Welcome to the Easy Converters Degrees to Radians Converter – your go-to solution for converting angle measurements from degrees to radians in just seconds. Whether you're a student, engineer, web developer, or data analyst, this tool simplifies angle conversions used in mathematics, physics, trigonometry, and programming.
Degrees (°) are a standard unit of measuring angles. A full circle has 360 degrees, with each degree representing 1/360th of a full rotation. Degrees are commonly used in geometry, navigation, surveying, and everyday life.
Radians are the SI (International System) unit for measuring angles based on arc length. A full circle is 2π radians, making radians ideal for use in higher mathematics, especially calculus and trigonometry.
In a circle, 1 radian is the angle created when the arc length equals the radius of the circle. Radians are used extensively in:
The formula to convert degrees to radians is:
radians = degrees × (π ÷ 180)Example:
| Degrees (°) | Radians (in π) | Radians (Decimal) |
|---|---|---|
| 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 |
function degreesToRadians(deg) {
return deg * (Math.PI / 180);
}
This function is commonly used in web and mobile apps for geometric transformations and canvas animations.
Learning how to convert degrees to radians helps students understand mathematical functions, polar coordinates, unit circles, and the deeper relationships in trigonometry. Our converter helps visualize how radians relate to real-world angular motion and geometry.
Our converter supports:
All results are shown both in decimal and simplified π-form, when applicable.
Radians are central to understanding the unit circle, where:
Understanding radians helps in memorizing trigonometric values for sine, cosine, and tangent functions.
No. We provide both fractional π output (e.g., π/4) and decimal approximations (e.g., 0.7854).
Negative angles are valid. For example, -90° becomes -π/2 radians.
1° = π/180 radians ≈ 0.01745 radians.
Yes! Physics formulas involving angular motion require angles in radians.
Use our companion tool: Radians to Degrees Converter for reverse conversion.
The degrees-to-radians conversion is a fundamental step in many areas of advanced science:
In calculus, functions like sin(x), cos(x), and tan(x) are defined using radians for smooth differentiation and integration:
lim(x→0) sin(x)/x = 1 is true only if x is in radiansThus, converting to radians ensures mathematical correctness when applying calculus rules.
This converter also supports input flexibility for various angle formats:
45.5°90 1/2° (converted to 90.5°)-270°450° = 2.5π radiansIdeal for astronomy, rotating machinery, and multi-cycle physics simulations.
If you're working offline, simply use this basic calculator formula:
Radians = Degrees × π ÷ 180Example: 120° → 120 × π ÷ 180 = 2π/3 ≈ 2.0944
Tip: Keep π ≈ 3.1416 handy for mental calculations.
| Degrees | Radians (π format) | Radians (Decimal) |
|---|---|---|
| 10° | π/18 | 0.1745 |
| 22.5° | π/8 | 0.3927 |
| 135° | 3π/4 | 2.3562 |
| 225° | 5π/4 | 3.9269 |
| 315° | 7π/4 | 5.4978 |
You can save or print this chart for quick offline access during exams, presentations, or technical fieldwork.
After converting degrees to radians, it’s often useful to validate your result by converting back:
Degrees = Radians × (180 ÷ π)Example: 2.0944 × 180 ÷ π = 120°
This is helpful in scripting, debugging, and confirming unit conversions in calculators and spreadsheets.
In most programming environments, angle functions like Math.sin(), Math.atan(), and Math.cos() require radians as input:
// JavaScript Example:
let angleDegrees = 45;
let radians = angleDegrees * (Math.PI / 180);
let y = Math.sin(radians);This use is vital in canvas animations, robot pathing, and 2D/3D game physics engines.
This converter is designed for optimal usability:
All features are built with responsive design and screen-reader friendliness in mind.
Degrees-to-radians conversion is used in:
By offering both exact (π-based) and approximate outputs, our converter is useful across disciplines.
Understanding radians is easier when paired with visuals. On a unit circle (a circle with radius 1):
We recommend pairing this converter with dynamic visualizations like rotating lines or animated circles to help learners develop intuition about angular relationships.
This converter serves as an excellent companion in classrooms and online courses. Here’s how educators and students can use it effectively:
The concept of radians was introduced in the 18th century to unify angular measurements across math and science. Unlike degrees (which stem from ancient Babylonian base-60 systems), radians emerged from calculus, geometry, and analytical science.
Today, radians are the global standard in science and are preferred in:
To ensure correct and robust conversions, the converter includes input validation to address:
Error messages will guide users to enter proper angle formats. This helps reduce frustration and build better understanding.
math.pi or JavaScript’s Math.PI for accuracy instead of manually entering 3.1416.These best practices help you maintain clean, predictable, and portable code across platforms.
Need to convert hundreds of degree values? Use the bulk input or CSV mode (coming soon). Simply paste a list of values like:
0
90
135
270
315
And get the corresponding radian values in one go. Perfect for GIS applications, physics simulations, or batch-processing tools.
Looking to embed angle conversion into your own tools or apps? Our API (coming soon) will allow you to convert degrees to radians programmatically:
POST /api/degrees-to-radians{ "angle": 120 }{ "radians": 2.0944 }This allows easy integration into web calculators, engineering dashboards, or educational apps.
We’ve designed the Degrees to Radians Converter to be fully accessible and inclusive:
The Degrees to Radians Converter is a must-have tool for professionals, students, and developers working with angles, geometry, motion, and trigonometry. This fast, accurate, and mobile-friendly utility ensures that your calculations are correct, consistent, and ready for real-world applications. Whether you're building a physics simulation, solving math problems, or animating elements in a web app, converting to radians is now easier than ever.