Updated · Built and checked by the PlinzoTools team, formulas tested against published sources
Calculate a square's area and perimeter from its side length.
This tool calculates both the area and perimeter of a square from a single input: its side length.
Enter the side length. Area and perimeter appear instantly.
Area = side²
Perimeter = 4 × side
For a square, one measurement determines everything. The area is the space enclosed, in square units, and the perimeter is the distance around the edge, in ordinary units. The calculator uses whichever unit you type and shows both results to four decimal places. The side length must be a positive number.
Suppose a hypothetical square patio has sides of 3.5 meters. Enter 3.5 as the side length.
Area = 3.5 × 3.5 = 12.25 square meters
Perimeter = 4 × 3.5 = 14 meters
You would need 12.25 square meters of paving, plus an allowance for cuts, and 14 meters of edging around the border. Notice how the area does not increase in proportion to the side: it grows with the square of the side.
If you double the side length, the perimeter doubles but the area becomes four times as large. If you triple the side, the perimeter triples and the area becomes nine times as large. This is useful in practical planning. Going from a 2 meter square to a 4 meter square does not merely double the amount of paint or paving you need; it quadruples it. Conversely, halving the side leaves only one quarter of the area.
If you know the area and need the side, take the square root of the area. A hypothetical 49 square foot square has a side of 7 feet. If you know the perimeter, divide it by 4. A perimeter of 26 gives a side of 6.5. Once you have the side, enter it in the tool to confirm the other measurement.
Many shapes called squares in everyday speech, such as floor tiles, picture frames, or garden plots, are only approximately square. If the two dimensions differ even slightly, the square formula will misstate the area. Measure both dimensions. If they differ, use the Rectangle Area & Perimeter Calculator instead. As a check that a shape really is square, its two diagonals should be equal and each corner should be a right angle.
A curious case: when the side is exactly 4, the area and perimeter have the same numerical value of 16. Because area is in square units and perimeter in plain units, this is a numerical coincidence, not a real equality.
Use the Rectangle Area & Perimeter Calculator, which takes separate length and width.
Take the square root of the area. If the area is 81 square units, the side is 9 units.
Area is the side multiplied by itself. Doubling the side gives 2 × 2 = 4 times as much surface, while the perimeter, which counts the side only four times over, merely doubles.
No. It works in whatever unit you enter, so use a single consistent unit and convert the answer yourself if needed.
Yes, any positive number works, and the results are shown to four decimal places.
Reference: NIST Weights and Measures