Triangle Dimensions
Calculation Result
The Pythagorean Theorem Calculator is a simple mathematical tool that allows you to calculate the missing side of any right-angled triangle. By entering just two known sides, the tool instantly figures out the length of the third side, as well as the total area and perimeter of the triangle.
How the Pythagorean Theorem Works
The Pythagorean theorem states that in a right-angled triangle, the square of the longest side (the hypotenuse) is exactly equal to the sum of the squares of the other two sides (the legs). The mathematical formula is written as a² + b² = c².
- Side A and Side B (Legs): These are the two sides that meet to form the 90-degree right angle.
- Side C (Hypotenuse): This is always the longest side of the right triangle, and it is positioned directly opposite the right angle.
How to Use This Calculator
You do not need to know all three sides. To find a missing side, simply type in the values for the two sides you already know and leave the third box completely blank.
- To find the Hypotenuse: Enter your numbers into Side A and Side B. Leave Side C empty.
- To find a Leg: Enter your known leg into either Side A or Side B, and enter your hypotenuse into Side C. Leave the missing leg blank.
Frequently Asked Questions
What is a Pythagorean Triple?
A Pythagorean triple consists of three positive whole numbers that fit the theorem perfectly without any decimal points. The most famous example is the 3-4-5 triangle. If you enter sides of 3 and 4, the hypotenuse is exactly 5. Other common triples include 5-12-13 and 8-15-17.
Why am I getting an Invalid Triangle error?
In any right triangle, the hypotenuse (Side C) must absolutely be the longest side. If you are trying to calculate a missing leg but you enter a hypotenuse that is shorter than your known leg, the math becomes impossible and the calculator will display an error.
Can I use this theorem on any triangle?
No. The standard Pythagorean theorem only works on right-angled triangles (triangles where one inside angle is exactly 90 degrees). If your triangle does not have a 90-degree angle, you would need to use different mathematical rules like the Law of Cosines to find missing lengths.