Right Triangle Calculator
Enter any two sides, or one side and one angle, to solve a right triangle: missing sides, both acute angles, area, perimeter and height.
Right triangle formulas
a² + b² = c² sin A = a ÷ c, cos A = b ÷ c, tan A = a ÷ b Area = a × b ÷ 2
Legs a and b meet at the right angle, c is the hypotenuse, and angle A is opposite side a. The two acute angles always add up to 90°.
Worked example
With legs 3 and 4, c = √(9 + 16) = 5. Angle A = arctan(3 ÷ 4) = 36.87° and angle B = 53.13°. The area is 3 × 4 ÷ 2 = 6 and the perimeter is 12.
Special right triangles
| Triangle | Side ratio |
|---|---|
| 45-45-90 | 1 : 1 : √2 |
| 30-60-90 | 1 : √3 : 2 |
| 3-4-5 | 3 : 4 : 5 (Pythagorean triple) |
| 5-12-13 | 5 : 12 : 13 (Pythagorean triple) |
Frequently asked questions
How do I find the hypotenuse?
Square both legs, add them and take the square root: c = √(a² + b²).
How do I 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).
How do I find an angle from two sides?
Use inverse trig. With both legs, A = arctan(a ÷ b). With a leg and the hypotenuse, A = arcsin(a ÷ c).
What units does the answer use?
The same units you enter for the sides. Area is in those units squared.
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