A rhombus with diagonals d1 = 10 and d2 = 8:
- Area = (10 x 8) / 2 = 40
- Side = sqrt(5² + 4²) = sqrt(41) = 6.403
- Perimeter = 4 x 6.403 = 25.612

## Frequently Asked Questions

**Q: What is the difference between a rhombus and a square?**

A: A square is a special type of rhombus where all angles are 90 degrees. Every square is a rhombus, but not every rhombus is a square. A general rhombus has two pairs of equal angles that are not necessarily 90 degrees, giving it a diamond-like shape.

**Q: How do I find the area of a rhombus from its diagonals?**

A: Multiply the two diagonals and divide by 2: Area = (d1 x d2) / 2. For example, if the diagonals are 12 and 8, the area is (12 x 8) / 2 = 48 square units. This works because the diagonals divide the rhombus into four right triangles.

**Q: Why do the diagonals of a rhombus bisect each other at right angles?**

A: Because all four sides are equal, each diagonal creates two congruent isosceles triangles. The point where the diagonals cross is equidistant from the endpoints of each diagonal, and the congruent triangles force the crossing angle to be 90 degrees. This perpendicular bisection is unique to rhombuses among parallelograms.

**Q: What is the difference between a rhombus and a parallelogram?**

A: A parallelogram has two pairs of parallel sides, but opposite sides are equal (not necessarily all four). A rhombus is a parallelogram where all four sides are equal. Every rhombus is a parallelogram, but a rectangle with unequal sides is a parallelogram that is not a rhombus.

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Source: https://vastcalc.com/calculators/math/rhombus
Category: Math
Last updated: 2026-04-08