Change to Degrees Calculator
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Reviewed by Calculator Editorial Team
Degrees are a fundamental unit of measurement for angles in geometry and trigonometry. This calculator helps you convert between different degree units and understand their practical applications.
What is Degrees?
A degree is a unit of measurement for angles, commonly used in geometry, trigonometry, and navigation. The degree symbol (°) is used to denote this unit. Degrees are divided into 60 minutes of arc, and each minute is divided into 60 seconds of arc.
Degrees are part of the sexagesimal system, which uses powers of 60. This system was developed by the Babylonians and later adopted by the Greeks and Romans.
Common Degree Units
There are several units used to measure angles, but degrees are the most commonly used. Other common units include radians, gradians, and revolutions.
| Unit | Symbol | Full Circle | Common Use |
|---|---|---|---|
| Degree | ° | 360° | Geometry, Trigonometry, Navigation |
| Radian | rad | 2π rad | Calculus, Physics |
| Gradian | grad | 400 grad | Engineering, Surveying |
| Revolution | rev | 1 rev | Rotational Mechanics |
Conversion Formulas
Converting between different angle units requires specific formulas. Here are the most common conversions:
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)
Practical Applications
Degrees are used in various practical applications, including:
- Navigation and map reading
- Architecture and construction
- Engineering and design
- Trigonometry and calculus
- Sports and athletics
In navigation, degrees are used to measure the angle between two points on a map. In architecture, degrees are used to measure the slope of a roof or the angle of a beam.
Common Mistakes
When working with degrees, it's easy to make common mistakes. Here are some of the most frequent errors:
- Confusing degrees with radians
- Using the wrong conversion formula
- Misinterpreting the direction of rotation
- Forgetting to account for the full circle (360°)
Always double-check your calculations and verify the units you're working with. Using a calculator can help prevent errors and ensure accuracy.
Frequently Asked Questions
- What is the difference between degrees and radians?
- A full circle is 360 degrees or 2π radians. Degrees are commonly used in geometry and navigation, while radians are commonly used in calculus and physics.
- How do I convert degrees to radians?
- To convert degrees to radians, multiply the number of degrees by π/180. For example, 90° is equal to 90 × (π/180) = π/2 radians.
- What are the common units for measuring angles?
- The common units for measuring angles are degrees, radians, gradians, and revolutions. Degrees are the most commonly used unit.
- How do I measure an angle with a protractor?
- To measure an angle with a protractor, align the center of the protractor with the vertex of the angle, align one side of the angle with the 0° line, and read the measurement where the other side of the angle crosses the protractor's scale.
- What is the difference between clockwise and counterclockwise rotation?
- Clockwise rotation is measured in the direction of the clock's hands, while counterclockwise rotation is measured in the opposite direction. The direction of rotation can affect the sign of the angle in some calculations.