Degrees to Radians Converter
Convert degrees to radians instantly with this free degrees to radians converter. Enter any value to get an accurate angle conversion, plus the formula, the conversion factor and a full reference table.
What is 1 degree in radians?
1 degree is equal to 0.017453293 radians.
1 ÷ 57.2957795 = 0.017453293 radians
Result
1 degree = 0.0174532925 radians
Degrees to Radians formula
rad = ° ÷ 57.2957795
The degrees to radians conversion factor is 0.01745329252, which is exact by definition. 1 degree = 0.01745329252 radians, and 1 radian = 57.2957795131 degrees.
Worked examples
- 5 degrees = 0.087266463 radians — 5 ÷ 57.2957795 = 0.087266463 radians
- 45 degrees = 0.785398163 radians — 45 ÷ 57.2957795 = 0.785398163 radians
- 180 degrees = 3.14159265 radians — 180 ÷ 57.2957795 = 3.14159265 radians
Degrees to Radians conversion table
Every value below is calculated with the exact conversion factor and rounded for display.
| Degrees (°) | Radians (rad) |
|---|---|
| 1 ° | 0.01745329 rad |
| 5 ° | 0.08726646 rad |
| 10 ° | 0.17453293 rad |
| 15 ° | 0.26179939 rad |
| 30 ° | 0.52359878 rad |
| 45 ° | 0.78539816 rad |
| 60 ° | 1.0471976 rad |
| 90 ° | 1.5707963 rad |
| 120 ° | 2.0943951 rad |
| 180 ° | 3.1415927 rad |
| 270 ° | 4.712389 rad |
| 360 ° | 6.2831853 rad |
When you need to convert degrees to radians
- Comparing specifications written for a different market.
- Checking a figure quoted in an unfamiliar unit before acting on it.
- Converting values consistently across a spreadsheet, report or shopping list.
Common mistakes to avoid
- Dividing when you should multiply. Because 1 degree = 0.017453 radians, the answer should be smaller than the number you started with.
- Rounding too early. Convert first at full precision, then round the final answer to the precision the task actually needs.
How precise does the answer need to be?
Round only at the end, and only to the precision your task actually needs. The converter above keeps full double precision internally and rounds for display.
How these units are defined
- Degree (°): 1/360 of a full turn. This unit's relationship to the SI base unit is exact by definition, so no rounding enters the conversion factor.
- Radian (rad): The SI angle unit: the angle subtending an arc equal to the radius. This unit's relationship to the SI base unit is exact by definition, so no rounding enters the conversion factor.
Related conversions
Frequently asked questions
- What is 1 degree in radians?
- 1 degree is equal to 0.017453293 radians.
- How many degrees are in one radian?
- There are 57.2957795 degrees in 1 radian.
- How do you convert degrees to radians?
- Multiply the number of degrees by 0.017453293 — or use the formula rad = ° ÷ 57.2957795.
- What is 45 degrees in radians?
- 45 degrees is 0.785398163 radians. 45 ÷ 57.2957795 = 0.785398163 radians.
- Is the degrees to radians conversion exact?
- Yes. The relationship is fixed by definition, so 0.01745329252 is an exact conversion factor — only the displayed result is rounded.