What is a square calculator?
A square calculator computes the area, perimeter, and diagonal of a square from a single input: the side length. A square has four equal sides and four right angles, so one dimension defines the whole shape. Enter the side length and the calculator gives you the area (side²), the perimeter (4 × side), and the diagonal (side × √2). No sign-up or download is required; the tool runs in your browser and is useful for homework, design, tiling, and any task involving squares.
Squares appear in tiles, windows, plots, and many geometry problems. Knowing the area helps with material coverage; the perimeter helps with framing or edging; the diagonal is used in layout and when checking if a square object fits through a space. This free square calculator gives you all three from one input, in whatever units you use—meters, feet, inches—as long as you use the same unit for side, perimeter, and diagonal, and square units for area.
How to use this square calculator
Enter the side length of your square in the input box. The side must be a positive number. You can use decimals (e.g. 4.5) or whole numbers (e.g. 5). As soon as the value is valid, the results appear: area in square units, perimeter in units, and diagonal in units. The formulas are shown under the input: area = side², perimeter = 4 × side, diagonal = side × √2. If you enter zero or a negative value, the calculator will ask you to enter a positive side length. Use the same unit for side as you want for perimeter and diagonal; area will be in square units of that same measure.
Square area formula
The area of a square is A = side × side = side². For example, a square with side 5 units has area 5² = 25 square units. Because all four sides are equal, the square is a special case of the rectangle (length = width), so area = length × width becomes side². Area is the amount of space inside the square and is always in square units. Use it when you need to cover a square surface—tiles, paint, flooring—or when you need to know how much space a square plot or panel occupies. The square calculator applies this formula so you get an accurate area without doing the math by hand.
Perimeter of a square
The perimeter of a square is the total distance around it. Since all four sides are equal, P = 4 × side. For a square with side 5, the perimeter is 4 × 5 = 20 units. Perimeter is a length, so it uses the same unit as the side. Use it when you need the length of framing for a square frame, the border around a square tile layout, or the fencing for a square garden. The calculator gives you the perimeter as soon as you enter a valid side length.
Diagonal of a square
The diagonal of a square is the line from one corner to the opposite corner. It splits the square into two right triangles with legs equal to the side. By the Pythagorean theorem, diagonal d = side × √2 (since d² = side² + side² = 2 × side²). For side 5, d = 5√2 ≈ 7.07 units. The diagonal is longer than the side by a factor of √2 (about 1.414). Use the diagonal when laying out square corners (e.g. squaring a frame), when comparing to screen or display sizes given as diagonal, or when checking if a square object can pass through an opening. This calculator computes the diagonal from the same side length you enter for area and perimeter.
Square vs rectangle
A square is a special rectangle with length equal to width. So all rectangle formulas apply: area = length × width becomes side², perimeter = 2(l + w) becomes 4 × side, and diagonal = √(l² + w²) becomes side√2. If you have a rectangle calculator, you can use it for squares by entering the same value for length and width. This square calculator is dedicated to squares, so you only enter one value (the side) and get area, perimeter, and diagonal without entering two dimensions. Both approaches give the same results for a square.
Applications of square calculations
Square area, perimeter, and diagonal are used in many fields. In construction and tiling, area determines how many tiles or how much material you need; perimeter is used for trim and borders. In landscaping, square plots are common; area and perimeter help with fencing and planting. In design and manufacturing, square panels and frames use the same formulas. In education, the square is a fundamental shape in geometry. This square calculator gives you quick, accurate results for any of these uses. Always keep units consistent: same unit for side, perimeter, and diagonal, and square units for area.
Summary
This square calculator finds the area, perimeter, and diagonal of a square from the side length. Enter the side (a positive number) and get area = side², perimeter = 4 × side, and diagonal = side × √2 instantly. The tool is free, runs in the browser, and requires no account. Use it for tiles, frames, plots, or any square shape. One input gives you all three measurements. Keep units consistent for accurate results.