Degrees to RadiansFree online conversion calculator — instant results, no sign-up
Convert degrees to radians and back.
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About the Degrees to Radians
The Degrees to Radians calculator converts an angle entered in degrees into radians using π/180. It also displays the reverse conversion relationship from radians to degrees. With the default input of 1 degree, the result is 0.017453 radians.
- Value in degrees (degrees)
- The angle to convert, measured in degrees, with a default value of 1.
Formula and method
r = d × π / 180; reverse conversion: d = r × 180 / π.
- dThe angle measured in degrees.
- rThe angle measured in radians.
- πPi, the mathematical constant used to relate degrees and radians.
Multiply the degree input by π/180 to obtain radians. For the default input, r = 1 × π/180, displayed as 0.017453 radians. The reverse relationship uses 180/π radians-to-degrees scaling: 1 radian is displayed as 57.29578 degrees.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Value in degrees1 degrees
Results
- radians0.017453
- 1 degrees =0.017453 radians
- 1 radians =57.29578 degrees
How to use the Degrees to Radians
- 1Enter the angle in the Value in degrees (degrees) field, or leave the default value of 1.
- 2Read the radians result produced by multiplying the input by π/180.
- 3For the default input, verify that the radians result is 0.017453.
- 4Read the degree-to-radian row as 1 degree = 0.017453 radians.
- 5Use the reverse relationship row, 1 radian = 57.29578 degrees, to understand conversion in the opposite direction.
Reading your result
The “radians = 0.017453” row is the converted value for the default degree input. The “1 degrees = = 0.017453 radians” row repeats that result as an equivalence; the duplicated equals sign is display formatting, not an additional operation. The “1 radians = = 57.29578 degrees” row gives the reverse unit relationship. It does not mean that the original 1-degree angle equals 57.29578 degrees.
Limitations
Displayed results are rounded: 0.017453 and 57.29578 are approximations, while the formulas using π are exact. The listed input accepts degrees; the reverse relationship should not be mistaken for a separate radian input. Conversion changes the unit, not the angle, and the formula does not normalize angles to a single revolution.
Common questions
Why does 1 degree become 0.017453 radians?+
Degrees convert to radians by multiplying by π/180. For 1 degree, the exact result is π/180 radians, displayed here as 0.017453.
Why does the calculator also show 1 radian = 57.29578 degrees?+
That row shows the reverse conversion factor, 180/π. It describes an angle of 1 radian, not the degree input converted a second time.
Can I enter a radian value in the degree field to convert it back?+
No. The listed field interprets its value as degrees. To convert a radian value back to degrees, multiply it by 180/π instead.
Does converting a negative degree value remove its sign?+
No. Because π/180 is positive, a negative degree value produces a negative radian value, preserving the angle's direction under the chosen sign convention.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.