The Pythagorean Theorem Calculator finds the missing side of a right triangle from the other two using a² + b² = c².
b = 4
| b | 4 |
Calculation steps:
| a² + b² = c² | b² = 5² − 3² = 16 |
| b = √… | 4 |
In a right triangle the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c². It is named after the Greek mathematician Pythagoras, though Babylonian and Indian mathematicians knew it earlier.
Hypotenuse: c = √(a² + b²). Leg: a = √(c² − b²).
Worked example (defaults): a = 3, c = 5 gives b = √(25 − 9) = 4, the famous 3-4-5 triangle.
Whole-number solutions such as 3-4-5, 5-12-13, 8-15-17 and 7-24-25 are called Pythagorean triples. Builders use 3-4-5 (or 6-8-10) to check that corners are square.
Distance between points, ladder and ramp lengths, screen diagonal sizes, navigation and many physics problems rely on the theorem. Its converse tests for right angles: if a² + b² = c², the triangle is right-angled.
Does it work for all triangles? Only right triangles; others need the law of cosines.
Which side is c? Always the longest, opposite the right angle.
Can sides be decimals? Yes.