Convert Arcminutes to Radians
Arcminutes to radians is the conversion you need when a small angle measured in arcminutes has to go into a formula that expects radians — the natural unit for trigonometry and physics. One arcminute is approximately 0.0002908882086657216 radians, a very small number, because an arcminute is a tiny slice of a full turn.
Arcminutes to Radians conversion table
| Arcminutes (′) | Radians (rad) |
|---|---|
| 1 | 0.000291 |
| 2 | 0.000582 |
| 3 | 0.000873 |
| 5 | 0.001454 |
| 10 | 0.002909 |
| 20 | 0.005818 |
| 50 | 0.014544 |
| 100 | 0.029089 |
| 500 | 0.145444 |
| 1,000 | 0.290888 |
The formula
To convert arcminutes to radians, multiply the number of arcminutes by 0.0002908882086657216:
radians = arcminutes × 0.0002908882086657216
A worked example
Say you have 60 arcminutes and want it in radians:
60 × 0.0002908882086657216 = 0.017453293 rad
So 60 arcminutes is about 0.017453293 radians — which is exactly one degree expressed in radians.
Why it's an approximation
The factor 0.0002908882086657216 is rounded. A radian comes straight from the geometry of a circle: one full turn is 2π radians, and π is an irrational number whose digits run on forever without repeating. Since converting arcminutes to radians divides that turn into 21,600 equal slices and scales by π, the result can never be written out exactly — you always stop at some number of decimals. More decimals give you more precision when you need it.
When you'll use it
Feeding a small angle into a trig or physics formula that expects radians, working in a programming language whose math functions take radians, or checking a scientific calculation where the angle started out in arcminutes.
Frequently asked questions
How many radians are in an arcminute?
About 0.0002908882086657216 radians. It's a rounded figure — the exact value involves π, which never ends, so the decimal is cut off at a practical point.
How do I convert arcminutes to radians?
Multiply the number of arcminutes by 0.0002908882086657216. For example, 60 arcminutes × that factor comes to 0.017453293 radians, which is exactly one degree in radians.
Why does the arcminute to radian conversion involve π?
A radian is defined by the geometry of a circle, and a full circle is 2π radians. Converting any degree-based unit like the arcminute into radians pulls in π, so the factor can only ever be an approximation.