Pythagorean Theorem Calculator
Solve for a missing side of a right triangle
In a right triangle, the two short sides (legs) and the long side (hypotenuse) follow a simple rule: a² + b² = c². Use this to find whichever side you don't know.
Use a² + b² = c² to solve for the hypotenuse or a missing leg of a right triangle.
Hypotenuse
5.0000
c = √(3² + 4²) = 5.0000
How to Use This Calculator
- Choose whether you're solving for the hypotenuse or a missing leg.
- Enter the two sides you know.
- Read the missing side.
Why Use This Calculator?
- Finding the length of a diagonal, like across a rectangular room.
- Checking that a corner is square in building work.
- Verifying right-triangle homework.
Real-World Examples
Legs 3 and 4
The hypotenuse is √(9 + 16) = √25 = 5.
Hypotenuse 5, known leg 3
The missing leg is √(25 − 9) = √16 = 4.
Which side is the hypotenuse?
The hypotenuse is the longest side — the one opposite the 90° angle. It's always the side you solve for when you know the two legs, and it's always longer than either leg.
Frequently Asked Questions
Does this work for any triangle?
No — only right triangles (ones with a 90° angle). For other triangles you'd use the law of cosines instead.
Why do I get an error solving for a leg?
The hypotenuse must be longer than the known leg. If you entered a known leg larger than the hypotenuse, double-check your values.
Can the sides be decimals?
Yes. Any positive numbers work, including decimals and fractions entered as decimals.
Important Disclaimer
Applies only to right triangles. Results are exact for valid inputs.
Privacy
Your entries stay in your browser and aren't stored or sent.
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