FabLayout

Square up calculator: 3-4-5 and diagonal

Enter the run and the rise of a right angle. You get the diagonal that proves it is square, and the angle.

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Export from the Truemark app

The PDF cut sheet with this drawing and your marks is made in Truemark. It works offline on site and keeps your jobs.

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DiagonalDiagonal6060″″RunRun3636″″RiseRise4848″″
Scale drawing

Diagonal

60in

Exact geometry

Angle
In the app

Every result is in Truemark

The free web version shows the main result and the drawing. Truemark gives you every mark and measurement, and exports a cut sheet. It is free to download.

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How to lay it out

  1. Measure along the first line

    Measure the run along one line from the corner and make a mark.

  2. Measure along the second line

    Measure the rise along the other line from the same corner and make a second mark.

  3. Check the diagonal

    Measure between the two marks. When it equals the diagonal shown, the corner is square.

  4. Adjust and re-measure

    If the diagonal is long, the angle is over 90°; if it is short, it is under. Move one line and measure again.

Good to know

  • FabLayout runs the same code as Truemark; the result is exact geometry.
  • Source: Plane trigonometry; same calculation as the Truemark app

Method and formula

A right triangle's diagonal is fixed by its two sides. Measure both sides from a corner, and the diagonal tells you whether the corner is square. The 3-4-5 rule is the same check with whole numbers: any multiple of 3, 4 and 5 is a right angle.

  • Diagonal = √(run² + rise²).
  • Angle = arctan(rise ÷ run), the angle at the run end.

The longer the sides you measure, the smaller the error in the corner. Use the longest run and rise the layout allows.

Worked example

The page defaults: a 36″ run and a 48″ rise, which is 3-4-5 scaled by 12. The diagonal is √(36² + 48²) = 60″. If your tape reads 60″ between the marks, the corner is square. The angle at the run end is 53.1301°.

Questions

What is the 3-4-5 rule?

A triangle with sides 3, 4 and 5 has a right angle between the 3 and 4 sides. Any multiple works: 6-8-10, 9-12-15 or 36-48-60 inches.

Do I have to use 3-4-5 numbers?

No. Enter any run and rise and the calculator gives the diagonal for those sides.

Which way is the corner out if the diagonal is wrong?

A diagonal longer than shown means the angle is more than 90°. A shorter one means it is less.

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