Pythagorean theorem calculator
Solve a² + b² = c² in either direction. Find the hypotenuse from the two legs, or find a missing leg from the hypotenuse and the other leg. The formula used is shown alongside each result, so it doubles as a quick way to check your own working in geometry, construction and trigonometry.
How it works
The theorem relates the three sides of a right triangle, where c is the hypotenuse (the side opposite the right angle):
hypotenuse: c = √(a² + b²)
missing leg: b = √(c² − a²)When solving for a leg, the calculator checks that the hypotenuse is longer than the known leg, since a real right triangle cannot have a leg as long as or longer than its hypotenuse.
Example
Hypotenuse from legs 3 and 4:
- c = √(3² + 4²) = √(9 + 16) = √25 = 5
Missing leg from hypotenuse 5 and leg 3:
- b = √(5² − 3²) = √(25 − 9) = √16 = 4
| Solve for | Known sides | Result |
|---|---|---|
| Hypotenuse | a=3, b=4 | c = 5 |
| Hypotenuse | a=5, b=12 | c = 13 |
| Leg | c=5, a=3 | b = 4 |
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