Pythagorean Theorem Calculator
Pythagorean Theorem Calculator
The Pythagorean theorem calculator finds the hypotenuse of a right triangle given the two other sides, using one of the most famous formulas in mathematics.
Conversion Formula
c = √(a² + b²). The hypotenuse c is always the longest side and is opposite the 90-degree angle.
Step-by-Step Examples
a=3, b=4 = c = 5
√(9 + 16) = √25 = 5. The classic 3-4-5 triple.
a=5, b=12 = c = 13
√(25 + 144) = √169 = 13.
a=1, b=1 = c = 1.41421356
√(1 + 1) = √2 ≈ 1.414. The diagonal of a unit square.
History
Although named after Pythagoras (c. 570-495 BC), the relationship was known to Babylonian mathematicians over a thousand years earlier, as evidenced by the clay tablet Plimpton 322.
Common Use Cases
- Construction and carpentry
- Navigation and surveying
- Physics force calculations
- Computer graphics and game development
Frequently Asked Questions
What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
What is the hypotenuse?
The hypotenuse is the longest side of a right triangle, opposite the right angle.
Can I find a missing leg instead?
Yes. Rearrange to a = √(c² - b²). Enter the known leg and hypotenuse, then solve.
What are Pythagorean triples?
Sets of three whole numbers that satisfy a² + b² = c², such as (3,4,5), (5,12,13), and (8,15,17).
Does this work for non-right triangles?
No. The Pythagorean theorem only applies to right triangles. For others, use the law of cosines.
What is a 3-4-5 triangle?
A right triangle with sides 3, 4, and 5 — the simplest Pythagorean triple, commonly used in construction to verify right angles.
Can sides be decimals?
Yes. The theorem works with any positive real numbers.
How is this used in real life?
Construction workers use it to square corners, navigators calculate distances, and it is the basis of the distance formula in coordinate geometry.