Pythagorean Theorem Calculator
Quickly solve for the hypotenuse (c) of a right-angled triangle given the lengths of the two legs (a and b). A fundamental tool for geometry, construction, and engineering calculations.
Carpentry Standards
The Golden Rule of Geometry
The Pythagorean theorem is one of the most famous principles in mathematics. It establishes a precise relationship between the three sides of a right-angled triangle. Whether you're calculating the diagonal of a TV screen, the pitch of a roof, or the distance between two GPS coordinates, Pythagoras is the foundation.
The Legs (a & b)
The two shorter sides that meet at a 90-degree angle. These are often called the base and the perpendicular height.
The Hypotenuse (c)
The longest side, always directly opposite the right angle. It represents the direct distance between the two ends of the legs.
The Mathematical Power
UNIVERSAL FORMULA
a² + b² = c²
To find the hypotenuse, we take the square root of the sum of the squares of the legs. This formula only works for triangles with a 90° angle.
Common Pythagorean Triples
Leg A Leg B Hypotenuse (C) 3 4 5 5 12 13 8 15 17 7 24 25 20 21 29 9 40 41 Carpentry & Construction: Structural Benchmarks
Construction Task Run (a) Rise (b) Length (c) Squaring (3-4-5) 3 ft 4 ft 5 ft Standard Stair 11 in 7 in 13.04 in Deck Bracing 24 in 24 in 33.94 in Common Rafter 12 ft 5 ft 13 ft Fence Post Support 36 in 36 in 50.91 in Frequently Asked Questions