Radians To Degrees CalculatorFree online math calculator — instant results, no sign-up
Convert an angle in radians to degrees.
Sign in to save results and favorites.
About the Radians To Degrees Calculator
The Radians To Degrees Calculator converts an angle measured in radians into its equivalent in degrees. It multiplies the radian value by 180/π, using the relationship that π radians equals 180 degrees. With the default input of 3.141592653589793 radians, the result is 180 degrees.
- Radians
- The angle to convert, expressed in radians, with a default value of 3.141592653589793.
Formula and method
θ_deg = θ_rad × (180/π)
- θ_degThe converted angle in degrees.
- θ_radThe input angle in radians.
- πThe mathematical constant pi, approximately 3.141592653589793.
Multiply the input in radians by 180/π to express the same angle in degrees. For the default input, θ_deg = 3.141592653589793 × (180/π), which gives the displayed result of 180 degrees using numerical precision.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Radians3.141592653589793
Results
- Result180
How to use the Radians To Degrees Calculator
- 1Enter the angle in the Radians field, or keep the default value of 3.141592653589793.
- 2Check that the entered value is in radians rather than degrees.
- 3Run the conversion to multiply the radian value by 180/π.
- 4Read the Result as an angle in degrees; the default input produces 180.
Reading your result
The Result row shows the converted angle in degrees. For the default input of 3.141592653589793 radians, Result = 180 means 180°, a half-turn. The conversion preserves the input's sign and does not reduce angles to a single revolution.
Limitations
The conversion assumes the input is already in radians. The finite decimal input and numerical representation of π can introduce small rounding differences, so the displayed 180 for the default input should not be interpreted as proving that its finite decimal value equals π exactly. Very large or highly precise inputs may also be affected by numerical precision. This conversion changes units only; it does not determine an angle's quadrant or normalize it to a standard range.
Common questions
Why does 3.141592653589793 radians give 180 degrees?+
The default value is a numerical approximation of π, and π radians equals 180 degrees. Multiplying it by 180/π therefore produces the displayed result of 180.
Does a negative radian input become a positive degree value?+
No. Because 180/π is positive, a negative radian input produces a negative degree result, preserving the angle's direction under the chosen sign convention.
Are angles greater than a full turn reduced to between 0° and 360°?+
No. The formula converts the full angle without wrapping it. An input greater than 2π radians therefore converts to more than 360 degrees.
Should I multiply or divide by π to convert radians to degrees?+
Multiply the radian value by 180 and divide by π. Multiplying by π/180 instead performs the reverse conversion, from degrees to radians.
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.
You might also like
Law Of Sines Calculator
Find a triangle side using two angles and a known opposite side.
Law Of Cosines Calculator
Find a triangle's third side from two sides and their included angle.
Degrees To Radians Calculator
Convert an angle in degrees to radians.
Sine Calculator
Calculate the sine of an angle in degrees.
Cosine Calculator
Calculate the cosine of an angle in degrees.
Tangent Calculator
Calculate the tangent of an angle in degrees.
Results are estimates for informational purposes and are not financial, medical or legal advice.