Right Triangle Calculator
This right triangle calculator solves the whole triangle from any two values you know. Give it two sides, or one side and an angle, and you'll get every side, both acute angles, the area, and the perimeter, plus a diagram that redraws to match. It uses the Pythagorean theorem and trig behind the scenes, and it's got the steps so the method stays clear.
- All sides and angles
- From sides or an angle
- Area and perimeter
- Live triangle diagram
- Steps shown
Last updated August 3, 2026 Pythagoras + trig Written by the Calcowa team
A right triangle calculator finds the sides and angles of a right triangle (also spelled right-angled triangle) from any two known values. Enter two sides, or one side and one acute angle, and it returns the third side using the Pythagorean theorem a² + b² = c², both acute angles from trig, plus the area and perimeter. To instead check whether three sides make a right triangle, confirm that its two smaller sides squared add up to the longest side squared.
Enter two valid values. The hypotenuse must be the longest, and an angle must be between 0 and 90.
c = √(3² + 4²) = 5
What is a right triangle?
A right triangle is a triangle with one 90-degree angle, the square corner. The two sides that form that corner are the legs, a and b, and the long side across from it is the hypotenuse, c. The other two angles are acute and always add up to 90 degrees. That fixed shape is what lets you solve the whole triangle from just two known values, and it's why two inputs are enough.
How to solve a right triangle
Say you've got the two legs, 3 and 4. Here's how the whole triangle falls out:
- 1
Find the hypotenusec = √(3² + 4²) = √25 = 5.
- 2
Find one angleA = arctan(3 ÷ 4) ≈ 36.87°.
- 3
Find the last angleB = 90 − 36.87 ≈ 53.13°, since the two add to 90.
- 4
Get area and perimeterArea = ½ × 3 × 4 = 6, perimeter = 3 + 4 + 5 = 12.
Finding a missing side or angle
For sides, the Pythagorean theorem does the heavy lifting: the hypotenuse is √(a² + b²), and a leg is √(c² − b²). For angles, you reach for trig: the sine, cosine, and tangent link a side to an angle. If you've got a side and an angle, sine and cosine give the remaining sides, and if you've got two sides, the inverse tangent gives an angle. The calculator picks the right relationship for whichever mode you choose, so you don't have to remember which is which.
How to check if three sides make a right triangle
If you already have all three sides and just want to know whether the corner is square, you run the Pythagorean theorem backward. Square the two shorter sides, add them, and compare that total to the longest side squared. If the two match exactly, it's a right triangle; if the sum falls short the triangle's obtuse, and if it overshoots the triangle's acute.
Take the shorter pair, 24 and 45, and square them: 24² = 576 and 45² = 2025. Their sum is 576 + 2025 = 2601. Now square the longest side: 51² = 2601. The two totals are equal, so 24-45-51 is a right triangle. Drop the two legs into the "Two legs" mode above and the calculator returns a hypotenuse of 51 to confirm it.
Special right triangles
A few right triangles show up so often they're worth knowing on sight, and the calculator'll handle them like any other.
| Triangle | What it is | The rule |
|---|---|---|
| 45-45-90 | Two equal legs | Legs equal, hypotenuse = leg × √2 |
| 30-60-90 | Half an equilateral triangle | Sides in the ratio 1 : √3 : 2 |
| 3-4-5 | The classic Pythagorean triple | Angles about 37° and 53° |
Common Pythagorean triples
A Pythagorean triple is a right triangle whose three sides are all whole numbers, so a² + b² lands exactly on c². These come up constantly in homework and layout work, and any multiple of one (like 6-8-10 from 3-4-5) is a right triangle too.
| Sides (a, b, c) | The check | Acute angles |
|---|---|---|
| 3, 4, 5 | 9 + 16 = 25 | 36.87° and 53.13° |
| 5, 12, 13 | 25 + 144 = 169 | 22.62° and 67.38° |
| 8, 15, 17 | 64 + 225 = 289 | 28.07° and 61.93° |
| 7, 24, 25 | 49 + 576 = 625 | 16.26° and 73.74° |
| 9, 40, 41 | 81 + 1600 = 1681 | 12.68° and 77.32° |
Just need the missing side from two you know? The Pythagorean theorem calculator focuses on exactly that.
Frequently asked questions
How many values do you need to solve a right triangle?
Two, on top of the right angle itself. That's either two sides, or one side and one acute angle. With any two of those, every other side and angle is fixed, which is why the calculator only asks for two inputs.
You need any two pieces besides the right angle, then trig and the Pythagorean theorem'll give the rest. From two legs, the hypotenuse is √(a² + b²) and the angles come from the tangent. From a side and an angle, sine and cosine fill in the other sides. The calculator does all of it from whatever two values you've entered.
If you know the two legs, the hypotenuse is √(a² + b²). If you know the hypotenuse and a leg, the other leg is √(c² − a²). If you have a side and an angle, you use sine, cosine, or tangent. Pick the matching mode above and it's worked out for you.
One angle is always 90 degrees, and the other two add up to 90, so they're never a mystery. From the sides, an angle equals the inverse tangent of the opposite leg over the adjacent leg, so angle A is arctan(a ÷ b). The calculator reports both acute angles in degrees.
It's a right triangle with two equal legs, so the two non-right angles are both 45 degrees. The hypotenuse is always a leg times the square root of 2. Enter equal legs above and you'll see those 45-degree angles appear.
It's half of an equilateral triangle, with angles of 30, 60, and 90 degrees. Its sides follow the fixed ratio 1 : √3 : 2, so the side opposite 30° is the shortest and the hypotenuse is twice it. The calculator confirms the angles whenever the sides match, so you don't second-guess it.
Yes, like every triangle. Since one angle is 90 degrees, the other two must add to 90, which is why knowing one acute angle instantly gives you the other. That's a quick check on any answer.
The hypotenuse is √(6² + 8²) = √100 = 10. That's just a scaled 3-4-5 triangle, so the two acute angles stay at about 37° and 53°. Enter 6 and 8 as the two legs above and you'll get the same 10, with the area, perimeter, and steps filled in.
Square the two shorter sides and add them, then square the longest side. If those two totals match, the sides form a right triangle. Sides of 5, 6, and 8 give 25 + 36 = 61, but 8² is 64, so they fall just short and make an obtuse triangle instead. When the sum matches the longest square exactly, the corner is square.
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