Math and relationships

Squares and square roots

Square numbers or measured lengths and recover a square’s side from its area.

A square’s area is side × side. Squaring a measured length produces square units; taking the square root of an area returns a length. Labeling an existing number with square units does not square it.

Find a square’s area or side

Use a square’s side to find its area, or its area to find the side.

Square, then undo it

x² multiplies a number by itself. √x undoes that square. A 12 ft side gives 144 ft²; the square root takes you back to 12 ft.

A square with 12 foot sides has an area of 144 square feet. Squaring the side gives the area. The square root of the area gives the side.144 ft²12 ft
Schematic, not to scale.

Try it · a 12 ft square

Use 2nd if Feet is above its key.

  1. Start fresh

    Press Clear entry, then Clear entry, then Select length units.
  2. Enter one side and square it

    Press 12, then feet, then Square.
  1. Area144 square feet

Get the side back

  1. Take the square root

    Press Square root.
  1. Side length12 feet 0 inches

Also useful for

Square floor sections, sheet-metal blanks, access panels and square pads. For similar shapes, square root turns an area ratio into a length ratio.

Remember

This finds a side only for a square. For a rectangle, multiply length by width.

Square root of an area

Label the area with square units before taking its square root.1

Start a new calculation

  1. Press Clear entry, then Clear entry.

Calculate

  1. Area

    Press 144, then Second, then Select area units, then Square inches, then Square root.
  1. Example result12 inches

Square area

Enter the side length with its unit, then square it.2

Start a new calculation

Use 2nd if a unit is above its button.

  1. Start fresh

    Press Clear entry, then Clear entry.
  2. Press the keys

    Press Select length units.

Calculate

  1. Side length

    Press 7, then feet, then 4, then inches, then Square.
  1. Example · Area53.77778 square feet

Display assumptions

  1. Fraction format: Simplified. ↩

  2. Area units: Automatic. ↩

Keep the guide beside your calculation.

These examples are built into Figure. Open Help while you calculate, then return to the same guide and reading position.

See Help in Figure →