In 1 degrees there are 0.017453 radians. Meanwhile in 1 radians there are 57.29578 degrees. Keep reading to learn more about each unit of measure and how they are calculated. Or just use the Radians to Degrees calculator above to convert any number.
* Values rounded to 6 decimal places for readability
To convert degrees to radians, use this rule: multiply the degree value by π/180.
Formula (degrees → radians):
[
\text{radians}=\text{degrees}\times \frac{\pi}{180}
]
Quick steps:
Example: Convert 60° to radians
[
60\times \frac{\pi}{180}=\frac{60}{180}\pi=\frac{\pi}{3}
]
Common degree to radian conversions:
Use this method any time you need a clear degrees to radians conversion for trig, geometry, or the unit circle.
Use this formula to convert degrees to radians:
radians = degrees × (π / 180)
Since π radians equals 180 degrees, the conversion always uses π/180.
Use the reverse formula:
degrees = radians × (180 / π)
This helps when a value is given in radians and you need degrees for angles or bearings.
Radians are the standard unit for many math and physics formulas. Most trig formulas work best in radians, especially in calculus. You also see radians in engineering, motion, waves, and rotations.
Here are popular angle conversions:
A full circle is 360°, which equals 2π radians.
A half circle is 180°, which equals π radians.
1° = π/180 radians, which is about 0.0174533 rad.
This is useful when you need a quick estimate for small angles.
1 rad = 180/π degrees, which is about 57.2958°.
A radian is a bit less than 60 degrees.
Keep π as a symbol and reduce the fraction:
Example: 150° × π/180 = 150π/180 = 5π/6
Convert the same way, then keep the negative sign:
radians = (negative degrees) × (π / 180)
Example: -45° = -45π/180 = -π/4
No. They measure angles using different scales.
Both are correct; the best choice depends on the task.
Trig functions can use either, but many math courses and most higher math use radians. If you’re entering values into software or code, radians are often the default. Always check what unit the input expects.
π connects angles to circles. A circle’s circumference is 2πr, and the radian comes from arc length divided by radius. Since 180° matches half a circle, it equals π radians, which makes π part of the conversion.
Multiply by π/180 and simplify, leaving π in the result.
Example:
225° × π/180 = 225π/180 = 5π/4
This format is common in geometry and trigonometry.
Use this shortcut:
radians ≈ degrees × 0.01745
Example:
60° ≈ 60 × 0.01745 ≈ 1.047 rad
For exact work, keep π/180 instead of rounding.
Use radians when you work with:
Degrees are often used for basic geometry, bearings, and everyday angle measures.
The Calculate Box tool to convert degrees to radians uses the open source script Convert.js to convert units of measurement. To use this tool, simply type a degrees value in the box and have it instantly converted to radians.