Right Triangle Calculator
Choose which side to solve for, enter the other two, and get the missing side plus the area and both acute angles.
How the Pythagorean theorem works
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c².
Once all three sides are known, the area is ½ × a × b (using the two legs as base and height), and the two acute angles can be found using inverse trigonometric functions — angle A = arcsin(a/c), with the other angle being 90° minus angle A, since all triangle angles sum to 180° and one angle is already 90°.
Frequently asked questions
What is the Pythagorean theorem used for?
It's used to find an unknown side of a right triangle when the other two are known — common in construction, navigation, and any situation involving right-angle measurements.
Which side is the hypotenuse?
The hypotenuse is always the longest side of a right triangle, located opposite the 90° angle.
What's a "Pythagorean triple"?
A Pythagorean triple is a set of three whole numbers that satisfy a² + b² = c², like 3-4-5 or 5-12-13 — useful for quick mental checks or examples since all three sides come out as clean integers.