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How to use
This calculator uses a²+b²=c² for right triangles only, where c is the hypotenuse opposite the right angle. After finding the missing side it also returns area, perimeter and the two acute angles.
- Choose whether to find hypotenuse c, leg a or leg b.
- Enter the two known lengths; when solving for a leg, the hypotenuse must be longer than the known leg.
- Calculate to see all sides, area, perimeter and acute angles.
How it is calculated
Example
Example: with a=3 and b=4, c=5. Area is 6, perimeter is 12, and the acute angles are about 36.8699° and 53.1301°.
Important notes
The Pythagorean theorem in this form applies only to right triangles. Do not assume a 90° angle for a general triangle. Inputs must be positive, and leg-solving modes reject cases where the hypotenuse is not longer than the known leg.
Worked examples and interpreting results
In a right triangle with perpendicular legs 3 and 4, the hypotenuse is 5. It lies opposite the right angle and is the longest side; knowing two sides does not justify using Pythagoras in a non-right triangle.
| Case | Calculation | Result |
|---|---|---|
| Find the hypotenuse | √(3² + 4²) | 5 |
| Find a leg | √(5² − 4²) | 3 |
How to check the result
Use the same unit for every length. When solving for a leg, the hypotenuse must exceed the other leg; a negative radicand means the side selection or inputs need checking.
Frequently asked questions
Which side is the hypotenuse?
Hypotenuse c is opposite the right angle and is the longest side of a right triangle.
How do I find a leg when the hypotenuse is known?
Use √(c²−other leg²).
Does the calculator find angles too?
Yes. Once all sides are known it calculates both acute angles, which sum to 90° apart from display rounding.