Degrees To Radians CalculatorFree online math calculator — instant results, no sign-up
Convert an angle in degrees to radians.
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About the Degrees To Radians Calculator
The Degrees To Radians Calculator converts an angle measured in degrees into its equivalent in radians using the factor π/180. With the default input of 180 degrees, it returns 3.1415926536 radians, the rounded decimal value of π.
- Degrees
- The angle to convert, measured in degrees (°), with a default value of 180.
Formula and method
r = d × π / 180; for d = 180, r = 180 × π / 180 = π ≈ 3.1415926536 radians.
- rThe converted angle in radians.
- dThe input angle in degrees.
- πPi, the mathematical constant equal to the ratio of a circle's circumference to its diameter.
Multiply the degree input by π and divide by 180. This conversion follows from the equivalence of 180 degrees and π radians. For the default input, the factors of 180 cancel, leaving π radians, displayed as 3.1415926536.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Degrees180
Results
- Result3.1415926536
How to use the Degrees To Radians Calculator
- 1Enter the angle in the Degrees field, or keep the default value of 180.
- 2Check that your input is in degrees rather than radians.
- 3Run the conversion to apply r = d × π / 180.
- 4Read the Result as an angle in radians; for 180 degrees, it is 3.1415926536.
Reading your result
The Result row reports the converted angle in radians, not degrees. For the default input of 180 degrees, Result = 3.1415926536 represents a half-turn. Its exact value is π radians; the displayed decimal is rounded.
Limitations
The conversion assumes the input is a numeric angle expressed in degrees. Degrees, minutes, and seconds must first be combined into decimal degrees. The formula preserves the sign and number of turns rather than reducing the angle to a single revolution. Decimal results approximate values involving π, and rounding can affect later calculations if the displayed value is reused.
Common questions
Why does 180 degrees give 3.1415926536 radians?+
A half-turn is both 180 degrees and π radians. Multiplying 180 by π/180 gives exactly π, which rounds to 3.1415926536 at ten decimal places.
Can I convert negative degree angles to radians?+
Yes. The conversion factor π/180 is positive, so a negative degree input produces a negative radian result and preserves the angle's direction.
Does the conversion remove extra full turns?+
No. Multiplying by π/180 preserves the entire angle, including any full turns. Finding an equivalent angle within one revolution is a separate operation.
Should I use degree mode or radian mode with the converted result?+
Use radian mode when entering the converted result into a trigonometric function. Use degree mode only when working with the original degree input.
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.