Why convert to radians for math code?
Most low-level trigonometric functions in programming languages and scientific tools use radians by default.
Angle
Convert Degree (°) to Radian (rad) instantly.
Formula
value × 0.0174532925199
| Sample | Converted |
|---|---|
| 1 ° | 0.0174532925 rad |
| 5 ° | 0.0872664626 rad |
| 10 ° | 0.1745329252 rad |
| 100 ° | 1.745329252 rad |
| 1,000 ° | 17.4532925199 rad |
Use this page to convert degrees to radians when geometry or engineering source angles need trigonometric-ready SI output.
Degree-to-radian conversion is a foundational preprocessing step for reliable trig-based computation.
Normalize to radians before evaluating sine, cosine, or tangent in most technical stacks.
Keep source degrees for traceability in UI and reporting layers.
Avoid reusing rounded radian display values as computational inputs.
Direction-specific pages reduce common conversion-order mistakes in geometry workflows.
This route bridges human-friendly angle entry and machine-friendly math execution.
Degrees are intuitive for humans, but radians are native in many equations and software functions.
A dedicated conversion path keeps model inputs consistent and reproducible.
Explicit direction helps avoid reciprocal errors in technical pipelines.
Convert in one shared utility used by API, UI, and batch processes.
Store source and transformed angles in separate, unit-tagged fields.
Document conversion checkpoints in engineering runbooks.
Test known points such as 180° = π rad and 90° = π/2 rad.
Verify trig outputs against expected benchmarks.
Inspect unit labels first when geometry results appear inconsistent.
Definition: Degree (deg) is the source angle unit in this conversion direction.
History/Origin: Degrees have long been the dominant practical unit for navigation, drafting, and everyday geometry.
Current use: Source degree values are commonly converted to radians for computational geometry and engineering models.
Definition: Radian (rad) is the destination SI-derived unit on this page.
History/Origin: Radians became standard in higher mathematics and technical software for angle-based equations.
Current use: Converted radian values are used in trig functions, simulations, and analytical pipelines.
| Degree [°] | Radian [rad] |
|---|---|
| 0.01 ° | 0.0001745329 rad |
| 0.1 ° | 0.0017453293 rad |
| 1 ° | 0.0174532925 rad |
| 2 ° | 0.034906585 rad |
| 5 ° | 0.0872664626 rad |
| 10 ° | 0.1745329252 rad |
| 20 ° | 0.3490658504 rad |
| 50 ° | 0.872664626 rad |
| 100 ° | 1.745329252 rad |
1 ° = 0.0174532925 rad
1 rad = 57.2957795131 °
Formula: value × 0.0174532925199
Example: 15 ° = 0.2617993878 rad
Precision note: Trigonometric models can be sensitive near boundaries, so preserve precision through calculations and round only for display.
Most low-level trigonometric functions in programming languages and scientific tools use radians by default.
Only if precision loss is acceptable for your downstream formulas.
The inverse is rad to deg.