3-4-5 Triangle Calculator

The 3-4-5 triangle is the smallest Pythagorean triple: three whole-number side lengths that form a right triangle. Plug in 3, 4 and 5 as sides a, b and c, and you get a triangle with exactly one 90° angle, an area of 6, and a perimeter of 12.

Builders, surveyors and DIY carpenters use the 3-4-5 method to lay out a true right angle without a protractor. Measure 3 feet along one wall, 4 feet along an adjacent wall, and confirm the diagonal between those marks is exactly 5 feet. If it is, the corner is square. If it isn't, adjust until it is.

3-4-5 Triangle Properties

Property	Value
Sides	a=3, b=4, c=5 (hypotenuse)
Angles	A ≈ 36.87°, B ≈ 53.13°, C = 90°
Area	6 (½ × 3 × 4)
Perimeter	12
Type	Right scalene

Why 3-4-5 Works

The Pythagorean theorem states a² + b² = c² for any right triangle. For 3-4-5: 9 + 16 = 25, and 5² = 25. The math holds, so the triangle is a right triangle by definition.

Any integer multiple of 3-4-5 is also a valid right triangle: 6-8-10, 9-12-15, 12-16-20. Same proportions, bigger scale. Pick whichever scale your tape measure handles cleanly.

How to Square a Corner with 3-4-5

1. Mark a starting point at the corner you want to square.
2. Measure 3 feet (or meters) along one wall and mark.
3. Measure 4 feet along the adjacent wall and mark.
4. Measure the diagonal between the two marks. If it reads 5 feet, the corner is at 90°. If it is more, the angle is obtuse. If less, acute.
5. Adjust one of the legs until the diagonal hits exactly 5.

Other Common Pythagorean Triples

• 5-12-13: angles ≈ 22.62°, 67.38°, 90°.
• 8-15-17: angles ≈ 28.07°, 61.93°, 90°.
• 7-24-25: angles ≈ 16.26°, 73.74°, 90°.
• 20-21-29: angles ≈ 43.60°, 46.40°, 90° (nearly isosceles).

Use the Full Calculator

The Triangle Calculator handles every scenario described on this page. For the deeper math and worked examples, read the companion guide.