Square Calculator — Side, Diagonal, Perimeter, Area

Enter any one value (or more). Private by design — runs locally in your browser.

Diagram & Inputs

Tip: Any one value (or more). We recover the side s, then compute everything else. If inputs disagree, we’ll warn and still show a best-fit result.

Results

How the Square Calculator Works

All square measures derive from the side \(s\):

  • Perimeter: \(P=4s\)
  • Area: \(A=s^2\)
  • Diagonal: \(d=s\sqrt{2}\)
  • Inradius: \(r=\tfrac{s}{2}\) (inscribed circle)
  • Circumradius: \(R=\tfrac{s}{\sqrt{2}}\) (circumcircle)

Enter any one value (or more). The solver first infers \(s\), checks for consistency if multiple values are provided, then outputs all properties. Everything runs locally in your browser.

Understanding Squares with Visuals

A square is a special rectangle with four equal sides and four right angles. Because of this symmetry, one measurement determines them all: from the side length s you can find perimeter P = 4s, area A = s², and the corner-to-corner diagonal d = s√2. This calculator lets you enter any one value (or more) and instantly computes the rest, checking consistency when multiple inputs are provided. The visuals below show the key relationships at a glance and help learners connect formulas to geometry.

Side & Area

s A = s²

The square’s area grows with the square of the side: doubling s makes the area four times larger.

Diagonal (Pythagoras)

s s d = s√2

The diagonal is the hypotenuse of a right triangle with equal legs: d = √(s²+s²) = s√2.

Perimeter

P = 4s

Walking once around the boundary adds four equal sides, so the perimeter is simply four times s.

Inradius & Circumradius

r = s/2 R = s/√2

The inscribed circle touches each side at the midpoint (r = s/2), while the circumscribed circle passes through the corners (R = s/√2).

In practice, these relationships make it easy to convert measurements. If you know the tabletop’s diagonal, you can recover the side for cutting material; if you know floor-tile area, you can find the tile width and perimeter trim. The calculator runs entirely in your browser (client-side JavaScript), so results are instant and private, and unit labels keep outputs clear: lengths are shown in your chosen unit, while area automatically uses the squared unit (e.g., cm² or in²).

5 Fun Facts about Squares

Diagonal = side × √2

The 45°-45°-90° triangle inside every square makes the diagonal a clean s·√2—a geometric shortcut hiding in plain sight.

Hidden triangle

Perimeter and area collide

A side of 4 gives perimeter 16; a side of 4 also gives area 16. That tidy overlap is rare outside squares.

Number quirk

Two circles, perfect fit

Inradius = s/2, circumradius = s/√2. Double the inradius and you hit the diagonal—circles and squares align exactly.

Circle pairing

Scaling lessons

Perimeter scales linearly with side, but area scales with the square. Halve s → perimeter halves, area shrinks to one-quarter—a crisp demo of quadratic growth.

Scaling intuition

Ancient magic squares

Over 2,000 years ago, Chinese mathematicians arranged numbers in square grids so each row, column, and diagonal summed to the same constant—numerical symmetry as art.

Math lore

Square Calculator: FAQs

Which inputs are valid?

Any one of: side \(s\), diagonal \(d\), perimeter \(P\), area \(A\), inradius \(r\), circumradius \(R\). Multiple inputs are OK; we check consistency.

What about units?

Lengths use your chosen unit; area is shown with squared units (e.g., cm²).

Is this private?

Yes—100% client-side.

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