Math

Pythagorean Theorem Calculator

Find the missing side of a right triangle. Enter any two sides and the third will be calculated.

Enter any two values. Leave one field empty to calculate it.

Missing Side
Area of Triangle
Perimeter
Pythagorean Theorem:
a² + b² = c²

Solve for c: c = √(a² + b²)
Solve for a: a = √(c² − b²)
Solve for b: b = √(c² − a²)

What is the Pythagorean Theorem?

The Pythagorean Theorem is one of the most fundamental principles in mathematics, attributed to the ancient Greek philosopher Pythagoras (~570–495 BC). It states that in any right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The Formula

a² + b² = c²

Where a and b are the lengths of the two legs, and c is the length of the hypotenuse. The hypotenuse is always the longest side and is opposite the 90° angle.

Common Pythagorean Triples

abcVerification
3459 + 16 = 25
5121325 + 144 = 169
8151764 + 225 = 289
7242549 + 576 = 625

Real-World Applications

  • Construction: Ensuring walls are square (3-4-5 rule)
  • Navigation: Calculating straight-line distance between two points
  • Architecture: Finding diagonal measurements, roof pitch
  • Computer Graphics: Calculating distances between pixels