Degré Radian Calculator
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This calculator helps you convert between degrees and radians, two common units for measuring angles. Whether you're working with trigonometry, physics, or engineering, understanding how to convert between these units is essential.
What is Degré Radian?
Degrees and radians are two different units used to measure angles. They are related through a simple conversion factor, making it easy to switch between them when needed.
One degree is equal to π/180 radians. This means that a full circle, which is 360 degrees, is equal to 2π radians (since 360 × π/180 = 2π).
Degrees are commonly used in everyday contexts, such as measuring the angle of a slope or the direction of a compass. Radians are more commonly used in advanced mathematics, physics, and engineering, particularly in calculus and trigonometry.
How to Convert Degrees to Radians
To convert degrees to radians, you can use the following formula:
For example, to convert 90 degrees to radians:
This means that a 90-degree angle is equivalent to π/2 radians.
How to Convert Radians to Degrees
To convert radians to degrees, you can use the following formula:
For example, to convert π radians to degrees:
This means that π radians is equivalent to 180 degrees.
When to Use Degrees vs Radians
Degrees and radians are used in different contexts, depending on the application:
- Degrees: Used in everyday contexts, such as measuring the angle of a slope, the direction of a compass, or the angle of a protractor.
- Radians: Used in advanced mathematics, physics, and engineering, particularly in calculus and trigonometry. Radians are the natural unit for measuring angles in these fields.
In general, degrees are more intuitive for everyday use, while radians are more useful for more advanced calculations.
Common Angle Conversions
Here are some common angle conversions between degrees and radians:
| Degrees | Radians |
|---|---|
| 0° | 0 |
| 30° | π/6 ≈ 0.5236 |
| 45° | π/4 ≈ 0.7854 |
| 60° | π/3 ≈ 1.0472 |
| 90° | π/2 ≈ 1.5708 |
| 180° | π ≈ 3.1416 |
| 270° | 3π/2 ≈ 4.7124 |
| 360° | 2π ≈ 6.2832 |
This table provides a quick reference for common angle conversions between degrees and radians.
FAQ
What is the difference between degrees and radians?
Degrees and radians are two different units used to measure angles. Degrees are based on the division of a circle into 360 equal parts, while radians are based on the radius of a circle. One radian is equal to the angle subtended at the center of a circle by an arc that is equal in length to the radius.
How do I convert degrees to radians?
To convert degrees to radians, multiply the number of degrees by π/180. For example, 90 degrees is equal to 90 × π/180 = π/2 radians.
How do I convert radians to degrees?
To convert radians to degrees, multiply the number of radians by 180/π. For example, π radians is equal to π × 180/π = 180 degrees.
When should I use degrees versus radians?
Degrees are more commonly used in everyday contexts, such as measuring the angle of a slope or the direction of a compass. Radians are more commonly used in advanced mathematics, physics, and engineering, particularly in calculus and trigonometry.