Pythagorean Theorem Calculator
For any right triangle, the two legs determine the hypotenuse directly — a² + b² = c². This also reports the angle opposite side a, useful when you need the triangle's shape, not just its longest side.
Inputs
Result
c = 5
Angle A = 36.87°
How it works
a² + b² = c²
How the pythagorean theorem calculator works
Hypotenuse: c = √(a² + b²).
Angle A (opposite side a) = arctan(a ÷ b), converted from radians to degrees for readability.
Worked example: legs 3 and 4
- c = √(3² + 4²) = √(9+16) = √25 = 5 — the classic 3-4-5 right triangle.
- Angle A = arctan(3÷4) ≈ 36.87°.
Common mistakes to avoid
Entering the hypotenuse as one of the two inputs
This tool expects the two legs (the sides forming the right angle), not the hypotenuse itself — entering the hypotenuse in place of a leg gives a geometrically meaningless result.
Assuming this works for non-right triangles
The Pythagorean theorem is only valid when the triangle has a genuine 90° angle. For any other triangle, use the Law of Cosines or Heron's formula (via the Triangle Area Calculator) instead.
Frequently asked questions
How do I find a missing leg instead of the hypotenuse?
Rearrange to b = √(c² − a²) — subtract the known leg's square from the hypotenuse's square, then take the square root.
What are some other common Pythagorean triples besides 3-4-5?
5-12-13, 8-15-17, and 7-24-25 are all whole-number right-triangle combinations that satisfy a² + b² = c² exactly.
Why does the calculator also give an angle?
Knowing just the hypotenuse tells you the triangle's size but not its shape — the angle pins down exactly how 'tall and narrow' versus 'short and wide' the right triangle is.
Does the order of entering the two legs matter?
Not for the hypotenuse (addition is symmetric), but it does matter for which angle is reported — swapping a and b swaps which angle you're seeing.
Related calculators
Triangle Area Calculator
Heron's formula area from three sides.
Geometry Calculator
Area and perimeter of common 2D shapes.
Circle Calculator
Area, circumference and diameter from a radius.
Quadratic Equation Solver
Roots of ax² + bx + c = 0 with discriminant analysis.
Root Calculator
Square, cube and nth roots.