Pythagorean Theorem Calculator

Find the missing side of a right triangle using a² + b² = c²

Enter the two known sides. The selected side is calculated from them.

Your result will appear here.

About the Pythagorean Theorem Calculator

Right triangles have a special relationship between their three sides: the square of the hypotenuse equals the sum of the squares of the two shorter sides. This calculator solves for whichever side is missing.

The theorem applies only to right triangles. If the included angle is not 90 degrees, another triangle relationship is needed.

How to Use the Pythagorean Theorem Calculator

  1. Identify the hypotenuse, which is the side opposite the 90-degree angle.
  2. Enter the two known side lengths.
  3. Choose which side is unknown if required.
  4. Calculate the missing side and keep all lengths in compatible units.

How the Calculation Works

For legs a and b and hypotenuse c, a² + b² = c².

To find the hypotenuse, c = √(a²+b²). To find a missing leg, a = √(c²−b²), provided c is the longest side and the radicand is non-negative.

Worked example

Pythagorean Theorem Calculator Worked Example

Right triangle with legs 3 and 4

c = √(3² + 4²) = √(9+16) = √25 = 5. The side lengths form the familiar 3-4-5 right triangle.

Result guide

Understanding Your Pythagorean Theorem Calculator Result

The calculated missing side completes a right triangle under the entered measurements. If the real-world angle is not exactly 90 degrees, the result will not describe the actual geometry.

Before you rely on the answer

Assumptions and Limitations

  • The triangle contains a right angle.
  • The hypotenuse is correctly identified as the longest side.
  • All side lengths use compatible units.

Practical tip

Using This Result in Practice

In construction layout, a 3-4-5 proportion can be scaled to 6-8-10 or 9-12-15 and used as a practical check for a right angle. A quick check is that the calculated hypotenuse must be longer than either leg, while a calculated leg must be shorter than the hypotenuse.

Related calculations

Useful Calculations to Continue With

If the triangle is not right-angled or you need area and other properties, use the Triangle Calculator.

Distance Between Two Points Calculator — Coordinate distance uses the same underlying relationship when horizontal and vertical differences form the two legs.

Common questions

Pythagorean Theorem Calculator FAQ

Which side is c in the Pythagorean theorem?

c is the hypotenuse, the side opposite the right angle and the longest side of a right triangle.

Can the theorem be used on any triangle?

No. The formula a²+b²=c² specifically describes right triangles.

Why is the distance formula related to the Pythagorean theorem?

Horizontal and vertical coordinate differences act as perpendicular legs, while the straight-line distance is the hypotenuse.