Free · Plane geometry calculators 🔺

Square Boundary Length and Diagonal

Calculate square boundary length and diagonal with bidirectional inputs, compatible units and clear geometric assumptions.

  • Formula & worked example
  • Private in your browser
  • No signup
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A square with side 3 has area 9, perimeter 12 and diagonal 3√2 in compatible units.

A = a²; P = 4a; diagonal = a√2

Worked example

Enter these known values and leave the other values blank.

Side (a)
3 cm
Diagonal (d)
4.243 cm
Perimeter
12 cm

Assumptions and limitations

  • All four sides are equal and adjacent sides are perpendicular. The side root is the positive geometric branch.
  • Length and area selectors are converted before calculation. A squared-length unit is not the same as a length unit.
  • The supplied measurements must be mutually consistent. Clear an unknown value rather than supplying conflicting dimensions.
  • Arithmetic uses 64 significant digits and full-precision π where applicable; displayed values are rounded separately.

Common questions

Does the side recovered from area have a negative solution?

The geometric side is positive; the negative algebraic square root does not describe a side length.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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