Pythagorean Theorem Calculator
Find missing side of a right triangle.
Input
Result
What is a Pythagorean Theorem Calculator?
A Pythagorean theorem calculator finds the missing side of a right triangle using a2 + b2 = c2. It can solve for the hypotenuse or either leg, making triangle problems quick and error-free.
How to calculate the Pythagorean theorem manually (the formula)
For a right triangle, a2 + b2 = c2 where c is the hypotenuse. To find c: c = √(a2 + b2). To find a leg: a = √(c2 − b2).
Example calculation
A right triangle has legs of 3 and 4. Hypotenuse c = √(32 + 42) = √(9 + 16) = √25 = 5. The 3-4-5 triangle is the most famous Pythagorean triple.
Common mistakes
- Adding instead of squaring first — Square each leg first, then add. Do not add the legs and then square the sum.
- Using the theorem on non-right triangles — The Pythagorean theorem only applies to right triangles. For other triangles, use the law of cosines.
- Forgetting the square root — After summing the squares, take the square root to get the side length, not half the sum.
Frequently asked questions
What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, a\u00b2 + b\u00b2 = c\u00b2, where a and b are the legs and c is the hypotenuse.
How do you find the hypotenuse?
Take the square root of the sum of the legs squared: c = \u221a(a\u00b2 + b\u00b2). For legs 3 and 4, c = \u221a(9 + 16) = \u221a25 = 5.
Can you use the Pythagorean theorem on any triangle?
No. The theorem only works on right triangles (triangles with one 90\u00b0 angle).
How do you find a missing leg?
Rearrange the formula: a = \u221a(c\u00b2 - b\u00b2). Subtract the square of the known leg from the square of the hypotenuse, then take the square root.
What is a Pythagorean triple?
A Pythagorean triple is a set of three whole numbers that satisfy a\u00b2 + b\u00b2 = c\u00b2, such as (3, 4, 5) and (5, 12, 13).
How is the Pythagorean theorem used in real life?
It is used in construction (squaring corners), navigation (shortest distance), screen size measurements (diagonal), and many engineering fields.