Quick answer
A rhombus with diagonals p and q has area pq ÷ 2, side √((p/2)² + (q/2)²) and perimeter 4 × side. Diagonals of 6 and 8 give area 24, side 5 and perimeter 20.
Enter the two diagonals. The calculator returns the area, side and perimeter.
Related tools: Triangle Calculator: Area, perimeter, angles and type of a triangle from its three sides. Circle Calculator: Radius, diameter, circumference and area of a circle from any one of them. Circumference Calculator: Circumference of a circle.
How to use the Rhombus Calculator
- Enter diagonal p (above 0).
- Enter diagonal q (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Diagonal p | A number | > 0 |
| Diagonal q | A number | > 0 |
Formula and method
Formula
A = pq ÷ 2; side = √((p/2)² + (q/2)²); P = 4 × side
IEEE-754 double precision; shown to at most 6 decimal places.
The diagonals bisect each other at right angles.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Diagonal p = 6; Diagonal q = 8.
| Result | Value |
|---|---|
| Area | 24 |
| Side | 5 |
| Perimeter | 20 |
Example 2
Inputs: Diagonal p = 10; Diagonal q = 10.
| Result | Value |
|---|---|
| Area | 50 |
| Side | 7.071068 |
| Perimeter | 28.284271 |
The first line is the headline result (area). Below it the rhombus Calculator lists side and perimeter, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Right triangles inside
The diagonals bisect each other at right angles, forming four right triangles with legs 3 and 4 and hypotenuse 5. So each side is 5, the perimeter 20 and the area 4 × (½ × 3 × 4) = 24.
Properties
All four sides are equal, opposite angles are equal and the diagonals are perpendicular. A square is a rhombus with equal diagonals. Both diagonals must be positive.
How the result changes with diagonal p
Holding every other input at the first worked example, this table changes only diagonal p. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Diagonal p | Area | Side | Perimeter |
|---|---|---|---|
| 3 | 12 | 4.272002 | 17.088007 |
| 6 | 24 | 5 | 20 |
| 12 | 48 | 7.211103 | 28.84441 |
| 24 | 96 | 12.649111 | 50.596443 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Diagonal p: entering "0" shows "Diagonal p must be greater than 0." beside that field and no result.
Choosing between the Rhombus Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Triangle Calculator](/math/triangle-calculator/) | side a, side b and side c | Area |
| [Circle Calculator](/math/circle-calculator/) | i know the and value | Area |
| [Circumference Calculator](/math/circumference/) | i know the and value | Circumference |
| [Area of a Circle Calculator](/math/area-of-a-circle/) | i know the and value | Area |
| [Rectangular Prism Volume Calculator](/math/rectangular-prism-volume/) | length, width and height | Volume |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Diagonals must be positive
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for diagonal p to confirm this.
Frequently asked questions
What is the area if the diagonals are 10 and 4?
With diagonals 10 and 4 the area is 10 × 4 ÷ 2 = 20.
Is a rhombus a parallelogram?
Yes. A rhombus has two pairs of parallel sides, so it is a parallelogram with four equal sides.
Can I find the angle?
tan(half angle) = p/q relation.
What does the Rhombus Calculator calculate?
Area, side and perimeter of a rhombus from its diagonals. It returns Area, Side and Perimeter.
What formula does the Rhombus Calculator use?
A = pq ÷ 2; side = √((p/2)² + (q/2)²); P = 4 × side. The diagonals bisect each other at right angles.
What do I need to enter in the rhombus Calculator?
You enter Diagonal p and Diagonal q.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Diagonals must be positive.
What is an example of a rhombus result?
With diagonal p 6 and diagonal q 8, the area is 24.
Related calculators
- Triangle Calculator — Area, perimeter, angles and type of a triangle from its three sides.
- Circle Calculator — Radius, diameter, circumference and area of a circle from any one of them.
- Circumference Calculator — Circumference of a circle.
- Area of a Circle Calculator — Area of a circle from its radius, diameter or circumference.
- Rectangular Prism Volume Calculator — Volume of a rectangular prism (box).
- Circle Diameter Calculator — Diameter of a circle from radius, circumference or area.
Sources
- Standard Euclidean geometry formulas (e.g. NIST Digital Library of Mathematical Functions §4, CRC Standard Mathematical Tables)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.