Convert Degree to Radian (° to rad)
Converting Degree to Radian is a frequent requirement in the field of angle. Whether you are working on a technical project, studying for an exam, or just need a quick reference, this calculator provides an instant and accurate solution. It includes the precise formula, a conversion table, and practical examples to help you understand the relationship between these two units.
Conversion Table
| Degree (°) | Radian (rad) |
|---|---|
| 0.001 | 0.0000174533 |
| 0.01 | 0.000174533 |
| 0.1 | 0.00174533 |
| 1 | 0.0174533 |
| 5 | 0.0872664 |
| 10 | 0.174533 |
| 50 | 0.872664 |
| 100 | 1.74533 |
| 500 | 8.72664 |
| 1000 | 17.4533 |
Formula
The conversion from Degree to Radian is based on the ratio of their definitions relative to the base unit. To convert a value from Degree to Radian, you multiply the value by the conversion factor. Conversely, to convert from Radian to Degree, you divide by this factor (or multiply by its reciprocal).
Examples
Let's look at some examples. Converting 1 ° to rad demonstrates the basic ratio. For larger quantities, such as 100 °, the result scales linearly. These examples help visualize the magnitude difference between the two units.
Reverse Formula
The process is fully reversible. If you have a value in Radian and need to find the equivalent in Degree, you simply apply the inverse operation. Our calculator handles this automatically with the "Swap" button, but knowing the reverse formula is useful for manual checking.
Common Mistakes
A common mistake when converting Degree to Radian is ignoring significant figures. While the calculator provides high precision, real-world measurements have limits. Another error is confusing similar-sounding units (like US vs UK gallons). Always ensure you have selected the exact unit variant intended.
Accuracy Notes
FastConverto uses double-precision floating-point math to ensure the highest possible accuracy. However, for extremely large or small numbers, floating-point arithmetic can introduce minute rounding errors. For most practical and scientific purposes, the results are more than sufficiently precise.
Industry Use
This specific conversion (° to rad) is often used in industries such as engineering, construction, and international logistics. When data is shared across borders or between different technical disciplines, standardizing units via accurate conversion is critical to project success and safety.
Frequently Asked Questions
How do I convert Degree to Radian?
Enter the amount in the "From" field above, and the result will appear instantly in the "To" field.
What is the formula for ° to rad?
The formula involves multiplying by the specific conversion factor defined by international standards.
Is the conversion exact?
The conversion factors are exact by definition or high-precision standards, though the displayed result may be rounded.
Can I convert Radian back to Degree?
Yes, the conversion is reversible. Use the swap button to switch the direction.
Why is this conversion important?
It allows for interoperability between systems using Degree and those using Radian, which is essential in a globalized world.
Do you support bulk conversions?
You can use the conversion table below for multiple values or download the data as a CSV file.