Pythagorean Theorem Calculator
Find the hypotenuse from two legs.
Result: b Find a leg from the hypotenuse and the other leg.
Result: a Find a leg from the hypotenuse and the other leg.
The Pythagorean Theorem
In a right triangle, the square of the hypotenuse equals the sum of squares of the two legs:
c² = a² + b²
The hypotenuse (c) is always the longest side, opposite the 90° angle. The legs (a, b) form the right angle.
Solving for Each Side
Find hypotenuse c: c = √(a² + b²).
Find leg a: a = √(c² - b²).
Find leg b: b = √(c² - a²).
Pythagorean Triples
Certain integer sets satisfy the theorem exactly. Common triples include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25). These appear frequently in construction and carpentry for creating right angles — the 3-4-5 method is the classic framing square check.
Real-World Applications
Construction: Verify walls are square, calculate rafter lengths, determine diagonal bracing.
Navigation: Find the shortest distance between two points (the straight-line distance is the hypotenuse of a right triangle formed by coordinate differences).
Physics: Resolve vectors into perpendicular components; calculate resultant force magnitude.
Computer graphics: Compute distances between pixels or points on a screen.
Sports: Calculate the distance of a throw from the outfield to home plate, or the diagonal of a sports field.
