Pythagorean Theorem Calculator

The Pythagorean theorem says that in a right triangle, the square on the hypotenuse equals the sum of the squares on the other two sides: a² + b² = c². This calculator finds the hypotenuse from the two shorter sides, or a missing shorter side from the hypotenuse and the other side.

Try:

How to use the pythagorean theorem calculator

  1. Choose whether to find the hypotenuse or a shorter side.
  2. Enter the two sides you know.
  3. Press Calculate to see the missing side, exactly and as a decimal.

Formula

a2+b2=c2a^2 + b^2 = c^2

Worked example: a = 3, b = 4

  • Find: Hypotenuse (c)
  • Side a: 3
  • Side b: 4

✓ Answer checked

c=5c = 5
Step-by-step working (3 steps)

  1. Write the theorem Pythagorean theorem

    In a right triangle, the square on the hypotenuse equals the sum of the squares on the other two sides.

    a2+b2=c2a^2 + b^2 = c^2

  2. Substitute

    Put in the two known sides.

    32+42=9+16=253^2 + 4^2 = 9 + 16 = 25

  3. Take the square root

    The result is a perfect square.

    c=25=5c = \sqrt{25} = 5
Formulas used
a2+b2=c2a^2 + b^2 = c^2
How this was checked
  • ✓ 5² = 25.
  • ✓ The three sides satisfy a² + b² = c².

Frequently asked questions

How do I find the hypotenuse?

Square the two shorter sides, add them, and take the square root. For sides 3 and 4: √(9 + 16) = √25 = 5.

How do I find a shorter side?

Square the hypotenuse, subtract the square of the known side, and take the square root. With c = 13 and a = 5: √(169 − 25) = 12.

Does it work for any triangle?

No, only right triangles, which have one 90° angle. The hypotenuse is the side opposite the right angle.

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