Pythagorean Theorem Calculator
Solve a right triangle with a² + b² = c². Find any missing side, plus the 3-4-5 method for squaring up foundations, decks, and walls.
Hypotenuse (c)
5
Angle A (opposite a)
36.87°
Angle B (opposite b)
53.13°
Formula: a² + b² = c² · The right angle is always 90°; the other two angles sum to 90°.
Frequently Asked Questions
What is the Pythagorean theorem?
The Pythagorean theorem states that in any right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c². It's one of the most fundamental relationships in geometry and is used everywhere from construction to navigation.
How do I use the 3-4-5 rule to square a foundation or deck?
The 3-4-5 rule is a practical application of the Pythagorean theorem. Measure 3 units along one side from a corner and 4 units along the other side. If the diagonal between those two points is exactly 5 units, the corner is a perfect 90°. Any multiple works — 6-8-10, 9-12-15, 12-16-20 — bigger triangles give greater accuracy. Use the "Square a Layout" mode above to calculate the diagonal for any rectangle.
How do I find the diagonal of a rectangle?
The diagonal of a rectangle with length L and width W is √(L² + W²). This is a direct application of the Pythagorean theorem, since the diagonal divides the rectangle into two right triangles. If both diagonals of your rectangle measure the same value, the rectangle is perfectly square (all corners are 90°).