3-4-5 square calculator
This is the diagonal that proves a 90° corner from the two sides you enter — pure geometry, nothing more. It assumes your two measurements are accurate and taken from the same point; a tape that slips or a mark that wanders throws the check off, so measure both legs twice before you trust the diagonal.
Enter the two legs of a corner and the tool gives the exact straight-line distance between their ends. When your tape reads that number across the diagonal, the corner is square. It also suggests the largest neat 3-4-5 multiple that fits, for a fast check without a calculator on site.
Worked example
Mark 3 ft along one wall and 4 ft along the other. The diagonal between those marks should be √(3² + 4²) = √25 = 5 ft exactly. Pull the corner until the tape reads 5 ft and it is square. Over a longer wall, 6-8-10 or 9-12-15 give the same right angle with room to spare.
The formula
diagonal = √(A² + B²)
This is Pythagoras: the two sides of the corner are the legs of a right triangle and the diagonal is the hypotenuse. The 3-4-5 triple is simply the smallest whole-number set that satisfies it, which is why the trade remembers it.
Questions
- How does the 3-4-5 method square a corner?
- Any triangle with sides in the ratio 3:4:5 has a right angle between the 3 and the 4. Measure 3 units along one side and 4 along the other; when the straight-line distance between those two marks is exactly 5 units, the corner is square. Bigger multiples — 6-8-10, 9-12-15 — are the same triangle and read more accurately over a long wall.
- What is the diagonal of a rectangle?
- It is the square root of the two sides squared and added — plain Pythagoras. For a 12 ft by 16 ft layout the diagonal is √(144 + 256) = √400 = 20 ft. If both diagonals of a rectangle measure the same, the corners are square and the shape is true.
- What if my sides are not 3 and 4?
- The 3-4-5 ratio is just the easiest triple to remember; the method works for any two legs. Enter whatever the two sides of your corner actually are and the tool gives the exact diagonal to look for. It also suggests the largest tidy 3-4-5 multiple that fits your shorter side, for a quick field check.
- Why measure a bigger triangle?
- A small error in the marks turns into a bigger angle error over a short triangle, so a 3-4-5 measured in inches is far less precise than the same triangle measured in feet. Use the largest multiple your space allows — the diagonal is easier to hit accurately and the corner ends up truer.
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