Instant and Accurate Angle Unit Conversion

Angles are a fundamental part of geometry, trigonometry, engineering, and navigation. While degrees are the most common unit, many scientific and mathematical applications rely on radians, gradians, or other precise measurements. Our free Angle Converter provides a simple and reliable way to convert between these units, ensuring your calculations are always accurate. Whether you're a student solving a trigonometry problem, an engineer designing a part, or a navigator plotting a course, this tool is designed to help.

This converter supports the most widely used angle units, including Degrees, Radians, Gradians, Milliradians, Arcminutes, and Arcseconds. Eliminate the hassle of remembering complex conversion formulas and get instant results for any application.

How to Use the Angle Converter

1. Enter Your Angle: Type the numeric value of the angle you want to convert into the "From" input field.
2. Select Units: Choose your starting unit (e.g., Degrees) and your target unit (e.g., Radians) from the dropdown lists.
3. Convert: Click the "Convert Angle" button to perform the calculation and see the result instantly.
4. Copy Result: Use the "Copy Result" button to easily save the converted value for your work.

Frequently Asked Questions About Angle Conversion

How to do angle conversion?

Angle conversion is done using established relationships between units. The most fundamental relationship is that a full circle is 360 degrees (deg), 2π radians (rad), or 400 gradians (grad). To convert from one unit to another, you use a conversion factor derived from these relationships. For example, to convert degrees to radians, you multiply by (π / 180).

How do you convert degrees to directions?

Degrees are converted to compass directions based on a 360-degree circle where 0° is North. The main cardinal directions are: North (0° or 360°), East (90°), South (180°), and West (270°). Intermediate directions fall in between, such as Northeast (45°), Southeast (135°), Southwest (225°), and Northwest (315°).

How to convert degrees to coordinates?

You cannot directly convert an angle to a single coordinate; you need a distance or radius (r) as well. An angle (θ) and a radius (r) define a point on a circle in a polar coordinate system. To convert this to Cartesian coordinates (x, y), you use trigonometry: x = r * cos(θ) and y = r * sin(θ). Ensure your angle is in radians for these formulas or convert it from degrees first.

How do you convert numbers to angles?

A plain number can represent an angle if you know the unit (e.g., the number 90 could mean 90 degrees or 90 radians). If the number is a ratio from a trigonometric function (like the ratio of a triangle's sides), you use an inverse trigonometric function (arcsin, arccos, arctan) to find the angle. For example, if the sine of an angle is 0.5, the angle is arcsin(0.5) = 30°.

What is the formula for the change of an angle?

The change of an angle, known as angular displacement, is the difference between the final angle and the initial angle. The formula is: Δθ = θ_final - θ_initial. The result (Δθ) represents the amount of rotation that has occurred. For example, if an object moves from a 30° position to a 75° position, the change of angle is 75° - 30° = 45°.