Numarly

Pythagorean Theorem Calculator

Find sides of a right triangle easily

What is it?

The Pythagorean theorem relates the three sides of a right triangle: the square of the hypotenuse (the longest side) equals the sum of the squares of the other two sides. This calculator solves for any one side given the other two.

Formula

a² + b² = c²

c = hypotenuse, a and b = the two legs of the right triangle

Formula Explanation

Rearranging a² + b² = c² lets you solve for any one side as long as you know the other two — take the square root of the sum (for the hypotenuse) or the difference (for a leg) of the squared known sides.

Example Calculation

For legs 3 and 4: c = √(3² + 4²) = √25 = 5 — the classic 3-4-5 right triangle.

How to Use

  1. Select what you want to find: the hypotenuse, or one of the two legs.
  2. Enter the two known side lengths.
  3. Click Calculate to see the missing side.

Benefits

  • Solves for any of the three sides depending on what you already know.
  • Shows the exact formula variant used for your selected mode.
  • Precise results even for irrational side lengths.

Use Cases

  • Finding the diagonal length of a rectangle, screen, or door frame.
  • Construction and carpentry for checking right angles and diagonal bracing.
  • Navigation and physics problems involving straight-line distance.

What Your Result Means

The result is the length of the missing side of your right triangle, using the same units as your inputs. Many right triangles produce irrational results, so the decimal shown is often an approximation.

Tips

  • The 3-4-5 triangle (and its multiples, like 6-8-10) is a handy way to verify a right angle without a calculator.
  • The hypotenuse is always the longest side and is always opposite the right angle.
  • Make sure you're solving for the correct missing side using the right mode.

Common Mistakes

  • Applying the theorem to a triangle that isn't actually a right triangle.
  • Mixing up which side is the hypotenuse when solving for a leg instead.
  • Subtracting the squares in the wrong order when solving for a leg, which would produce an invalid (negative) result under the square root.

FAQs

Does this only work for right triangles?

Yes, the Pythagorean theorem applies specifically to right triangles — triangles with one 90-degree angle.

Where is the Pythagorean theorem used?

It's widely used in construction, navigation, physics, and computer graphics to calculate distances, diagonal lengths, and right-angle checks.

What if my calculated value is not a whole number?

That's normal — many right triangles have irrational side lengths. The calculator rounds to 4 decimal places for readability.

Which side is the hypotenuse?

The hypotenuse is always the longest side of a right triangle, located directly opposite the 90-degree angle.

What are "Pythagorean triples"?

These are sets of three whole numbers that satisfy a² + b² = c² exactly, like 3-4-5, 5-12-13, and 8-15-17 — useful for quick mental checks.

Results are rounded to 4 decimal places for irrational side lengths.

Last updated: July 25, 2026