Use this Pythagorean theorem calculator to find the missing side of a right triangle. Choose which side to solve for, enter the other two, and you also get the area, perimeter and both angles.
The Pythagorean theorem
a² + b² = c²
In a right triangle, the square of the hypotenuse (c, the side opposite the right angle) equals the sum of the squares of the two legs. Rearranged: c = √(a² + b²) and a = √(c² − b²).
Worked example
A right triangle has legs of 3 and 4. c = √(9 + 16) = √25 = 5. Its area is 6, its perimeter is 12, and its angles are about 36.87° and 53.13°.
Frequently asked questions
Does it work for any triangle?
No, only right triangles. For other triangles, use the law of cosines.
What is a Pythagorean triple?
A set of three whole numbers that fit the theorem, such as 3-4-5, 5-12-13 and 8-15-17. Builders use 3-4-5 to check that corners are square.