Angle Converter
Why Convert Angles?
Angles are the building blocks of geometry, navigation, and engineering. However, different fields use different "languages" to describe them. While most of us learn about **Degrees** in school, advanced mathematics and physics rely almost entirely on **Radians**.
The CalculatorBud Angle Converter eliminates the confusion of manual trigonometry. Whether you are a student solving calculus problems or a developer rotating 3D objects in a game engine, this tool bridges the gap between these units instantly.
Common Uses for Angle Units
Used in Calculus and trigonometry because it simplifies formulas involving sine and cosine.
GPS coordinates and maps use Degrees, Minutes, and Seconds (DMS) for precision.
Used in rifle scopes and artillery because it correlates easily with distance estimations.
Degrees vs. Radians: What's the Difference?
This is the most common confusion in geometry. Here is the easiest way to visualize it:
- Degrees (°): Imagine slicing a pizza into 360 tiny, equal slices. One slice is one degree. It is an arbitrary number chosen by ancient Babylonians.
- Radians (rad): This is based on the radius of the circle. If you take the radius of a circle and wrap it along the edge, the angle created is exactly 1 radian.
Because the circumference of a circle is calculated using Pi (π), radians allow for cleaner mathematical equations. A full circle is 360° or 2π radians.
To convert Degrees to Radians, multiply by π / 180.
To convert Radians to Degrees, multiply by 180 / π.
What are Gradians and Arc Minutes?
Gradians (gon): This metric unit divides a right angle into 100 parts (instead of 90 degrees). A full circle is 400 gradians. It is rarely used today outside of some land surveying tasks.
Arc Minutes (') and Seconds ("): These are subdivisions of a degree, used for extreme precision in astronomy and latitude/longitude.
1 Degree = 60 Minutes.
1 Minute = 60 Seconds.
Frequently Asked Questions
One radian is approximately equal to 57.296 degrees. This is an irrational number derived from 180 divided by Pi.
Calculus functions (derivatives and integrals) of trigonometric functions like sin(x) only work simply if the angle is measured in Radians. If you use Degrees, the formulas become much messier with extra constants.
A Gradian (gon) is a unit that divides a right angle into 100 parts instead of 90. It was an attempt to make angles "metric" (base 10), but it never really caught on outside of specific land surveying fields.