About the Right Triangle Calculator
A right triangle calculator solves for the hypotenuse, the remaining angles, and the area from the two perpendicular sides. Right triangles are the foundation of trigonometry and appear constantly in construction, navigation, and any problem involving distance and slope.
The formula
c = √(a² + b²), θ = arctan(a / b), Area = ½aba and b are the legs meeting at the right angle, c the hypotenuse opposite it, and θ the angle between side b and the hypotenuse.
How to use this calculator
- 1Enter your Side A (opposite). The field starts at
3, which you can overwrite. - 2Enter your Side B (adjacent). The field starts at
4, which you can overwrite. - 3Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Side A (opposite) | 3 |
| Side B (adjacent) | 4 |
Result
Hypotenuse (c): 5.0000
Angle A: 36.8699°
Angle B: 53.1301°
Right Angle C: 90°
Area: 6.0000
Perimeter: 12.0000
sin A = 0.6000, cos A = 0.8000, tan A = 0.7500
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
The two legs determine everything else about a right triangle. The hypotenuse follows from Pythagoras, the angles from the inverse tangent of the leg ratio, and the area is simply half their product — because the legs are perpendicular, one serves as base and the other as height with no extra work.
The non-right angles always sum to 90 degrees, since all three must total 180. That makes them complementary, so finding one gives the other immediately. It is also why the sine of one equals the cosine of the other, a relationship that recurs throughout trigonometry.
Things worth knowing
- The hypotenuse is always the longest side, and always opposite the right angle.
- The 3-4-5 triangle and its multiples give exact integer right triangles, which is why builders use them to check for square.
- Roof pitch and road gradient are right triangle problems: the tangent of the angle is rise over run.
- The area needs no separate height, since the legs are already perpendicular.
- Check whether your calculator is in degrees or radians before using inverse trigonometric functions.
Frequently asked questions
How do I find the hypotenuse?+
Square both legs, add them, and take the square root. With legs of 3 and 4, the hypotenuse is √(9 + 16) = 5.
How do I find an angle from the sides?+
Use an inverse trigonometric function. The angle whose opposite side is a and adjacent side is b is arctan(a / b). With legs 3 and 4, that angle is about 36.87 degrees.
What are Pythagorean triples?+
Sets of three integers satisfying a² + b² = c², such as 3-4-5, 5-12-13, and 8-15-17. Builders use the 3-4-5 relationship to verify that corners are square.
Do the two non-right angles always add to 90 degrees?+
Yes. All three angles sum to 180 and one is already 90, so the other two are complementary. Knowing one immediately gives the other.