Enter any two values of a right triangle (sides or angles) and solve for all remaining properties. Angle C is always 90°.
Select what each value represents, then enter the number.
| Function | Definition |
|---|---|
| sin(A) | a / c (opposite / hypotenuse) |
| cos(A) | b / c (adjacent / hypotenuse) |
| tan(A) | a / b (opposite / adjacent) |
| Pythagorean | a² + b² = c² |
| A + B | = 90° (always) |
| Property | Value |
|---|---|
| Leg a | 3 |
| Leg b | 4 |
| Hypotenuse c | 5 |
| Angle A | 36.86989765° |
| Angle B | 53.13010235° |
| Angle C | 90° |
| Perimeter | 12 |
| Area | 6 |
| sin(A) | 0.6 |
| cos(A) | 0.8 |
| tan(A) | 0.75 |
Give this calculator legs of 1,000 and 1 and the hypotenuse comes back as 1,000.0005, only five ten-thousandths longer than the long leg, while angle A lands at 89.94270424°. A triangle that thin looks like a single line, and the numbers agree. The page works from any two of leg a, leg b, hypotenuse c, angle A and angle B, with angle C fixed at 90°.
Typical case: hypotenuse c = 12 and angle A = 35°. Leg a sits opposite angle A, so a = c × sin 35° = 6.88291724. Leg b = c × cos 35° = 9.82982453. Angle B = 90° − 35° = 55°. The perimeter is 28.71274177 and the area, ½ab, is 33.82893435. The page also lists the trig ratios of A: sin 0.57357644, cos 0.81915204 and tan 0.70020754.
Other pairs use the same toolkit. Two legs give c = √(a² + b²) and A = arctan(a / b). A leg plus the hypotenuse gives the other leg from √(c² − leg²). A leg plus an angle uses tangent for the other leg and sine for the hypotenuse. Results are rounded to eight decimals.
Now the awkward inputs. Leg a = 5 with c = 5 would force leg b to zero, and the page replies Invalid combination, check your values. Leg a = 5 with c = 4 triggers Hypotenuse must be greater than any leg. An angle of 0° or 90° is rejected with a message that the angle must be between 0° and 90°, and a zero or negative side is caught too. Two angles with no side give no result at all, because angles fix a shape, not a size. Finally, angles are read as degrees only: with a = 10, typing 0.6 meaning radians is treated as 0.6° and yields b = 954.8947517.
Leg a is opposite angle A, and leg b is opposite angle B. Swapping the labels swaps A and B but leaves c, perimeter and area unchanged. The page's own ratios say sin A = a / c and tan A = a / b.
Two angles in a right triangle are not independent, since A + B = 90°, and neither says anything about size. The page needs at least one side, so it simply shows nothing until you provide one.
Use Leg a as the rise and Leg b as the run. For a ramp rising 1 for every 12 of run, angle A is 4.76364169° and tan A is 0.08333333, which is a grade of 8.33 percent when multiplied by 100.
They swap. sin B equals cos A and cos B equals sin A, while tan B is 1 divided by tan A. For the 3-4-5 triangle, A = 36.86989765° and B = 53.13010235°.
No. Angle C is always 90°. For other triangles, use the general triangle calculator, which uses the laws of sines and cosines.