Right Triangle Calculator
Solve all sides, angles, area and altitude of a right triangle given any two pieces of information — sides, angles or a mix.
How to use the Right Triangle Calculator
- Enter your inputs into the Right Triangle Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
The right triangle relationships
a² + b² = c² · · · sin(A) = a/c · · · cos(A) = b/c · · · tan(A) = a/b · · · Area = ½·a·b
In a right triangle, the right angle is C; A and B are the acute angles. a, b are the legs; c is the hypotenuse. Six trig ratios connect sides and angles.
Worked example
Given legs a = 6 and b = 8: c = √(36+64) = 10. A = arctan(6/8) ≈ 36.87°. B = 90° − A ≈ 53.13°. Area = ½·6·8 = 24. Altitude to hypotenuse = (a·b)/c = 4.8.
Frequently asked questions
What's the altitude to the hypotenuse?
The perpendicular distance from the right-angle vertex to the hypotenuse. Equal to (a·b)/c. Divides the right triangle into two smaller similar right triangles.
How do I solve from one angle and one side?
Use the right angle (90°) plus the given angle to find the third angle. Then use trig ratios (sin, cos, tan) with the known side to find the unknown sides.
What if I only know the two legs?
Use Pythagorean for hypotenuse, then arctan for the angles. The calculator does this automatically when you enter only the legs.