Pythagorean Theorem Calculator

Solve for the sides and properties of a right-angled triangle using the equation a² + b² = c² with step-by-step solutions.

Please provide any 2 values below to solve the Pythagorean equation: a² + b² = c².

Triangle Sides

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Triangle Diagram

bca

Simple right triangle with sides labeled a, b, and c

Detailed Triangle

bcaαβh

Right triangle with angles α, β and height h to hypotenuse

About Pythagorean Theorem

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) equals the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².

Key Properties:

  • • c is always the longest side
  • • c² = a² + b²
  • • α + β = 90°
  • • Area = (a × b) / 2
  • • Height to hypotenuse = (a × b) / c

Common Applications:

  • • Construction and carpentry
  • • Navigation and surveying
  • • Computer graphics
  • • Physics calculations
  • • Engineering design