Angle Conversion - Angle Unit Conversion
Angle Conversion is an online angle unit conversion tool that helps you quickly solve conversions between degrees, radians and gradians. It supports degree to radian, radian to degree and gradian conversion, outputs accurate results in real time, and comes with a common angle reference table and a full-featured angle conversion calculator. Whether for math study or engineering drafting, you can easily complete angle unit conversion.
Input Parameters
About Angle Conversion and Angle Unit Conversion
What Is Angle Conversion
Angle conversion is the mathematical operation of converting values between different angle units. Common angle units include degrees (°), radians (rad) and gradians (grad). A degree divides a full circle into 360 equal parts, a radian measures the central angle using the radius as the unit, and a gradian defines a right angle as 100 equal parts. Angle unit conversion is widely used in trigonometry, calculus, engineering drafting, navigation and computer graphics. As an online angle conversion calculator, this tool helps you quickly perform degree to radian, radian to degree and gradian conversion, and displays accurate results in real time.
How to Use the Angle Conversion Calculator
Using this angle conversion calculator is very simple. Step one, enter the value to be converted in the "Angle Value" input box, which supports decimals and negative numbers. Step two, select the corresponding unit of the value in the "Input Unit" drop-down box, choosing from degree, radian or gradian. Step three, click the "Calculate" button, and the page will immediately display the conversion results of the angle in the other two units, along with the exact π form expression of the radian. If you need to copy the result, click the "Copy Result" button to save it in one click. To start over, click the "Reset" button to restore the default state. The entire conversion process is completed locally in your browser and can be used continuously without an internet connection.
Angle Conversion and the Common Angle Reference Table
When learning angle unit conversion, mastering the common angle reference table can greatly improve conversion efficiency. For example, 30° equals π/6 radian, 45° equals π/4 radian, 60° equals π/3 radian, 90° equals π/2 radian, 180° equals π radian, and 360° equals 2π radian. These special angles appear frequently in trigonometry, and memorizing their conversion relationships helps you solve problems quickly. In addition, how many degrees is 1 radian is also a common question — 1 radian is approximately 57.29578 degrees, and the conversion formula is 180 ÷ π. For gradian conversion, 1 right angle equals 100 grad, and 1 full circle equals 400 grad, with the formula grad = degree × 10 ÷ 9. Mastering these angle conversion formulas will help you work more confidently in mathematics, physics and engineering.
Common Angle Reference Table
| Degree (°) | Radian (rad) | Radian (π form) | Gradian (grad) |
|---|---|---|---|
| 0° | 0 | 0 | 0 |
| 30° | 0.523599 | π/6 | 33.3333 |
| 45° | 0.785398 | π/4 | 50 |
| 60° | 1.047198 | π/3 | 66.6667 |
| 90° | 1.570796 | π/2 | 100 |
| 180° | 3.141593 | π | 200 |
| 270° | 4.712389 | 3π/2 | 300 |
| 360° | 6.283185 | 2π | 400 |
Angle Conversion Calculator FAQ
How many degrees is 1 radian?
1 radian is approximately 57.29578 degrees, and the conversion formula is 180 ÷ π. Conversely, 1 degree is approximately 0.0174533 radian, or π ÷ 180. A full circle equals 2π radian, approximately 6.283185 rad. You can use the angle conversion calculator to quickly verify this result and avoid manual calculation errors.
What is the difference between gradian conversion and degree?
Gradian, also known as gon, defines a right angle as 100 grad, so a full circle is 400 grad. A degree defines a full circle as 360°. The gradian conversion relationship is: grad = degree × 10 ÷ 9, degree = grad × 0.9. Gradians are more common in surveying, geodesy and some European engineering standards. This angle unit conversion tool supports bidirectional conversion between degrees and gradians.
Is this angle conversion calculator accurate?
Yes. The conversion logic is based on standard angle conversion formulas, using double-precision floating-point numbers calculated locally in your browser, keeping 6 decimal places by default and automatically removing trailing zeros. All input is processed locally only and is not uploaded to any server, so you can confidently perform degree to radian, radian to degree and gradian conversion.
Why does the π form sometimes show "—"?
When the input radian value cannot be expressed as a simple rational multiple of π (for example, 1 rad or 2.5 rad), the tool shows "—" to indicate that no concise π fractional expression exists. In this case, please refer directly to the decimal value of the radian (rad). This design avoids inaccurate approximate expressions and ensures the credibility of the angle conversion result.
Does the angle conversion calculator require an internet connection?
The page needs an internet connection to load for the first time, and can be used offline after the page is loaded. All angle unit conversion is completed in your browser, with no software to download or install and no usage limits, making it a practical helper for math study and engineering calculations.