Pythagorean Theorem Calculator
Pythagorean Theorem Calculator
The Pythagorean theorem relates the three sides of any right triangle: the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides (the legs). Choose which side is unknown, enter the two you know, and this calculator solves for it, along with a diagram and the step-by-step working.
- a² + b² = c², so legs of 3 and 4 give a hypotenuse of √(3² + 4²) = √25 = 5 - the famous "3-4-5" right triangle.
- To find a leg instead of the hypotenuse, rearrange the formula: a = √(c² - b²) or b = √(c² - a²) - the hypotenuse must be longer than either leg, since it's always the longest side.
- This theorem only applies to right triangles (triangles with a 90° angle) - for other triangles, use the Law of Cosines instead.
How do I find the hypotenuse of a right triangle?
Use c = √(a² + b²), where a and b are the two legs. For legs 3 and 4: c = √(9 + 16) = √25 = 5.
How do I find a missing leg instead of the hypotenuse?
Rearrange the theorem: a = √(c² - b²) or b = √(c² - a²). For a hypotenuse of 5 and leg 4: a = √(25 - 16) = √9 = 3.
Pythagorean Theorem Calculator
The Pythagorean theorem relates the three sides of any right triangle: the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides (the legs). Choose which side is unknown, enter the two you know, and this calculator solves for it, along with a diagram and the step-by-step working.
- a² + b² = c², so legs of 3 and 4 give a hypotenuse of √(3² + 4²) = √25 = 5 - the famous "3-4-5" right triangle.
- To find a leg instead of the hypotenuse, rearrange the formula: a = √(c² - b²) or b = √(c² - a²) - the hypotenuse must be longer than either leg, since it's always the longest side.
- This theorem only applies to right triangles (triangles with a 90° angle) - for other triangles, use the Law of Cosines instead.
How do I find the hypotenuse of a right triangle?
Use c = √(a² + b²), where a and b are the two legs. For legs 3 and 4: c = √(9 + 16) = √25 = 5.
How do I find a missing leg instead of the hypotenuse?
Rearrange the theorem: a = √(c² - b²) or b = √(c² - a²). For a hypotenuse of 5 and leg 4: a = √(25 - 16) = √9 = 3.