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How to Convert from Degree [°] to Radian [rad]?
Learn how to convert angles from degrees to radians using our easy-to-use online unit converter. Understand the difference between degree and radian units and apply conversions for mathematics, physics, and engineering.
Please check your input. It must be a valid numeric value.
Degree [°] to Radian [rad] Conversion Table
| Degree [°] | Radian [rad] |
|---|
Custom Unit Conversion Table Generator – Instant Printable Conversion Tables
Enter the starting number (positive decimal or integer ≥ 0). Example: 0.1, 1, 5.
Enter the ending number (positive decimal or integer > Start Value). Example: 10, 50, 100.
Enter the step size (positive decimal > 0 and < End Value – Start Value). Example: 1.0, 2.5.
| Degree [°] | Radian [rad] |
|---|
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What Is This Tool?
This converter transforms angle measurements from degrees (°) into radians (rad), facilitating usage in mathematics, physics, engineering, and other scientific fields where radians are standard.
How to Use This Tool?
- Enter the angle value in degrees into the input field.
- Select 'degree [°]' as the original unit and 'radian [rad]' as the target unit.
- Press the convert button to see the angle value expressed in radians.
Key Features
- Converts plane angles from degrees to radians accurately based on a defined conversion rate.
- Supports common angle unit conversions used in geometry, navigation, and engineering.
- Browser-based and easy to use without any installation required.
Examples
- Convert 30° to radians: 30° × 0.0174532925 = 0.523598775 rad
- Convert 90° to radians: 90° × 0.0174532925 = 1.570796325 rad
Common Use Cases
- Specifying geographic coordinates such as latitude and longitude for mapping and GPS systems.
- Describing angular displacement and orientation in engineering and machining tasks.
- Using angles in mathematical functions, calculus, and mechanics requiring radians.
- Expressing phase angles in wave and signal processing applications.
Tips & Best Practices
- Always verify the unit of angle measurement required in your calculations before converting.
- Use radians for mathematical and physics problems involving functions like sin, cos, and angular velocity.
- Be cautious of rounding during conversion, as radians are dimensionless and high precision may be needed.
Limitations
- Radians being dimensionless require precise values; rounding may affect accuracy in trigonometric calculations.
- Degrees are limited to division of a full circle into 360 parts, which may be unsuitable for some scientific applications.
- Conversion does not alter the intrinsic meaning of angles—use the appropriate unit for your context.
Frequently Asked Questions
- Why should I convert degrees to radians?
- Radians are the standard unit in many mathematical and physical calculations, especially involving trigonometric functions and angular measurements in mechanics.
- What is the conversion rate from degrees to radians?
- One degree equals approximately 0.0174532925 radians.
- Are degrees and radians interchangeable?
- Degrees and radians both measure angles but serve different purposes; degrees are often more intuitive, while radians are suited for scientific and mathematical computations.
Key Terminology
- Degree [°]
- A unit of plane angle representing 1/360 of a full circle, used for geographic, navigational, and engineering angles.
- Radian [rad]
- An SI derived unit of plane angle defined by the angle created by an arc equal in length to the radius of a circle; dimensionless.
- Angular displacement
- A measure of rotation often expressed in radians, used in mechanics and physics.