Degree to Radian Converter
Convert degree (°) to radian (rad) instantly. Free, accurate, and easy to use.
Convert Degree to Radian
Result
1 Degree equals ? Radian
Degree to Radian Conversion Table
| Degree (°) | Radian (rad) |
|---|---|
| 1 ° | 0.017453293 rad |
| 2 ° | 0.034906585 rad |
| 3 ° | 0.052359878 rad |
| 5 ° | 0.087266463 rad |
| 10 ° | 0.17453293 rad |
| 15 ° | 0.26179939 rad |
| 20 ° | 0.34906585 rad |
| 25 ° | 0.43633231 rad |
| 50 ° | 0.87266463 rad |
| 75 ° | 1.30899694 rad |
| 100 ° | 1.74532925 rad |
| 250 ° | 4.36332313 rad |
| 500 ° | 8.72664626 rad |
| 1000 ° | 17.45329252 rad |
Formula: Degree to Radian
To convert from degree to radian, multiply the value in degree by the conversion factor 0.017453293. The result is the equivalent value in radian.
Understanding Degree to Radian Conversion
Converting from degree (°) to radian (rad) is one of the most common angle conversions performed worldwide. The conversion factor is 1 ° = 0.017453293 rad, which means that to convert any value from degree to radian, you simply multiply by 0.017453293. This relationship is fixed and exact, based on internationally agreed-upon definitions of both units. Whether you are a student solving homework problems, an engineer working on technical specifications, a scientist conducting research, or simply someone who needs a quick conversion for everyday purposes, understanding this relationship between degree and radian is valuable knowledge that applies across countless practical situations.
What is a Degree?
The degree (°) is a unit of angle measurement. It is used in various applications across science, engineering, commerce, and daily life. Understanding the degree in context helps appreciate why conversion to other units like the radian is frequently necessary. The degree may be part of the metric (SI) system, the Imperial/US Customary system, or a specialized measurement system used in a particular industry or scientific field. Regardless of its origin, the degree has a precise mathematical relationship to all other angle units, enabling accurate and reliable conversion.
What is a Radian?
The radian (rad) is another unit of angle measurement that serves its own set of applications and contexts. It may be preferred in certain countries, industries, or scientific disciplines. The relationship between the degree and the radian — specifically that 1 ° equals 0.017453293 rad — provides a bridge between different measurement traditions and allows seamless communication of angle values across different systems and contexts. Our converter makes this translation instant and error-free.
How to Convert Degree to Radian
The conversion from degree to radian follows a straightforward mathematical process. Take your value in degree, and multiply it by the conversion factor of 0.017453293. For example, to convert 5 ° to rad, calculate 5 × 0.017453293. This formula works for any value — whether you are converting small decimal values or very large numbers. For the reverse conversion (radian to degree), simply divide by the same factor, or equivalently, multiply by the reciprocal. Our converter handles both directions automatically, and you can swap the units with a single click to perform the reverse calculation.
Common Applications
The conversion between degree and radian arises in numerous practical scenarios. Students encounter it in physics, chemistry, and engineering courses. Professionals use it in technical documentation, product specifications, and international communications. Travelers may need it when interpreting measurements in unfamiliar units. Online shoppers converting product dimensions or weights between systems rely on accurate conversions. Scientists publishing research must often present data in multiple unit systems for international audiences. In all these cases, having a reliable, instant converter eliminates errors and saves valuable time.
Tips for Accurate Conversion
When converting between degree and radian, keep these best practices in mind. First, always verify which specific unit variant you are working with — some unit names have multiple definitions depending on context (e.g., US vs Imperial gallons, short vs long tons). Second, consider the precision required for your application — our converter provides results to 10 significant figures, but your application may only need 2-3 decimal places. Third, for critical applications in engineering or science, always double-check conversions using a second source or method. Fourth, be aware of rounding — when converting back and forth between units, accumulated rounding errors can compound. Use the full-precision conversion factor rather than a rounded approximation for the most accurate results.
Common Degree to Radian Values
Frequently Asked Questions
How do I convert Degree to Radian?
Multiply the degree value by 0.017453293. For example, 5 ° × 0.017453293 = 0.087266463 rad.
What is 1 Degree in Radian?
1 Degree equals 0.017453293 Radian.
What is the formula for Degree to Radian?
The formula is: Radian = Degree × 0.017453293