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Right Triangle Calculator
Your triangle
Example: legs 3 and 4 → hypotenuse 5.00, angles 36.87° and 53.13°, area 6.00, perimeter 12.00.
Behind the numbers
How a right triangle is solved
Every right triangle has one 90° angle, so the two acute angles add up to 90°. Pick the two values you know, and the calculator fills in the rest: the Pythagorean theorem (a² + b² = c²) finds a missing side when two sides are known, and sine, cosine, and tangent find sides and angles when one side and one acute angle are known. Area is half the product of the two legs, and perimeter is the sum of all three sides.
Worked example with legs 3 and 4: hypotenuse c = √(3² + 4²) = √25 = 5.00. Angle A = tan⁻¹(3 ÷ 4) = 36.87°. Angle B = 90° − 36.87° = 53.13°. Area = ½ × 3 × 4 = 6.00. Perimeter = 3 + 4 + 5 = 12.00.
Examples
Example right triangles
| Legs (a, b) | Hypotenuse | Angles A / B | Area | Perimeter |
|---|---|---|---|---|
| 3, 4 | 5.00 | 36.87° / 53.13° | 6.00 | 12.00 |
| 5, 12 | 13.00 | 22.62° / 67.38° | 30.00 | 30.00 |
| 8, 15 | 17.00 | 28.07° / 61.93° | 60.00 | 40.00 |
| 6, 8 | 10.00 | 36.87° / 53.13° | 24.00 | 24.00 |
| 1, 1 | 1.41 | 45.00° / 45.00° | 0.50 | 3.41 |
Tips before you solve
The hypotenuse is always the longest side — if your entered hypotenuse is shorter than a leg, the triangle cannot exist.
Angles are in degrees, and each acute angle must be between 0° and 90°.
Enter matching units for both sides: mixing inches and centimeters gives a wrong answer.
For construction and framing, the 3-4-5 triangle is a quick way to check a square corner.
Good to know
Frequently asked questions
Can I solve a right triangle with only one side?
No — one side alone leaves an infinite number of possible triangles. You need any two known values: two sides, or one side and one acute angle.
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 works only for right triangles.
How do I find an angle from two sides?
Use an inverse trigonometric function: angle A = tan⁻¹(a ÷ b), or sin⁻¹(a ÷ c) if you know the hypotenuse. The other acute angle is 90° minus the first.
What is the area of a right triangle?
Half the product of the two legs: area = ½ × a × b. The legs meet at the 90° angle, so they act as base and height.