Perimeter of Rhombus Calculator
Enter the side of a rhombus, its two diagonals, or its area and height, to find its perimeter.
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Perimeter of Rhombus Calculator
Our Perimeter of Rhombus Calculator finds the perimeter of a rhombus from its side length, from its two diagonals, or from its area and height. It also gives the side, the area, the diagonals and the angles when they can be worked out, with a drawing to scale.
Quick answer
The perimeter of a rhombus is 4 times its side: P = 4 × 10 cm = 40 cm.
- From the diagonals: P = 2√(d₁² + d₂²), so 16 and 12 give 2√400 = 40
- From the area and height: P = 4A ÷ h, so 60 and 6 give 40
- Side from the perimeter: s = P ÷ 4
- Units: the perimeter is a length, so cm stays cm (not cm²)
What Is a Rhombus?
A rhombus is a four-sided shape with all four sides equal. Its opposite sides are parallel and its opposite angles are equal, so it looks like a diamond or a tilted square. The perimeter is the total length around the outside: the four equal sides added together.
Perimeter of a Rhombus Formulas
Use the formula that matches what you know. All three give the same perimeter for the same rhombus.
| You know | Formula |
|---|---|
| The side | P = 4 × s |
| Both diagonals | P = 2√(d₁² + d₂²) |
| Area and height | P = 4A ÷ h |
Perimeter From the Side
- Measure one side. s = 10 cm.
- Multiply by 4. 4 × 10 = 40.
- Write the answer in the same unit. 40 cm.
The angles and the height do not change the perimeter. A rhombus that leans over a lot has the same perimeter as a square with the same side, only a smaller area.
Perimeter From the Diagonals
The diagonals of a rhombus cross at a right angle and cut each other in half. Each side is the long side of a right triangle whose short sides are d₁ ÷ 2 and d₂ ÷ 2, so by Pythagoras s = ½√(d₁² + d₂²). Four sides give P = 2√(d₁² + d₂²).
- Square both diagonals. 16² = 256 and 12² = 144.
- Add them. 256 + 144 = 400.
- Take the square root. √400 = 20.
- Double it. 2 × 20 = 40, so each side is 10 and P = 40.
Rhombus Perimeter Examples
| Diagonals | Side | Perimeter |
|---|---|---|
| 6 and 8 m | 5 m | 20 m |
| 16 and 12 cm | 10 cm | 40 cm |
| 24 and 10 in | 13 in | 52 in |
| 10 and 8 cm | ≈ 6.403 cm | ≈ 25.61 cm |
| 5 and 5 ft | ≈ 3.536 ft | ≈ 14.14 ft |
Equal diagonals (the last row) mean the rhombus is a square. When d₁² + d₂² is not a perfect square, the exact answer has a root in it: diagonals of 10 and 8 give 2√164 = 4√41 ≈ 25.61.
Perimeter From the Area and Height
The area of a rhombus is side × height, so dividing the area by the height gives the side. An area of 60 cm² and a height of 6 cm give s = 60 ÷ 6 = 10 cm and P = 4 × 10 = 40 cm. The height can never be longer than the side, so h² must not be more than A.
Finding the Side or a Diagonal
Rearrange the formulas when you know the perimeter:
- Side: s = P ÷ 4. A perimeter of 52 in gives s = 13 in.
- Missing diagonal: d₂ = √((P ÷ 2)² − d₁²). P = 40 and d₁ = 16 give √(400 − 256) = 12.
- Area: you also need the height, an angle or both diagonals. A = s × h.
Common Mistakes
- Adding the diagonals: d₁ + d₂ is not the perimeter. Use 2√(d₁² + d₂²).
- Using half-diagonals twice: halve each diagonal once, inside the triangle, not again at the end.
- Square units: a perimeter is a length (cm, m, ft), not an area (cm²).
- Thinking the angle matters: the same side always gives the same perimeter.
- Mixing units: convert both diagonals to the same unit before squaring.
Key Terms
- Side
- Any of the four equal edges, s.
- Perimeter
- The distance all the way around, P = 4s.
- Diagonals
- Lines joining opposite corners, d₁ and d₂.
- Height
- Distance between two opposite sides, at a right angle, h.
How to Use the Perimeter of Rhombus Calculator
- Choose what you know. Pick Side if you know the side length, Diagonals if you know both diagonals, or Area & height.
- Enter the values. Type the lengths, such as 16 and 12, and pick a unit if you want one (mm, cm, m, km, in, ft, yd or mi). In Side mode the height is optional and adds the area, angles and diagonals. Decimals and fractions such as 3/4 work.
- Read and copy the result. The perimeter appears as you type, with a drawing to scale, the working, the side, the area, diagonals and angles when known, and the perimeter in other units. Press Copy to copy it, or Clear or Esc to start again.
Example: a diamond-shaped garden bed has diagonals of 24 ft and 10 ft. Choose Diagonals, enter 24 and 10 and pick ft. Each side is 13 ft, so you need 52 ft of edging.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you find the perimeter of a rhombus?
Multiply the side by 4, because all four sides of a rhombus are equal. A side of 10 cm gives 4 × 10 = 40 cm.
What is the formula for the perimeter of a rhombus?
P = 4 × s with the side, P = 2√(d₁² + d₂²) with the two diagonals, or P = 4A ÷ h with the area and height.
How do you find the perimeter of a rhombus from its diagonals?
Square both diagonals, add them, take the square root and double it. Diagonals of 16 and 12 give 2√(256 + 144) = 2 × 20 = 40.
How do you find the side of a rhombus from its perimeter?
Divide the perimeter by 4: s = P ÷ 4. A perimeter of 52 in gives a side of 13 in.
How do you find the perimeter of a rhombus from its area?
You also need the height (or another measurement). The side is A ÷ h, so an area of 60 cm² and a height of 6 cm give s = 10 cm and P = 40 cm.
Does the angle of a rhombus change its perimeter?
No. The perimeter depends only on the side. Leaning the rhombus over changes its area and diagonals, but every side stays the same length.
Is the perimeter of a rhombus the same as a square with the same side?
Yes. Both have four equal sides, so both have P = 4s. A square is a rhombus with right angles.
Is the Perimeter of Rhombus Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Perimeter of Rhombus Calculator to find the perimeter of any rhombus from its side, its diagonals, or its area and height.