Pythagorean theorem calculator

The missing side of a right-angled triangle, exactly where possible.

Formula Geometry

Missing side

Exact form: 5
Area: 6
Perimeter: 12
Angle opposite a: ≈ 36.8699 °
Angle opposite b: ≈ 53.1301 °

Step by step

c = √(3² + 4²)

How it works

In a right-angled triangle, the square on the hypotenuse (the side opposite the right angle) equals the sum of the squares on the other two sides.

To find the hypotenuse, add the squares of the legs and take the square root. To find a leg, subtract the square of the other leg from the square of the hypotenuse. With whole-number sides the answer is also shown as a simplified surd.

Formula

a² + b² = c²
c = √(a² + b²)
a = √(c² − b²)

Worked example

Legs 3 and 4 give c = √(9 + 16) = √25 = 5. Legs 1 and 1 give c = √2 ≈ 1.414213562, and legs 5 and 5 give 5√2.

Questions people ask

What is a Pythagorean triple?

Three whole numbers that fit a² + b² = c², such as 3, 4, 5 or 5, 12, 13.

Does the theorem work for any triangle?

Only for right-angled triangles. For others use the law of cosines, which adds a correction term.

How do I check whether a corner is square?

Measure 3 units along one side and 4 along the other. If the diagonal between the marks is 5, the corner is a right angle.