Convert Degrees to Radians
Enter an angle in degrees and instantly convert it to radians using the exact formula.
Formula used: radians = degrees × (π / 180)
What this degrees to radians calculator does
This calculator converts angles measured in degrees into radians. It is useful for students, engineers, programmers, and anyone working with trigonometry or geometry. Just type a degree value, click convert, and get a precise radian result in seconds.
You can also choose how many decimal places to show, making it easy to use for quick homework checks or higher-precision technical work.
Degrees vs. radians: a quick explanation
Degrees
Degrees split a full circle into 360 equal parts. This is the system most people learn first and is common in daily life, maps, and basic geometry.
Radians
Radians measure angles based on the radius of a circle. A full turn is 2π radians. In advanced math, physics, and computer science, radians are often preferred because many formulas become cleaner and more natural.
The conversion formula
To convert degrees to radians, multiply by π and divide by 180:
radians = degrees × π / 180
Example with 180 degrees:
- 180 × π / 180 = π
- So, 180° = π radians
Common degree-to-radian values
| Degrees | Radians (exact) | Radians (decimal) |
|---|---|---|
| 0° | 0 | 0.00000000 |
| 30° | π/6 | 0.52359878 |
| 45° | π/4 | 0.78539816 |
| 60° | π/3 | 1.04719755 |
| 90° | π/2 | 1.57079633 |
| 180° | π | 3.14159265 |
| 270° | 3π/2 | 4.71238898 |
| 360° | 2π | 6.28318531 |
Where radians are used
- Trigonometry: sin, cos, and tan are commonly evaluated in radians in higher-level math.
- Physics: angular velocity and harmonic motion formulas usually use radians.
- Programming: JavaScript, Python, and most scientific libraries expect radians for trig functions.
- Engineering: control systems, signal processing, and rotational analysis use radian-based formulas.
Practical tips
1) Keep your mode consistent
If your calculator or software is in degree mode but your formula expects radians (or vice versa), your answer can be completely wrong. Always check units first.
2) Use exact values when possible
For special angles like 30°, 45°, and 60°, exact π-based values are cleaner than decimals and reduce rounding error.
3) Use decimals for applied work
In coding or engineering calculations, decimal radians are usually required. This calculator gives both practical decimal output and exact form for common angles.
FAQ
How many radians is 180 degrees?
180 degrees equals π radians.
Can radians be negative?
Yes. Negative radians represent clockwise rotation when using standard math conventions.
How do I convert radians back to degrees?
Use the reverse formula: degrees = radians × 180 / π.
Final thoughts
A reliable degrees to radians calculator saves time and avoids common unit mistakes. Whether you are solving trig homework, building software, or checking engineering values, fast and accurate conversions help keep your work correct from the start.