Pythagorean Theorem Calculator · Practical guide
The 3-4-5 Rule for Squaring Corners
Measure 3 along one side and 4 along the other; if the diagonal reads 5, the corner is exactly 90 degrees.
At a glance
Quick answer
To square a corner, measure 3 units along one side and mark it, 4 units along the other side and mark that, then measure the diagonal between the marks. If the diagonal is exactly 5 units, the corner is a perfect 90 degrees — because 3² + 4² = 9 + 16 = 25 = 5².
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Pythagorean Theorem Calculator
Enter your own values, then compare the result with the examples below.
Results
Formula: a² + b² = c²
Scaling the Rule Up
Any multiple of 3-4-5 works, and longer measurements make small errors easier to spot. Builders routinely use 6-8-10 or 9-12-15 for decks, foundations, and fence lines.
| Scale | Side 1 | Side 2 | Diagonal | Good for |
|---|---|---|---|---|
| 1× | 3 ft | 4 ft | 5 ft | Cabinets, small frames |
| 2× | 6 ft | 8 ft | 10 ft | Deck corners, sheds |
| 3× | 9 ft | 12 ft | 15 ft | Patios, room layouts |
| 4× | 12 ft | 16 ft | 20 ft | Foundations, fence lines |
Worked Example: Laying Out a Deck
You are staking a deck corner and want it square. Run a tape 6 feet along the house and mark it, pull 8 feet out along the planned outer edge and mark that. The diagonal between the marks must read 10 feet. If it reads 10 ft 3 in, the corner is open past 90 degrees; pull the outer stake in until the tape says exactly 10. Verify the triple above with 6, 8, and 10 — the calculator classifies it as a valid right triangle.
Why It Works Both Ways
The Pythagorean theorem is reversible: if a² + b² = c² holds, the triangle must contain a right angle. That is why the 3-4-5 check is not an approximation — a 5-foot diagonal with 3- and 4-foot legs proves the corner is exactly square, no angle finder needed.
Frequently Asked Questions
Can I use the 3-4-5 rule in inches or meters?
Yes — any unit works as long as all three measurements use the same one. Thirty inches, 40 inches, and a 50-inch diagonal square a corner just like 3-4-5 feet.
What if the diagonal is slightly off, like 5 ft 1 in?
The corner is not quite square. Adjust one side until the diagonal matches the triple exactly; even an inch of error over 5 feet shows up in flooring and framing.
Is there a bigger triple for large layouts?
Keep multiplying: 15-20-25 or 30-40-50 both work for long foundation walls. The 5-12-13 triple (and its doubles) is another option when one side must be longer.
Does the rule work for existing corners?
Yes. Measure 3 and 4 feet out from the corner along both walls and check the diagonal. It is the fastest way to test whether an old room is square before installing cabinets or tile.