Square Calculator

Step 1: Measure One Side Length

Find the length s of any side (all sides are equal in a square).

Why: A square’s side defines all its properties; area, perimeter, and diagonal all depend on s.

Step 2: Verify Side Is Positive

Ensure s > 0; negative or zero side length is impossible.

Why: Geometric validity requires positive dimensions.

Step 3: Calculate Area

Use A = s² (side length squared).

Why: All four sides are equal, so area is the product of two sides: s × s = s².

Step 4: Calculate Perimeter

Use P = 4s (four equal sides).

Why: Perimeter is the total distance around; four sides sum to 4s.

Step 5: Calculate Diagonal

Use d = s√2 (diagonal of square, applying Pythagorean theorem to the two sides).

Why: The diagonal forms a 45-45-90 triangle with two sides, so d² = s² + s².