Right Triangle Calculator: Find Sides, Angles and Area
Pick the two values you know, type them in, and this right triangle calculator solves the rest: all three sides, both angles, the area and the perimeter, with the steps shown.
By Troopus · Updated: October 28, 2026
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Right triangle calculator
Angle C is the right angle (90 degrees). Side a is opposite angle A, side b is opposite angle B, and c is the hypotenuse. Results use the same unit you typed. Rounded to 4 decimals.
How does the right triangle calculator solve a right triangle?
To solve a right triangle you need two known values besides the 90 degree angle, and at least one of them must be a side. From those two, the Pythagorean theorem and sine, cosine and tangent give every other side and angle. Choose what you know in the "I know" menu.
Think of it as a right triangle solver. A right triangle has one 90 degree angle, called C. The side opposite it is the hypotenuse, c, and it is always the longest. The other two sides are the legs: a is opposite angle A, and b is opposite angle B. The two acute angles always add up to 90 degrees.
The calculator accepts nine combinations: two legs, a leg and the hypotenuse, or a side and one acute angle. Two angles alone are not enough, because many different sizes of triangle share the same angles. Tick through the options and the fields relabel themselves. Each combination starts filled in with a 3-4-5 triangle so you can see how the answer changes.
How do you find the hypotenuse with a hypotenuse calculator?
Find the hypotenuse by squaring both legs, adding them, and taking the square root: c = √(a² + b²). For legs of 5 and 12, c = √(25 + 144) = √169 = 13. This is the Pythagorean theorem, and it only works for right triangles.
Leave the menu on "Legs a and b" and type the two leg lengths. The steps box under the result shows the same working. This Pythagorean theorem calculator mode also reveals Pythagorean triples, which are common whole-number sets. Examples are 3-4-5, 5-12-13 and 8-15-17. They are handy because the answer is exact, and any multiple of a triple, such as 6-8-10, works too.
How do you find a missing leg with the right triangle calculator?
To find a missing leg, subtract the square of the known leg from the square of the hypotenuse and take the square root: b = √(c² - a²). With c = 13 and a = 5, b = √(169 - 25) = √144 = 12. The hypotenuse must be longer than the known leg.
Use these steps to find missing side of right triangle problems. Choose "Leg a and hypotenuse c" or "Leg b and hypotenuse c". If you enter a hypotenuse that is not longer than the leg, the calculator tells you so, because no right triangle can have a leg as long as its hypotenuse. This is also the quickest way to check a corner: if the sides of a frame measure 3, 4 and 5 feet, the corner is square.
How does a triangle angle calculator find the angles of a right triangle?
Find an acute angle with an inverse trig function: angle A = arctan(a / b), or arcsin(a / c), or arccos(b / c). For legs 3 and 4, A = arctan(3 / 4) = 36.87 degrees. The other acute angle is 90 minus that, so B = 53.13 degrees.
Remember the three ratios as opposite over hypotenuse (sine), adjacent over hypotenuse (cosine) and opposite over adjacent (tangent). When you know a side and an angle instead, the calculator turns the ratios around. For example, a hypotenuse of 10 with angle A = 30 degrees gives a = 10 x sin 30° = 5 and b = 10 x cos 30° = 8.66.
| You know | Find | Formula |
|---|---|---|
| a, b | c | √(a² + b²) |
| a, c | b | √(c² - a²) |
| c, angle A | a | c x sin A |
| c, angle A | b | c x cos A |
| a, angle A | b | a / tan A |
How do you find the area and perimeter of a right triangle?
The area of a right triangle is half the product of its legs: A = a x b / 2. The perimeter is a + b + c. For a 3-4-5 triangle, the area is 3 x 4 / 2 = 6 and the perimeter is 3 + 4 + 5 = 12. Both appear under the result.
The calculator also shows the height to the hypotenuse, which is a x b / c. In the 3-4-5 example that is 12 / 5 = 2.4. That is the length of the line from the right angle straight to the hypotenuse, and it is useful if you treat the hypotenuse as the base. Results use whatever unit you typed, so area is in square units of that length. Need to turn an area into a volume of soil or concrete? Try the cubic yard calculator.
Frequently asked questions
What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c². It lets you find any side when you know the other two. It does not apply to triangles without a 90 degree angle.
Can I solve a right triangle with only one side?
No. You need one more piece of information, either another side or one of the acute angles. With only a single side, many different right triangles are possible, so the answer would not be unique.
Why does the calculator say the hypotenuse must be longer?
The hypotenuse is always the longest side of a right triangle. If the number you enter as the hypotenuse is equal to or smaller than the leg, no triangle exists. Check that you picked the correct option in the I know menu.
What is a 3-4-5 triangle?
It is a right triangle with sides 3, 4 and 5 in the same unit, because 9 + 16 = 25. Builders use it to check that a corner is square. Angles are about 36.87 and 53.13 degrees, the area is 6 and the perimeter is 12.
What is the difference between angle A and angle B?
Angle A is opposite side a, and angle B is opposite side b. They are the two acute angles and always add to 90 degrees. Which one you call A is your choice, as long as a matches it.
Does it work in degrees or radians?
Angles are entered and shown in degrees. If you have radians, multiply by 180 and divide by 3.14159 first. For example, 0.5236 radians is about 30 degrees, so enter 30. To convert a result back to radians, multiply by 3.14159 and divide by 180.