A right triangle only needs two known measurements before everything else about it can be worked out. This calculator takes any two values you have, two sides, or one side and one angle, and returns every missing side, angle, the altitude, area, and perimeter. Whether you are checking geometry homework or measuring something real like a roof pitch or a stair angle, enter what you know, and the rest follows from there.
What Is a Right Triangle?
A right triangle has one angle that measures exactly 90 degrees. The two shorter sides are called legs, usually labeled a and b, and the longest side, sitting opposite the right angle, is the hypotenuse, labeled c. There is also the altitude, labeled h, which is the line running straight from the right angle down to the hypotenuse. When all three sides come out as whole numbers, like 3, 4, 5 or 5, 12, 13, that set of numbers is known as a Pythagorean triple, and triangles built from them show up constantly in textbook problems because the numbers work out cleanly.
How Does This Calculator Work?
Enter any two known values, either two sides or one side and one angle, and press "Calculate." The result includes every missing side and angle, plus the altitude, area, and perimeter, all worked out from what you typed in. One thing worth knowing before you start: at least one side has to be part of your input. Two angles on their own are not enough, since they describe the shape of a right triangle but not its actual size.
What Formulas Does This Calculator Use?
Everything the calculator returns comes from a small set of formulas. Here is what each one solves for.
Formula | What It Solves |
a² + b² = c² | Pythagorean theorem, used for a missing side when the other two are known |
sin, cos, tan of the angle | Used to find a missing side or angle when one side and one angle are known |
Area = ½ × a × b = ½ × c × h | Area of the triangle, calculated two different ways |
Perimeter = a + b + c | Sum of all three sides |
h = (a × b) ÷ c | Altitude, the distance from the right angle to the hypotenuse |
How Do You Solve a Right Triangle by Hand?
Take a triangle with legs a = 3 and b = 4. Start with the Pythagorean theorem to find the hypotenuse, c equals the square root of 3 squared plus 4 squared, which comes out to the square root of 25, or 5. From there, to find one of the acute angles, use inverse sine on the ratio of the opposite leg to the hypotenuse, sine inverse of 3 divided by 5, which gives an angle of about 36.87 degrees. The second acute angle is always just 90 minus the first, so in this case it comes out to about 53.13 degrees.
What Are Special Right Triangles (30-60-90 and 45-45-90)?
Two specific right triangles show up so often that their side ratios are worth memorizing outright, since they can be solved without touching trigonometry at all.
Triangle | Side Ratio | Example |
30-60-90 | 1 : √3 : 2 | If the short leg is 5, the long leg is 5√3, and the hypotenuse is 10 |
45-45-90 (isosceles right triangle) | 1 : 1 : √2 | If each leg is 5, the hypotenuse is 5√2 |
What Common Mistakes Cause Wrong Answers?
A handful of mix-ups account for most wrong answers with right triangle problems.
Mistake | What Actually Happens |
Mixing up opposite and adjacent | Using the wrong leg in a trig ratio depending on which angle you are solving for |
Confusing a leg with the hypotenuse | Treating one of the shorter sides as if it were the longest side |
Assuming two angles are enough | Trying to solve with only two angles and no side, which cannot fix the triangle's size |
Where Does This Fit Among Other Triangle and Trig Calculators?
A right triangle is just one case within a much wider set of triangle and trigonometry problems. Depending on what kind of triangle you actually have or what single piece of information you are after, a different calculator on this site might get you there faster.
How Is a Pythagorean Theorem Calculator Different?
A Pythagorean theorem calculator only solves for a missing side once you already know the other two sides. This page goes further, solving angles, altitude, area, and perimeter from any two values you give it, not just two sides.
How Does a General Triangle Calculator Differ From This One?
A general triangle calculator handles any triangle, including obtuse and acute ones, using the law of sines and the law of cosines. This page is built specifically for the right angle case, where the Pythagorean theorem and basic trig ratios apply directly.
Which Other Calculator Should You Use Instead?
Sometimes what you actually need is narrower than a full right triangle solve.
If You Only Need | Use This |
A quick single trig ratio lookup | SOHCAHTOA Calculator |
A non-right triangle with two angles and a side | Law of Sines Calculator |
A non-right triangle with all three sides known | Law of Cosines Calculator |
Just the area of any triangle, right or not | Triangle Area Calculator |
Frequently Asked Questions
How Do You Find the Missing Side of a Right Triangle?
Use the Pythagorean theorem when two sides are already known, or a trig ratio when you have one side and one angle.
How Do You Find a Missing Angle in a Right Triangle?
Use the inverse of the matching trig ratio, sine, cosine, or tangent, based on which two sides you already know.
What Is the Pythagorean Theorem?
It states that a squared plus b squared equals c squared, where c is the hypotenuse and a and b are the two legs.
Can You Solve a Right Triangle With Only One Known Value?
No. At least one side plus one more value, either a second side or an angle, is required. Two angles alone do not fix the triangle's actual size.
How Accurate Are the Calculator's Results?
Results use standard floating point precision and are accurate for schoolwork and most practical use, though critical professional applications should be independently verified.