Degrees to Radians Calculator
Enter degrees to find radians. rad = ° × 0.0174532925199.
How the result changes
Only degrees changes; all other inputs stay at your current values. The line illustrates the formula across the shown range. This is not a forecast of real-world outcomes.
About this calculation
Convert degrees (°) to radians (rad) while preserving the underlying angle quantity. The calculator updates when the input changes and shows the conversion rule and a worked example.
Formula
rad = ° × 0.0174532925199
Worked example
With Degrees: 1 °, radians is 0.017453 rad.
How to convert degrees to radians
Enter a value in degrees. Multiply it by the factor in the displayed formula to express the same quantity in radians. To reverse the relationship, divide by the same nonzero factor.
rad = ° × 0.0174532925199. As a reference point, 10 ° equals 0.174533 rad with this conversion. This is an example, not a recommended level or target.
What the unit relationship means
Degrees and radians represent the same amount of rotation or direction change. The numerical value depends on how a full turn is divided: degrees split it into 360 parts, radians relate arc length to radius, and gradians split it into 400 parts. A converted angle can be used in a formula only if that formula expects the target unit. The conversion changes notation, not the ray, bearing, or geometric shape.
Check the direction of the result
As a scale check, one ° corresponds to 0.017453 rad. Doubling the input from 10 ° to 20 ° changes the calculated output from 0.174533 rad to 0.349066 rad. Ordinary factor conversions are proportional: zero maps to zero and doubling the input doubles the result. If a copied value does not follow this pattern, check the source unit, decimal point, and formula direction.
When this conversion is useful
Convert degrees and radians when moving between geometry, trigonometry, and software that expects a particular angle unit.
What to check
Radians and degrees describe the same angle with different numbers. Check the input mode of a trigonometric function before using the converted value. In this direction the entered degrees is reported as radians; check both unit symbols when copying a figure from another source, because the reverse direction answers a different question.
Precision and reporting
Keep the angle symbol or unit in the final result. A small angular rounding difference can matter when the value is later used in surveying, navigation, or a trigonometric function. For an approximate source angle, round only after converting and using any necessary intermediate calculations. If the value represents a bearing, check its reference direction and clockwise convention too; changing degrees to another unit does not change how the direction itself is defined. For a separate reporting example, 7.3 ° produces 0.127409 rad. If 7.3 ° was an approximate reading, the converted digits should not be treated as a more accurate measurement.
Common questions
What is the reverse of degrees to radians?
To return from rad to °, divide by the nonzero factor shown in this calculator's formula.
Inputs
- Degrees (°)