3–4–5 setting-out triangle

Scales the 3–4–5 triangle to a size that suits the job, so you can set out a right angle with just a tape. Use it for setting out foundations, decks, partitions or any square corner.

k is the scale factor in metres. The two legs come out as 3k and 4k along the two lines that should meet at 90°. The diagonal between their ends should then read 5k.

Because 3² + 4² = 5², any triangle with sides in the ratio 3:4:5 has an exact right angle between the two shorter sides. Multiplying every side by the same k keeps the shape and the right angle.

With k = 1 the sides are 3, 4 and 5 m. With k = 0.6 they are 1.8, 2.4 and 3 m. A bigger triangle makes a few millimetres of tape error matter less.

Watch out: measure both legs from the same corner point and hook the tape the same way each time.