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Online Right Triangle Calculator
Solve a right triangle from any two known values and find every side, angle, height, area, perimeter, and radius.
| Result | |||
|---|---|---|---|
| a | 3 | ||
| b | 4 | ||
| c | 5 | ||
| h | 2.4 | ||
| α | 36.8699° = 0.6435011 rad | ||
| β | 53.1301° = 0.9272952 rad | ||
| S (area) | 6 | inradius | 1 |
| p (perimeter) | 12 | circumradius | 2.5 |
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What Is This Tool?
The Right Triangle Calculator solves a right triangle when you know any two of its values: the two legs a and b, the hypotenuse c, the acute angles α and β, the height h to the hypotenuse, the area, or the perimeter. It returns all sides, both acute angles in degrees and radians, the height, area, perimeter, inradius, and circumradius. For example, legs of 3 and 4 give a hypotenuse of 5, an area of 6, and a perimeter of 12.
How to Use This Tool?
- Enter exactly two known values in any of the fields.
- Use the angle boxes for α and β in degrees.
- Leave every other field empty.
- Click Calculate to solve the triangle.
Key Features
- Solves from any two known values, not just two sides.
- Accepts sides, angles, height, area, or perimeter.
- Reports both acute angles in degrees and radians.
- Calculates area, perimeter, height, and the two radii.
- Checks that the inputs form a valid right triangle.
Examples
- Legs 3 and 4 give a hypotenuse of 5 and an area of 6.
- A leg of 6 with an angle of 30° fixes the whole triangle.
- A hypotenuse of 10 with an area of 24 gives legs 6 and 8.
- An angle of 45° with a perimeter of 12 gives an isosceles right triangle.
Common Use Cases
- Solving right-triangle trigonometry problems.
- Finding missing sides or angles in construction.
- Working out roof pitch, ramps, and stair stringers.
- Checking surveying and layout measurements.
- Verifying right-triangle homework.
Tips & Best Practices
- Provide exactly two values, no more and no fewer.
- Enter both acute angles in degrees; each must be under 90°.
- Remember c is the hypotenuse, opposite the right angle.
- Use consistent units for every length you enter.
- Two angles alone cannot fix the triangle's size.
Limitations
- It works only for right triangles.
- Exactly two values are required, and they must be positive.
- Two angles, or height with perimeter, cannot be solved.
- Impossible combinations are reported as invalid.
Frequently Asked Questions
- Which two values can I enter?
- Any two of the legs, hypotenuse, the two acute angles, the height, the area, or the perimeter, as long as they describe a real right triangle.
- Why can't I enter two angles?
- The angles of a right triangle always sum to 90° beyond the right angle, so two angles fix only the shape, not the size.
- What is the height h?
- It is the altitude drawn from the right angle to the hypotenuse, equal to the product of the legs divided by the hypotenuse.
- What are the inradius and circumradius?
- The inradius is the radius of the circle that fits inside the triangle, and the circumradius is half the hypotenuse.
Key Terminology
- Hypotenuse
- The longest side of a right triangle, opposite the right angle.
- Leg
- Either of the two sides that meet at the right angle.
- Height
- The altitude from the right angle perpendicular to the hypotenuse.
- Inradius
- The radius of the circle that fits inside the triangle.
- Circumradius
- The radius of the circle through all three vertices, equal to half the hypotenuse.