Pythagorean Theorem Calculator
Calculate hypotenuse or missing leg using the Pythagorean theorem a²+b²=c². Find triangle area and perimeter at the same time.
Result
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Triangle Area —
Perimeter —
How to Use This Calculator
Select Solve For (hypotenuse or a missing leg), enter the two known values, and get the result plus the triangle's area and perimeter.
Formula
Hypotenuse: c = √(a²+b²) • Leg: a = √(c²−b²)
Example
a=3, b=4 → c=5, Area=6, Perimeter=12
Frequently Asked Questions
- For a right triangle with legs a and b and hypotenuse c: a²+b²=c². It only applies to right triangles.
- c = √(a²+b²). Example: a=3, b=4 → c=√(9+16)=√25=5.
- a = √(c²−b²). If hypotenuse=5 and one leg=4, then a=√(25−16)=√9=3.
- A set of three positive integers that satisfy a²+b²=c². Common triples: (3,4,5), (5,12,13), (8,15,17), (7,24,25).
- No — the Pythagorean theorem applies only to right triangles. Use the Triangle Calculator for other triangles.