Radians to DegreesFree online conversion calculator — instant results, no sign-up
Convert radians to degrees and back.
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About the Radians to Degrees
The Radians to Degrees calculator converts an angle in radians to degrees and shows the reverse conversion of the same numeric value from degrees to radians. With the default value of 1, it displays 57.29578 degrees for the radian-to-degree conversion and 0.017453 radians for the degree-to-radian conversion.
- Value in radians (radians)
- Enter the angle measured in radians; the default is 1 radian, and the reverse-conversion row interprets the same numeric value as degrees.
Formula and method
d = r × 180 / π; r = d × π / 180. For the default numeric value: 1 × 180 / π ≈ 57.29578 degrees; 1 × π / 180 ≈ 0.017453 radians.
- rAngle measured in radians.
- dAngle measured in degrees.
- πPi, the mathematical constant relating the two units: π radians equals 180 degrees.
Multiply the entered radian value by 180 / π to obtain degrees. For the reverse-conversion row, treat the entered numeric value as degrees and multiply it by π / 180 to obtain radians. These are two separate conversions of the same input number, not a conversion followed by a round trip.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Value in radians1 radians
Results
- degrees57.29578
- 1 radians =57.29578 degrees
- 1 degrees =0.017453 radians
How to use the Radians to Degrees
- 1Enter an angle in the Value in radians (radians) field, or leave the default value of 1.
- 2Read the degrees result, calculated by multiplying the input by 180 / π.
- 3Check the radian-to-degree row: with the default input, it reads 1 radians = = 57.29578 degrees.
- 4Read the reverse-conversion row: with the default input, it reads 1 degrees = = 0.017453 radians.
- 5Use the row corresponding to your starting unit, and retain the output unit when recording the result.
Reading your result
The output degrees = 57.29578 is the primary result for the default input of 1 radian. The row 1 radians = = 57.29578 degrees restates that conversion with both units. The row 1 degrees = = 0.017453 radians instead converts 1 degree to radians; it does not convert 57.29578 degrees back to radians. The repeated equals signs are display formatting, not an additional mathematical operation.
Limitations
Displayed results are rounded: the default degree result has five decimal places and the reverse radian result has six. The underlying conversions involve π, so these displayed decimals are approximations. The formulas convert units only; they do not automatically reduce angles to a single revolution or change the sign of a negative angle.
Common questions
Why does 1 radian equal 57.29578 degrees?+
Because π radians equals 180 degrees, each radian equals 180 / π degrees. Multiplying 1 by that factor gives approximately 57.29578 degrees.
Why does the reverse row show 0.017453 radians rather than 1 radian?+
The reverse row treats the original numeric input of 1 as degrees. It calculates 1 × π / 180, which is approximately 0.017453 radians, rather than converting the primary degree result back.
Can this conversion handle negative angles or angles larger than a full turn?+
Yes, the conversion formulas apply to both. They preserve the sign and number of turns rather than wrapping the result into a single-turn range.
Are the default results exact?+
No. For the default input, the exact expressions are 180 / π degrees and π / 180 radians for the respective directions. The displayed values 57.29578 and 0.017453 are rounded approximations.
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.