Right Triangle Hypotenuse Calculator
Enter the two legs of a right triangle (side a and side b), then click calculate.
What Is the Hypotenuse?
In a right triangle, the hypotenuse is the longest side. It always sits opposite the 90-degree angle. If you know the lengths of the other two sides (the legs), you can quickly find the hypotenuse with the Pythagorean theorem.
Pythagorean Theorem Formula
The relationship between the three sides of a right triangle is:
a² + b² = c²
Where:
- a and b are the two legs of the triangle
- c is the hypotenuse
To solve for the hypotenuse:
c = √(a² + b²)
How to Use This Calculator
- Enter the first leg in the Leg a field.
- Enter the second leg in the Leg b field.
- Optionally enter a unit such as cm, m, or ft.
- Click Calculate Hypotenuse to get the result instantly.
This calculator also shows the substitution step so you can verify your math.
Worked Examples
Example 1: Classic 3-4-5 Triangle
If a = 3 and b = 4:
c = √(3² + 4²) = √(9 + 16) = √25 = 5
So the hypotenuse is 5.
Example 2: Decimal Values
If a = 5.5 and b = 2.1:
c = √(5.5² + 2.1²) = √(30.25 + 4.41) = √34.66 ≈ 5.887
The hypotenuse is approximately 5.887 units.
Why This Matters in Real Life
Hypotenuse calculations are used in far more places than geometry class. Common applications include:
- Construction: finding diagonal braces, roof pitch distances, and layout checks
- Engineering: resolving vector magnitudes and component forces
- Navigation: straight-line travel distances from east-west and north-south movement
- Computer graphics: distance between two points on a grid
- DIY projects: measuring diagonals for frames, screens, and furniture
Common Mistakes to Avoid
- Using this formula for non-right triangles (it only works when one angle is 90°).
- Forgetting to square both legs before adding.
- Subtracting instead of adding a² and b².
- Rounding too early; keep extra decimals until the final answer.
- Mixing units (for example, one side in inches and the other in centimeters).
Quick FAQ
Can the hypotenuse be shorter than either leg?
No. In a right triangle, the hypotenuse is always the longest side.
Can I use negative side lengths?
No. Side lengths represent distance, so they must be positive numbers.
Is this calculator accurate?
Yes. It uses standard JavaScript math functions and returns a precise value, then displays a readable rounded result.
Final Tip
If you frequently solve right-triangle problems, bookmark this page. It gives you instant answers and shows the actual calculation step, making it useful for homework, exam prep, and practical field work.