What this calculator does
Once two sides of a right-angled triangle are known, the third side and every angle in the triangle are fixed. This right angle triangle calculator focuses on the angle specifically: enter whichever two sides you have, opposite and adjacent, opposite and hypotenuse, or adjacent and hypotenuse, and it returns the unknown angle directly.
Because the two non-right angles in a right triangle always add up to 90°, finding one automatically gives the other, so both are shown together along with the missing side and the triangle’s area.
The formula
With the two legs known (opposite and adjacent), angle = atan(opposite/adjacent). With the opposite side and hypotenuse known, angle = asin(opposite/hypotenuse). With the adjacent side and hypotenuse known, angle = acos(adjacent/hypotenuse). Whichever pair is entered, the missing side comes from Pythagoras and the other acute angle is 90° minus the one found.
| Term | Meaning |
|---|---|
| Opposite | The leg opposite the angle being solved for. |
| Adjacent | The leg next to the angle being solved for, not the hypotenuse. |
| Hypotenuse | The longest side of a right triangle, opposite the right angle. |
The inputs explained
| Field | What to enter |
|---|---|
| Known sides | Select which two sides you already know. |
| First known side (see selection above) | The first known side, matching the first item in the selection above. |
| Second known side (see selection above) | The second known side, matching the second item in the selection above. |
When to use it
Reading an angle off a ramp or roof pitch
A ramp or roof with a known rise and run is a right triangle with both legs known, and the angle of a right triangle here gives the actual slope angle directly.
Finding a bearing or elevation angle
Given a horizontal distance and a measured height, or a straight-line distance and a horizontal run, this right angle triangle calculator returns the angle of elevation or depression involved.
Checking a triangle calculator right angle result by hand
A trigonometry problem that gives two sides and asks for an angle is confirmed here, whichever pair of sides happens to be provided.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the angle change as one leg grows?
A fixed adjacent side of 4, across a range of opposite side lengths, using the two-legs method.
| Opposite side | Angle | Hypotenuse |
|---|---|---|
| 1 | 14.04° | 4.123 |
| 2 | 26.57° | 4.472 |
| 3 | 36.87° | 5.000 |
| 4 | 45.00° | 5.657 |
| 6 | 56.31° | 7.211 |
| 8 | 63.43° | 8.944 |
Solving the same right triangle from different known sides
The classic 3-4-5 right triangle, with its angle recovered from each of the three possible pairs of known sides in turn.
| Known sides | Angle |
|---|---|
| Opposite 3, adjacent 5 | 30.96° |
| Opposite 3, hypotenuse 5 | 36.87° |
| Adjacent 3, hypotenuse 5 | 53.13° |
Questions
How do you find an angle of a right triangle?
Use whichever inverse trig function matches the two sides you know: atan for the two legs, asin for the opposite side and hypotenuse, or acos for the adjacent side and hypotenuse.
What is a right angle triangle calculator used for?
It solves the missing side or angle of a right-angled triangle once enough measurements are known, commonly two sides, without needing to look up or rearrange the trigonometric formulas by hand each time.
How do the two acute angles in a right triangle relate to each other?
They always add up to 90°, since all three angles in any triangle sum to 180° and one of them is already the fixed 90° right angle.
Does a non right angle triangle formula apply here?
No, this calculator assumes one angle is exactly 90°. A triangle without a right angle needs the law of cosines or law of sines instead, covered by the general triangle calculator.
For the hypotenuse and both angles from two known legs, see the right triangle / Pythagoras calculator. For a triangle with no right angle, see the triangle calculator.