Hypotenuse Calculator
Calculate the hypotenuse of a right triangle using the Pythagorean theorem. Enter any two sides to find the third side of the triangle.
Calculation Results
Enter the lengths of two sides to calculate the third side of the right triangle.
| Side (a) | - |
|---|---|
| Side (b) | - |
| Hypotenuse (c) | - |
| Calculation Method | - |
About the Hypotenuse Calculator
The hypotenuse is the longest side of a right triangle, opposite the right angle. This calculator uses the Pythagorean theorem to calculate the hypotenuse or any other side of a right triangle when two sides are known.
The Pythagorean Theorem
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
a² + b² = c²
How to Use the Calculator
You can calculate the hypotenuse in two ways:
- From two legs: Enter the lengths of sides a and b to find the hypotenuse c.
- From one leg and hypotenuse: Enter one leg (a or b) and the hypotenuse (c) to find the other leg.
Example Calculation
For a right triangle with sides a = 3 and b = 4:
c = √(a² + b²) = √(3² + 4²) = √(9 + 16) = √25 = 5
This is the classic 3-4-5 right triangle.
Applications
The hypotenuse calculation is fundamental in many areas including:
- Construction and carpentry for ensuring right angles
- Navigation and surveying
- Computer graphics and game development
- Physics problems involving vectors
- Architecture and engineering designs
Frequently Asked Questions
Q: Can I use this calculator for non-right triangles?
A: No, the Pythagorean theorem only applies to right triangles. For other triangles, you would need to use the Law of Cosines.
Q: What if I get a negative result?
A: The calculator will only accept positive values for side lengths. If you see an error, check that you've entered valid positive numbers.
Q: How precise are the results?
A: The calculator provides results with up to 6 decimal places for maximum precision.