Pythagorean Theorem Calculator: Find Missing Sides of Right Triangles
The Pythagorean theorem is one of the most well-known and widely used formulas in mathematics. It states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a squared plus b squared equals c squared. This relationship was known to ancient civilizations including the Babylonians and Egyptians, but is named after the Greek mathematician Pythagoras who provided a proof around 500 BCE.
Our Pythagorean theorem calculator allows you to solve for any of the three sides of a right triangle. Simply select which side you want to find — the hypotenuse (c) or either leg (a or b) — enter the two known side lengths, and the calculator instantly computes the missing side. It also calculates the triangle area using the formula (a times b) divided by 2, the perimeter by summing all three sides, and the two non-right angles using inverse tangent.
The visual right triangle diagram updates dynamically to reflect the proportions of your specific triangle, with all side lengths and angles clearly labeled. This makes the calculator an excellent learning tool for students studying geometry or trigonometry. The diagram shows the right angle marker and each angle value in degrees, giving you a complete picture of the triangle.
Beyond solving for missing sides, the calculator includes a Pythagorean triple verifier. A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy the theorem, such as (3, 4, 5) or (5, 12, 13). Enter any three numbers and the tool will verify whether they form a valid triple. This feature is useful for number theory, construction, and verifying measurements in practical applications.