Find Angle Degrees Calculator

This angle degrees calculator helps you find angles in degrees using various geometric and trigonometric methods. Whether you're working with triangles, circles, or coordinate geometry, this tool provides quick and accurate results.

How to Use This Calculator

Using our angle degrees calculator is simple. Follow these steps:

Select the type of angle calculation you need (Triangle, Circle, or Coordinate Geometry).
Enter the required values in the input fields.
Click the "Calculate" button to get the angle in degrees.
Review the result and use the information as needed.

The calculator will display the angle in degrees along with a visual representation when available.

Formula Used

The formula used depends on the type of angle calculation you're performing:

Triangle Angle Formula

For a triangle with sides a, b, and c, the angle opposite side a can be found using the Law of Cosines:

cos(A) = (b² + c² - a²) / (2bc)

Then, A = arccos(cos(A)) in degrees

Circle Angle Formula

For a circle with radius r and arc length s, the central angle θ in degrees is:

θ = (s / r) × (180 / π)

Coordinate Geometry Angle Formula

For two lines with slopes m1 and m2, the angle θ between them in degrees is:

θ = arctan(|(m1 - m2) / (1 + m1m2)|) in degrees

Worked Examples

Triangle Angle Example

Given a triangle with sides a=5, b=6, c=7, find the angle opposite side a.

Using the Law of Cosines:

cos(A) = (6² + 7² - 5²) / (2 × 6 × 7) = (36 + 49 - 25) / 84 = 60/84 ≈ 0.7143

A ≈ arccos(0.7143) ≈ 44.42°

Circle Angle Example

Given a circle with radius 10 and arc length 15, find the central angle.

θ = (15 / 10) × (180 / π) ≈ 27.27°

Coordinate Geometry Angle Example

Given two lines with slopes m1=2 and m2=0.5, find the angle between them.

θ = arctan(|(2 - 0.5) / (1 + 2×0.5)|) = arctan(|1.5 / 2|) ≈ arctan(0.75) ≈ 36.87°

Frequently Asked Questions

What types of angles can I calculate with this tool?: You can calculate angles in triangles, circles, and between lines in coordinate geometry.
Is the calculator accurate?: Yes, the calculator uses standard mathematical formulas and provides precise results.
Can I use this calculator on my mobile device?: Yes, the calculator is fully responsive and works on all devices.
Do I need to register to use the calculator?: No, you can use the calculator without registration.
How do I interpret the results?: The calculator provides the angle in degrees and may include a visual representation for better understanding.