Right Triangle Calculator
Enter any two known sides of a right triangle to solve for the third side, both acute angles, area, and perimeter.
Known sides
Leave the unknown side blank. Fill in exactly two of the three sides.
Leg a:
Leg b:
Hypotenuse c:
Angle A (opposite a):
Angle B (opposite b):
Angle C: 90°
Area:
Perimeter:
The Pythagorean theorem
For any right triangle, a² + b² = c², where c is the hypotenuse (the side opposite the right angle) and a, b are the two legs. Given any two sides, the third follows directly from rearranging this formula, and the two acute angles can then be found using inverse trigonometric functions (arcsine, in this calculator's case) since the side ratios determine the angles uniquely.
Frequently asked questions
Why must the hypotenuse be the longest side? The hypotenuse is opposite the 90° angle, which is the largest angle in a right triangle — in any triangle, the longest side is always opposite the largest angle, so the hypotenuse is necessarily longer than either leg.
Do the two acute angles always add up to 90°? Yes — since all triangle angles sum to 180° and one angle is fixed at 90°, the remaining two angles must always add up to the other 90°.
What are some real-world uses of this? Right-triangle relationships are used constantly in construction (checking a corner is square, sizing a diagonal brace), navigation, and any situation involving a straight-line distance across two perpendicular measurements.