Measure in Degrees Calculator

Degrees are a fundamental unit of measurement for angles in geometry and trigonometry. This calculator helps you convert between degrees and other angle measurement units, including radians and gradians. Whether you're working on a geometry problem, designing a structure, or analyzing data, understanding angle measurements is essential.

What is measure in degrees?

The degree (symbol: °) is a unit of measurement for angles. It's defined as 1/360th of a full circle, which means a full circle contains 360 degrees. Degrees are commonly used in geometry, navigation, engineering, and many other fields.

There are two main types of degrees:

Plane angle degrees: Used to measure angles in a plane (2D space)
Spherical angle degrees: Used to measure angles on a sphere (3D space)

Degrees are often used alongside other angle measurement units:

Radians: The standard unit in mathematics and physics
Gradians: Used in some European countries
Minutes and seconds: Subdivisions of a degree

How to use this calculator

Using our measure in degrees calculator is simple:

Enter the angle value you want to convert in the input field
Select the unit you're converting from in the "From" dropdown
Select the unit you want to convert to in the "To" dropdown
Click the "Calculate" button
View your results in the output section

Tip: You can convert between degrees, radians, and gradians. The calculator will automatically use the appropriate conversion formula based on your selections.

Common angle measurements

Here are some common angle measurements and their degree equivalents:

Angle Name	Degrees	Radians	Gradians
Right angle	90°	π/2	100g
Straight angle	180°	π	200g
Full circle	360°	2π	400g
Golden angle	137.5°	2.418π	185g

Conversion formulas

The measure in degrees calculator uses these conversion formulas:

Degrees to Radians: radians = degrees × (π/180)

Radians to Degrees: degrees = radians × (180/π)

Degrees to Gradians: gradians = degrees × (10/9)

Gradians to Degrees: degrees = gradians × (9/10)

Where π (pi) is approximately 3.141592653589793.

Practical applications

Understanding angle measurements in degrees has many practical applications:

Construction: Measuring and constructing angles for buildings and structures
Navigation: Determining directions and positions using compass bearings
Engineering: Designing mechanical parts and systems
Art and Design: Creating accurate geometric shapes and patterns
Astronomy: Calculating positions of celestial bodies

Frequently Asked Questions

What is the difference between degrees and radians?: Degrees and radians are both units of angle measurement, but they use different scales. A full circle is 360 degrees or 2π radians. Radians are the standard unit in mathematics and physics.
How do I convert degrees to radians?: To convert degrees to radians, multiply the degree value by π/180. For example, 90 degrees is equal to 90 × (π/180) = π/2 radians.
What are gradians, and how do they compare to degrees?: Gradians are another unit of angle measurement used in some European countries. A full circle is 400 gradians, so 1 degree is equal to 10/9 gradians, and 1 gradian is equal to 9/10 degrees.
Why are degrees used instead of radians in some applications?: Degrees are often used in applications where angles are more intuitive to humans, such as navigation and construction. Radians are preferred in mathematical calculations because they simplify many trigonometric formulas.
What are some common angle measurements in everyday life?: Common angle measurements in everyday life include 90° (right angles in corners), 180° (straight angles in lines), and 360° (full circles in rotations).