The 3-4-5 Rule & Pythagorean Layout
Diego is squaring a 12×16 deck. If the corners aren't 90°, every joist will twist and the decking will look crooked from the porch.
- Two tape measures
- Chalk line
- Stakes & string
- A helper
- 1
Mark 3 along one edge
From the corner, measure 3 ft (or any multiple — 6, 9, 12) along edge A. Mark it.
- 2
Mark 4 along the other
From the same corner, 4 ft along edge B.
- 3
Measure the diagonal
Hypotenuse must equal exactly 5 ft. If not, swing edge B until it does.
- 4
Scale up for accuracy
On a 16 ft deck, use 6–8–10 or 9–12–15. Bigger triangle = smaller % error.
You framed a 14×20 ft deck and need to prove it's square before nailing joists. A speed square checks 90° at a 6" scale — useless over 20 ft. Use the Pythagorean theorem at full deck scale: pick a 3-4-5 multiple that fits, then measure the diagonal. If it's off by even 1/2", the far corner is over an inch out of square.
Tap Show next step to reveal the math one piece at a time.
Square a 12 × 16 deck
Given: Legs of 12 ft and 16 ft
- 1
Recognize the ratio
12 : 16 = 3 : 4 (×4)
Pythagoras on non-3-4-5 legs
Given: Legs of 5 ft and 12 ft
- 1
Square each leg
5² = 25 · 12² = 144