Degrees to Radians Converter
Convert degree measure to radians and radians back to degrees. The result also shows pi multiples and normalized angles for unit circle and trigonometry work.
Live converter
Degrees and radians inputs
Convert degrees to radians and radians to degrees with the pi multiple visible for exact trigonometry work.
Radians from degrees
3.141593
Pi multiple
1pi
Degrees from radians
180 deg
Normalized degrees
180 deg
Normalized radians
3.141593
Degrees and radians conversion formulas
Degrees to radians
radians = degrees x pi / 180
Radians to degrees
degrees = radians x 180 / pi
How it works in three quick steps.
Enter degrees
Add an angle in degrees to calculate radians and the pi multiple.
Enter radians
Add an angle in radians to calculate the matching degree value.
Use normalized output
Read the normalized degree and radian values when an angle should be wrapped into one full turn.
Use exact pi notation before rounding radians
Degrees and radians measure the same turn with different units. The converter is most useful when its decimal output is read alongside the pi multiple: exact notation preserves the mathematical relationship, while the decimal is convenient for a numeric input field or a measured result.
Common angles worth recognizing
These equivalents follow from 180 degrees = pi radians. Fractions can be reduced before any decimal approximation is calculated.
- 30 degrees
- pi/6 radians; one twelfth of a full turn.
- 45 degrees
- pi/4 radians; one eighth of a full turn.
- 60 degrees
- pi/3 radians; one sixth of a full turn.
- 90 degrees
- pi/2 radians; one quarter turn.
- 180 degrees
- pi radians; one half turn.
- 270 degrees
- 3pi/2 radians; three quarter turns.
Normalize without changing the terminal side
Adding or subtracting a complete 360-degree turn produces a coterminal angle. For example, 450 degrees and 90 degrees end on the same unit-circle ray because 450 - 360 = 90.
This page normalizes the degree input into the interval from 0 inclusive to 360 exclusive, then converts that normalized degree value to radians. A -45-degree input therefore becomes 315 degrees and 7pi/4 radians in the normalized fields.
Separate symbolic and numeric work
For a proof, identity, or standard-angle exercise, keep pi in the result. Writing 5pi/4 preserves an exact relationship that 3.927 can only approximate.
For software, measurement, or plotting that accepts a decimal, use enough digits for the task and round once at the end. Repeatedly rounding intermediate angle values can compound error in later sine, cosine, or coordinate calculations.
Know what the two inputs do
The degree field drives radians, the pi multiple, and both normalized outputs. The radian field independently drives the degrees-from-radians result, so the two input boxes are conversion examples rather than a synchronized pair.
The unit label matters. Radians are dimensionless in SI expressions, but the symbol rad is retained here to make the angle quantity explicit and prevent a plain number from being mistaken for degrees.
Worked check: convert 225 degrees
- 1Multiply 225 by pi/180.
- 2Reduce 225/180 to 5/4, giving the exact result 5pi/4 radians.
- 3The decimal result is approximately 3.926991 radians; 225 already lies inside the normalization interval, so its normalized degree value stays 225.
Interpretation and copy limits
- This conversion changes angle measure only. Angular velocity, angular acceleration, bearings, and slope units need their own time, direction, or ratio context.
- The pi-multiple display is a decimal coefficient followed by pi. For a familiar rational angle, reduce that coefficient into a fraction when exact symbolic notation is required.
- Copied output contains the displayed numeric precision. It does not carry hidden exact digits, so retain the original input or exact pi fraction when another calculation needs greater precision.
Sources and definitions
- NIST SP 330, Section 5: Units outside the SI
Reference for the radian and accepted angle-unit conventions used in SI work.