Conversion tool
Convert degrees to radians instantly
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Disclaimer: Use calculations at your own risk. For critical applications, verify results against your governing standards/specifications.
How it works
We use rad = deg x 0.0174532925199.
Exact relationship: 1 deg = 0.0174532925199 rad.
Example: 30 deg = 0.524 rad.
Notes: Results are rounded in the default view.
Examples
- 30 deg = 0.524 rad
- 45 deg = 0.785 rad
- 90 deg = 1.571 rad
FAQ
What physical quantity do degrees and radians express?
Degrees express angular measurement, meaning rotational position or geometric opening rather than linear distance or frequency. Radians express angle in a mathematically natural form and are common where angular measurements need to align directly with equations.
What is the difference between degrees and radians?
Degrees and radians both express angular position or opening, but they are favored in different geometric, drafting, analytical, and precision-measurement contexts.
What is the history of the degree?
Degrees come from long-established geometry and astronomy practice and remain the most familiar angular unit in engineering and drafting.
What is the history of the radian?
Radians emerged from mathematical analysis and became standard in physics, controls, and analytical engineering work.
Were the degree and radian discovered by a specific person?
Degrees are a historical geometric convention rather than something discovered by one person. Radians are a mathematical convention rather than a unit discovered by a specific person.
Where are degrees and radians used in science and engineering?
Degrees are used in geometry, CAD, machining, surveying, print reading, and inspection work. Radians are used in dynamics, controls, trigonometry, vibration, robotics, and analytical engineering calculations.
Why do angle units matter in calculations?
Angle units affect geometry, motion analysis, trigonometric calculations, print interpretation, and setup work. Keeping the unit attached helps prevent errors when moving between intuitive drafting units and equation-friendly analytical units.
Can I trust this for critical angular calculations?
Use this for convenience and verify against your governing drawing, standard, or controlled engineering source for critical work. High-precision angular work may also depend on tolerance, datum strategy, and measurement method.
References
- Exact constant used: 1 deg = 0.0174532925199 rad.
- Angle conversions are derived from consistent relationships anchored to the radian.