Pythagorean Theorem Calculator
Enter your values below and click Calculate for instant results.
Solve for any side of a right triangle using the Pythagorean theorem. Enter any two sides and find the third.
Enter your values below and click Calculate for instant results.
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. Written as a formula: a squared plus b squared equals c squared. It is one of the most famous and widely applied theorems in all of mathematics.
Common Pythagorean triples (whole number combinations that satisfy the theorem) include 3-4-5, 5-12-13, 8-15-17, and 7-24-25. Multiples of these also work: 6-8-10, 9-12-15, and so on. Recognizing these triples can save calculation time in geometry problems.
Enter any two sides and leave one blank. The calculator solves for the missing side using the theorem. Note that the hypotenuse is always the longest side. If you enter a value for c that is shorter than either leg, the triangle is impossible and the calculator will warn you.
The Pythagorean theorem appears in carpentry (checking whether corners are square), navigation (calculating straight-line distance between coordinates), construction (determining the length of a diagonal brace), physics (calculating resultant vectors), and countless engineering applications. A quick test for a right angle: measure 3 feet along one wall, 4 feet along the perpendicular wall, and check whether the diagonal is exactly 5 feet.