Pythagorean Theorem Calculator
Solve a right triangle for the hypotenuse or a missing leg with a² + b² = c², plus area, perimeter and angles.
Your inputs
Results
Side c
5
- Triangle area
- 6
- Perimeter
- 12
- Angle opposite a
- 36.8699 °
✓Exact calculation — rounded only for display
What this calculator does
In any right triangle, the square of the hypotenuse equals the sum of the squares of the legs.
Formula and method
c = √(a² + b²); a = √(c² − b²)
Worked example
Calculated by this tool with its default inputs:
Inputs
- Solve for: Hypotenuse c
- Leg a: 3
- Leg b: 4
Results
- Side c: 5
- Triangle area: 6
- Perimeter: 12
- Angle opposite a: 36.8699 °
How to read the results
3-4-5 is the classic whole-number right triangle.
Assumptions and limitations
- The hypotenuse must be the longest side.
Questions
What is a Pythagorean triple?
Three whole numbers satisfying a² + b² = c², like 5-12-13.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 3 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy