Right Triangle Calculator
Give any two values — one side and an angle, or two sides — and solve the whole right triangle: every side, both acute angles, the area, and the perimeter.
Solved triangle
at least one side is required
How the solver works
“Solving” a triangle means finding every unknown side and angle. In a right triangle the 90° angle is already known, so two more facts — at least one of them a length — pin the figure down completely. If you supply an acute angle and a side, the tool scales the triangle with sine and cosine; if you supply two sides, it recovers the angle with an inverse trig function and the hypotenuse with the Pythagorean theorem.
The two acute angles are complementary, so once one is known the other is simply 90° minus it. Every result is rounded for readability, and the area is reported as one-half of the product of the two legs.
Frequently Asked Questions
What do I need to know to solve a right triangle?
A right triangle has one 90° angle, which leaves two acute angles and three sides. Because one angle is already fixed, you only need two more independent facts — and at least one of them must be a side. That could be one side and one acute angle, or two sides. From there the trig ratios and the Pythagorean theorem fill in the rest.
Which trig ratio should I use?
SOHCAHTOA is the guide: sine = opposite / hypotenuse, cosine = adjacent / hypotenuse, and tangent = opposite / adjacent, all relative to the acute angle you are working from. This calculator picks the right relationship automatically based on which side and angle you supply.
How does it find a missing angle?
When you enter two sides but no angle, the tool uses an inverse trig function. For example, if you know the opposite and adjacent legs it takes the arctangent of their ratio; if you know a leg and the hypotenuse it uses arcsine or arccosine. The second acute angle then follows because the two acute angles always add up to 90°.
Why do I get an error when a leg is longer than the hypotenuse?
In a right triangle the hypotenuse is always the longest side — it sits opposite the 90° angle. If you enter a leg that is equal to or longer than the hypotenuse, no such triangle can exist, so the calculator flags it instead of returning an impossible answer.
Educational tool only. Results are trigonometric estimates rounded for display; verify any figure that matters for coursework, construction, or engineering against a full-precision method.