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Pythagorean Theorem Calculator

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Enter any two sides and the calculator finds the third.

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About the Pythagorean Theorem Calculator

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Enter any two sides and the calculator finds the third.

How to use the Pythagorean Theorem Calculator

  1. Enter the two sides you know in Side A (Base), Side B (Height) or Side C (Hypotenuse).
  2. Leave the unknown side at 0.
  3. Press Calculate to find it.

Formula and method

a² + b² = c²

Hypotenuse: c = √(a² + b²). A leg: a = √(c² − b²).

Worked example

With sides 3 and 4, c = √(9 + 16) = √25 = 5. Another common triple is 5-12-13.

A ladder. A ladder leaning against a wall reaches a height of 12 ft with its foot 5 ft from the wall. Its length is √(12² + 5²) = √169 = 13 ft.

When to use the Pythagorean Theorem Calculator

  • Finding the length of a diagonal, a ladder or a ramp.
  • Checking that a corner is square in building and woodwork.
  • Solving right-triangle problems in geometry.

Common mistakes to avoid

  • Using it on a triangle that has no right angle.
  • Mixing up the hypotenuse with the shorter sides.
  • Forgetting to take the square root at the end.

Tips

  • The hypotenuse is always the longest side and sits opposite the right angle.
  • Use the same units for all sides.

Frequently asked questions

Does the theorem work for all triangles?
No, only right triangles. For other triangles use the law of cosines.
What is a Pythagorean triple?
Three whole numbers that satisfy a² + b² = c², such as 3-4-5 or 5-12-13.
How do I check a square corner with it?
Measure 3 units along one side and 4 along the other. If the diagonal is exactly 5, the corner is a right angle.