Convert Angle to Degrees Calculator

Convert angles between degrees, radians, and gradians with our precise calculator. Learn the conversion formulas, common values, and practical applications.

How to Use This Calculator

Our angle conversion calculator is simple to use:

Enter the angle value in the input field
Select the unit you're converting from (degrees, radians, or gradians)
Click "Calculate" to see the converted values
View the results in all three units
Use the "Reset" button to clear the calculator

The calculator provides instant conversions and displays the results in a clear format. You can also see a visual representation of the angle conversion.

Angle Conversion Formulas

Angles can be measured in different units: degrees (°), radians (rad), and gradians (grad). Here are the conversion formulas between these units:

Degrees to Radians

radians = degrees × (π/180)

Degrees to Gradians

gradians = degrees × (10/9)

Radians to Degrees

degrees = radians × (180/π)

Radians to Gradians

gradians = radians × (200/π)

Gradians to Degrees

degrees = gradians × (9/10)

Gradians to Radians

radians = gradians × (π/200)

These formulas allow you to convert between any two angle units. The calculator uses these formulas to provide accurate conversions.

Common Angle Conversions

Here are some common angle conversions that are frequently used in various fields:

Degrees	Radians	Gradians	Common Use
0°	0 rad	0 grad	Starting point for measurements
30°	0.5236 rad	33.333 grad	Common angle in triangles
45°	0.7854 rad	50 grad	Diagonal of a square
60°	1.0472 rad	66.667 grad	Common angle in equilateral triangles
90°	1.5708 rad	100 grad	Right angle
180°	3.1416 rad	200 grad	Straight angle
270°	4.7124 rad	300 grad	Three-quarter turn
360°	6.2832 rad	400 grad	Full circle

These common angle values are useful for quick reference and can be used in various calculations and measurements.

Practical Applications

Angle conversion is used in many practical applications across various fields:

Navigation

In navigation, angles are used to determine directions and positions. Converting between degrees and radians is essential for accurate navigation calculations.

Engineering

Engineers use angle conversions in design and construction. Whether working with structural angles or mechanical components, precise angle measurements are crucial.

Physics

In physics, angles are used to describe the orientation of objects and the direction of forces. Converting between different angle units helps in solving various physics problems.

Computer Graphics

In computer graphics, angles are used to rotate objects and create 3D models. Converting between degrees and radians is essential for accurate transformations.

Everyday Life

Even in everyday life, angle conversion is useful. For example, when measuring the angle of a slope or the tilt of a surface, knowing how to convert between different units can be helpful.

Our angle conversion calculator makes it easy to perform these conversions quickly and accurately.

FAQ

What is the difference between degrees, radians, and gradians?: Degrees, radians, and gradians are different units for measuring angles. Degrees are commonly used in everyday life, radians are used in mathematics and physics, and gradians are used in some European countries.
How do I convert degrees to radians?: To convert degrees to radians, multiply the degree value by π/180. For example, 90° × (π/180) = 1.5708 radians.
What is the formula for converting radians to degrees?: The formula for converting radians to degrees is degrees = radians × (180/π). For example, 3.1416 radians × (180/π) = 180°.
Why is angle conversion important?: Angle conversion is important because different fields use different angle units. Being able to convert between these units allows for accurate measurements and calculations.
Can I use this calculator for scientific calculations?: Yes, this calculator can be used for scientific calculations. The formulas used are accurate and reliable for converting between degrees, radians, and gradians.