Pythagorean Theorem
Calculate missing side using Pythagorean theorem
How to use Pythagorean Theorem
- 1State the known sides: legs a and b, or one leg and hypotenuse c.
- 2Enter the known values and leave the unknown blank (you can solve for the hypotenuse only).
- 3Read the third side and see the algebraic steps of the theorem.
What is the Pythagorean theorem?
a² + b² = c² (c is the hypotenuse)The Pythagorean theorem says that in a right triangle, the square of the two legs equals the square of the hypotenuse. It is a foundation of Euclidean geometry and is used in construction, navigation, graphics and signal processing.
For the hypotenuse use √(a²+b²); if you know the hypotenuse and one leg, the other leg is √(c²−a²). It applies only to right triangles; others need the law of cosines.
Frequently asked questions
Only for right triangles?
Yes. The theorem holds only for right triangles; general triangles use the law of cosines c²=a²+b²−2ab·cosC.
How do I find the hypotenuse?
Square the legs, add them, then take the square root: c = √(a²+b²).
Must the units match?
Yes. a, b and c must share one length unit, or the result is meaningless.