From the side
P = 4 × c
Four sides of equal length.
Perimeter of a Square Calculator (Side or Diagonal)
Calculate the perimeter of a square from its side (P = 4s) or its diagonal (P = 2√2 × d). Formulas explained, finding the side from the perimeter, edging and fencing examples, in the length unit of your choice.
Perimeter
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How does this tool work?
This calculator gives the perimeter of a square, the total length of its four sides, from the side or the diagonal. Use it to check an elementary or middle school exercise, or to plan the edging for a square raised bed, the fencing for a pen or the piping around a cushion.
All four sides of a square have the same length s, so its perimeter is P = s + s + s + s = 4 × s. A square with 6 cm sides has a perimeter of 24 cm.
When only the diagonal d is known, the tool recovers the side with the Pythagorean theorem: d² = 2s², so s = d ÷ √2. The perimeter is then P = 4d ÷ √2 = 2√2 × d, about 2.828 times the diagonal.
The result is a length in the same unit as the value you entered. Because the relationship is proportional, doubling the side doubles the perimeter, while the area is multiplied by four.
For the reverse operation, just divide by four: a square with a 36 cm perimeter has 9 cm sides. This tells you how large a square you can lay out with a given length of edging or fencing.
How to use this tool
Pick the measurement you know
Side or Diagonal, depending on what the problem gives or what you can measure.
Enter the value and its unit
All common length units, metric and imperial, are available.
Read the perimeter
It appears in the same unit and updates as you type.
Formulas for the perimeter of a square
The perimeter follows from the side or the diagonal.
From the diagonal
P = 2√2 × d
The side equals d ÷ √2, by the Pythagorean theorem.
Side from the perimeter
c = P ÷ 4
The inverse operation.
- P
- perimeter, in length units
- c
- length of one side (also written s)
- d
- diagonal
Example: s = 2.5 m, P = 10 m.
Use cases
Garden and fencing
Work out the edging for a square vegetable bed or sandbox, or the fencing for a square pen.
DIY and trim work
Plan the molding, sealant or trim around a square hatch, mirror or panel.
School
Check a perimeter exercise and understand the link between side, diagonal and the square root of 2.
Sewing
Measure the piping or bias tape needed around a cushion or a square of fabric.
Examples
From the side
4 × 6 = 24 cm.
Input
s = 6 cmResult
P = 24 cmFrom the diagonal
The side is 10 ÷ √2 ≈ 7.07 cm, so P ≈ 4 × 7.07 ≈ 28.28 cm.
Input
d = 10 cmResult
P ≈ 28.28 cmRaised bed edging
Four 1.2 m boards, or 4.8 m of flexible edging.
Input
square with 1.2 m sidesResult
P = 4.8 mSquare pen
60 m of fencing, minus the width of the access gate.
Input
s = 15 mResult
P = 60 mWorking backwards
20 ÷ 4 = 5 m per side, for a pen of 25 m².
Input
20 m of fencing availableResult
maximum side of 5 mTips and best practices
- Perimeter is a length (cm, m, ft), unlike area, which is in square units.
- With the diagonal, do not simply multiply it by 4: divide it by √2 first.
- For a fence, subtract the width of the gate and add a margin for fastening.
- A square does not have to sit level: a square turned on its corner keeps the same perimeter.
Sources and references
- Weisstein E.W., Square (opens in a new tab), Wolfram MathWorldPage in English
- Weisstein E.W., Perimeter (opens in a new tab), Wolfram MathWorldPage in English
- Programme de mathématiques pour le cycle 3 (opens in a new tab), Ministère de l’Éducation nationalePage in French
Frequently asked questions
What is the formula for the perimeter of a square?
P = 4 × s, where s is the length of one side. With the diagonal d, P = 2√2 × d ≈ 2.828 × d.
How do you find the side of a square from its perimeter?
Divide the perimeter by 4: s = P ÷ 4. A square with a 48 cm perimeter has 12 cm sides.
How do you find the perimeter of a square from its diagonal?
Divide the diagonal by √2 (about 1.414) to get the side, then multiply by 4. A 14.14 cm diagonal gives a 10 cm side and a 40 cm perimeter.
Do a square and a rectangle with the same perimeter have the same area?
No. With a 20 m perimeter, a 5 m square covers 25 m², while an 8 × 2 m rectangle covers only 16 m². The square gives the largest area.
Why is the perimeter of a square proportional to its side?
Because it is simply the sum of four equal sides. The constant of proportionality is 4.
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