The 3-4-5 Rule: The Complete Guide to Squaring Corners
Every square building, deck, slab and tiled floor begins with a single right angle. Get that first corner right and everything else lines up; get it wrong and the error grows with every course of brick, every joist and every row of tile. The 3-4-5 rule is the oldest, cheapest and most reliable way to make that corner with nothing but a tape measure.
The rule in one sentence
Measure 3 units along one line from the corner, 4 units along the other, and move the lines until the straight distance between those two marks is exactly 5 units. The angle at the corner is then 90°.
Why it works
The Pythagorean theorem says that in any right triangle, the squares of the two short sides add up to the square of the long side: a² + b² = c². With 3, 4 and 5, that is 9 + 16 = 25. The converse is what makes the rule useful on site: if three lengths satisfy a² + b² = c², the triangle they form must have a right angle. There is no other way for a 3-4-5 triangle to close.
Builders have used this relationship for thousands of years. Knotted ropes divided into twelve equal segments could be pegged out as a 3-4-5 triangle, giving a right angle without any instruments. The method has survived because it needs nothing more than a measuring tape and two people.
Step by step on a real layout
- Set your first line. This is the reference — usually a house wall, a property line or a string between two stakes. Everything else is squared to it.
- Mark the corner. Drive a nail or stake at the exact corner point.
- Measure the first leg. From the corner, measure along the reference line and mark at 3 units (or a multiple — see below).
- Pull the second line roughly square. Run a string or tape out at what looks like 90°.
- Mark the second leg at 4 units (same multiple) from the corner along the second line.
- Measure the diagonal between the two marks. Swing the second line until the diagonal reads exactly 5 units.
- Lock it. Drive the stake or tie off the string, then measure again to confirm nothing moved.
Scale it up for accuracy
The ratio works at any size: 6-8-10, 9-12-15, 12-16-20, 15-20-25. Bigger is better, because measuring errors stay the same size while the triangle grows. An eighth-inch mistake on a 5 ft diagonal throws the corner off by about 0.2°; carried across a 40 ft wall, that becomes roughly 2" at the far end. The same eighth-inch on a 25 ft diagonal is about 0.05° — negligible. Use the largest multiple your layout allows.
| Triangle | Use it for |
|---|---|
| 3-4-5 ft (0.9-1.2-1.5 m) | Tile lines, cabinet bases, small frames |
| 6-8-10 ft (1.8-2.4-3.0 m) | Wall plates, sheds, small decks |
| 9-12-15 ft (3-4-5 m) | Patios, garage slabs, rooms |
| 12-16-20 ft and up | House foundations, large decks, site layout |
You are not limited to whole multiples. Any two leg lengths work if you compute the matching diagonal — our 3-4-5 squaring calculator does it instantly, and it will also tell you how far out a corner is if you enter a measured diagonal.
Other Pythagorean triples
When 3-4-5 does not fit the space, other whole-number triples work the same way: 5-12-13, 8-15-17, 7-24-25 and 20-21-29. These are handy when one side of the layout is long and narrow. See our guide to Pythagorean triples for a full table.
Check the whole rectangle, not just one corner
Squaring one corner does not guarantee a square rectangle. After laying out all four corners, measure both diagonals. In a true rectangle with equal opposite sides, the diagonals are equal. If they are not, rack the layout along the long diagonal until they match. Use the diagonal check calculator to see whether the difference is within tolerance.
Common mistakes
- Measuring from different reference points. If one leg is measured to the inside of a form and the other to the outside, the triangle is wrong before you start.
- Slack or sagging tapes. A tape that drapes over grass or rubble reads long. Keep it taut and level.
- Using the smallest triangle on a big job. 3-4-5 ft on a 30 ft foundation amplifies tiny errors. Scale up.
- Forgetting to recheck. Stakes get bumped and strings stretch. Recheck after every disturbance and again before concrete or framing.
- Mixing units. Feet and inches in one leg and decimal feet in another is a common source of error. Pick one system.
Where you will use it
Foundations and slabs, deck ledgers and rim joists, wall layout on a subfloor, fence corners, patio pavers, tile reference lines, garden beds and sport courts. Any time two lines need to meet at 90°, the 3-4-5 rule is the tool.
Watch
Questions
Is the 3-4-5 rule accurate enough for a house foundation?
Yes, when scaled up (for example 15-20-25 ft) and combined with a diagonal check of the whole rectangle. Surveyors and builders still use it alongside transits and lasers.
Do I measure to the inside or outside of the lines?
Either works, as long as every measurement uses the same reference. Most builders measure to the string-line intersection or the outside face of the forms.
What if my space is too small for a 3-4-5 triangle?
Use smaller units: 300-400-500 mm or 9-12-15 inches. For very small work, a framing square is faster.