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Right Triangle Calculator
Why Use This Tool?
This right triangle calculator helps you find all unknown sides and angles of a right triangle when you know just two values. Whether you're a student, engineer, architect, or DIY enthusiast, this tool saves time and ensures accurate calculations for any right triangle problem.
How It Works
A right triangle has one 90-degree angle (angle C) and two acute angles (A and B) that sum to 90 degrees. Using the Pythagorean theorem (a² + b² = c²) and trigonometric functions, this calculator can determine all unknown values from any two known measurements.
Formulas Used:
- Pythagorean Theorem: a² + b² = c²
- Sine: sin(A) = a/c, sin(B) = b/c
- Cosine: cos(A) = b/c, cos(B) = a/c
- Tangent: tan(A) = a/b, tan(B) = b/a
- Angle Sum: A + B = 90°
Step-by-Step Instructions
- Look at the triangle diagram above to understand which side or angle corresponds to each input
- Enter any two known values (e.g., two sides, or one side and one angle)
- Click "Calculate" to find all unknown values
- The calculator will display all sides, angles, area, and perimeter
- Use "Clear All" to reset and start a new calculation
Calculator
Enter any two values to calculate the rest:
Use this right triangle calculator to solve right triangles fast. Enter any two values. The tool finds every side and angle. It also shows area and perimeter. It suits students and engineers. It also helps architects and do it yourself users.
How It Works
A right triangle has one angle of 90 degrees, named C. Angles A and B add to 90 degrees. Sides a and b form the legs. Side c is the hypotenuse and it is the longest side. The calculator uses the Pythagorean theorem and basic trigonometry. It solves the missing values from any two inputs. Angles are in degrees. Use the same units for all lengths.
Math and checks
- Pythagorean theorem: a² + b² = c²
- Sine: sin A = a divided by c
- Cosine: cos A = b divided by c
- Tangent: tan A = a divided by b
- Angle sum: A + B = 90 degrees
- Area: a times b divided by 2
- Perimeter: a plus b plus c
- Inputs: use values greater than zero
- Angles: A and B lie between 0 and 90 degrees
- Hypotenuse: c is larger than a and b
- Data: enter at least two fields
- Angles only: include a side if you set both angles
How to Use This Tool
- Pick any two known values.
- Type them in the matching fields.
- Use degrees for angles A and B.
- Use the same unit for all lengths.
- Press Calculate.
- Read the sides and angles.
- Read the area and the perimeter.
- Press Clear All to start a new case.
You can enter two sides. You can enter one side and one angle. You can enter the hypotenuse and one angle. You need at least one side if you set both angles.
What Each Input Means
- Side a: the leg opposite angle A. Enter its length.
- Side b: the leg opposite angle B. Enter its length.
- Hypotenuse c: the side across from the right angle. Enter its length.
- Angle A: an acute angle. Enter degrees greater than 0 and less than 90.
- Angle B: the other acute angle. Enter degrees greater than 0 and less than 90.
Results and how to read them
- Side a: length of the leg opposite angle A. Shown to four decimals.
- Side b: length of the leg opposite angle B. Shown to four decimals.
- Hypotenuse c: longest side across from the right angle. Shown to four decimals.
- Angle A: acute angle. Shown in degrees with two decimals.
- Angle B: acute angle. Shown in degrees with two decimals.
- Angle C: right angle with 90 degrees.
- Area: space inside the triangle. Shown to four decimals.
- Perimeter: sum of all sides. Shown to four decimals.
- Use consistent units for all side inputs.
- Use values greater than zero.
- Angles A and B add to 90 degrees.
- Hypotenuse c stays larger than a and b.
- Small rounding differences may appear near extreme angles.
Examples
- Set a as 3 and b as 4. You get c equal to 5. Angle A is 36.87 degrees. Angle B is 53.13 degrees. Area is 6. Perimeter is 12.
- Set c as 10 and A as 30 degrees. You get a equal to 5. Side b is 8.6603. Angle B is 60 degrees. Area is 21.6506. Perimeter is 23.6603.
Use this right triangle calculator for homework, roof pitch, ramps, and layout. Enter two inputs and get clean results. Quick, clear, and accurate.
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