Pythagorean Theorem Calculator
Calculate the hypotenuse of a right triangle from two positive perpendicular side lengths and inspect their squared sum.
Calculate a right triangle hypotenuse
How this tool works
The Pythagorean theorem applies specifically to right triangles and relates the two perpendicular legs to the side opposite the right angle. This calculator reports both the squared sum and resulting hypotenuse.
For perpendicular legs a and b and hypotenuse c, c²=a²+b², so c=√(a²+b²). All three lengths use the same measurement unit.
How to use it
- Enter the first positive perpendicular side length.
- Enter the second positive perpendicular side length.
- Read the hypotenuse and verify the displayed squared sum.
Worked examples
Three-four-five triangle
- Input
- Sides 3 and 4
- Output
- Hypotenuse 5
The squared sides sum to nine plus sixteen, or twenty-five. Taking the square root produces a hypotenuse of exactly five.
Equal legs
- Input
- Sides 1 and 1
- Output
- Hypotenuse approximately 1.4142
The squared sum is two, so the hypotenuse is the square root of two, an irrational value shown as a decimal approximation.
Limitations
- The theorem does not apply to triangles without a right angle.
- Measurement uncertainty and application-specific rounding are not included.