Degrees to Radians Converter (° to rad)
Convert degrees (°) to radians (rad) instantly with real-time two-way calculation, exact formulas, and comprehensive reference tables.
Conversion Formula & Exact Calculation
How to convert Degrees to Radians: Multiply by 0.017453.
Degrees to Radians Quick Reference Table
| Degrees (°) | Radians (rad) |
|---|---|
| 1 ° | 0.017453 rad |
| 2 ° | 0.034907 rad |
| 5 ° | 0.087266 rad |
| 10 ° | 0.174533 rad |
| 25 ° | 0.436332 rad |
| 50 ° | 0.872665 rad |
| 100 ° | 1.745329 rad |
| 250 ° | 4.363323 rad |
| 500 ° | 8.726646 rad |
| 1,000 ° | 17.453293 rad |
| 5,000 ° | 87.266463 rad |
⚠️ 5 Fatal Metrology & Dimensional Analysis Traps
Unit conversion errors have historically caused catastrophic aerospace accidents, structural overloads, and pharmacological dosage failures. Watch out for these 5 traps:
Linear conversions do not scale linearly into area or volume. While 1 meter = 100 centimeters, 1 square meter = 10,000 cm² (100²), and 1 cubic meter = 1,000,000 cm³ (100³). Applying linear conversion ratios to surface area, HVAC ductwork, or tank volume causes severe 100× to 1,000× estimation errors.
US fluid ounces (29.57 mL) and British Imperial fluid ounces (28.41 mL) are different. Even more drastically, a US liquid gallon is 128 US fl oz (3.785 L), while a UK Imperial gallon is 160 UK fl oz (4.546 L)—a massive 20.1% volume discrepancy that causes critical miscalculations in aviation fueling and chemical synthesis.
Standard formulas (°F = °C × 1.8 + 32) apply strictly to absolute scale readings. When converting temperature differentials or temperature changes (ΔT), the +32 offset MUST be omitted: a temperature change of 1°C equals a change of exactly 1.8°F. Adding 32 to heat pump delta-T metrics, building insulation R-values, or thermal expansion calculations corrupts engineering calculations.
Hardware manufacturers sell storage in decimal SI prefixes (1 GB = 1,000,000,000 bytes = 10⁹), whereas operating systems like Windows calculate filesystem allocation in binary IEC prefixes (1 GiB = 1,073,741,824 bytes = 2³⁰). This causes a 1 TB drive to register as approximately 931 GB in OS file explorers, leading to unexpected disk partition shortfalls.
Truncating decimal places during intermediate conversion steps compounds floating-point error across multi-stage formulas. In aerospace telemetry, CNC metal fabrication, or pharmaceutical microgram compounding, conversions must retain full IEEE 754 64-bit double precision until final display formatting.