How to convert arcminutes to radians
rad = ′ × 0.0002908882087Multiply the value in arcminutes by 0.0002908882087. To go the other way, multiply by 3,437.746771 (or divide by 0.0002908882087).
An arcminute is smaller than a radian: it takes 3,437.746771 arcminutes to make one radian.
Worked examples
- 1 arcminute1 ′ × 0.0002908882087 = 0.0002908882087 rad
- 5 arcminutes5 ′ × 0.0002908882087 = 0.001454441043 rad
- 10 arcminutes10 ′ × 0.0002908882087 = 0.002908882087 rad
- 20 arcminutes20 ′ × 0.0002908882087 = 0.005817764173 rad
- 100 arcminutes100 ′ × 0.0002908882087 = 0.02908882087 rad
Arcminutes to radians conversion table
Values are calculated by the conversion engine and rounded to 8 significant figures.
| Arcminutes (′) | Radians (rad) |
|---|---|
| 0.1 ′ | 0.000029088821 rad |
| 0.25 ′ | 0.000072722052 rad |
| 0.5 ′ | 0.0001454441 rad |
| 1 ′ | 0.00029088821 rad |
| 2 ′ | 0.00058177642 rad |
| 3 ′ | 0.00087266463 rad |
| 4 ′ | 0.0011635528 rad |
| 5 ′ | 0.001454441 rad |
| 6 ′ | 0.0017453293 rad |
| 7 ′ | 0.0020362175 rad |
| 8 ′ | 0.0023271057 rad |
| 9 ′ | 0.0026179939 rad |
| 10 ′ | 0.0029088821 rad |
| Arcminutes (′) | Radians (rad) |
|---|---|
| 12 ′ | 0.0034906585 rad |
| 15 ′ | 0.0043633231 rad |
| 20 ′ | 0.0058177642 rad |
| 25 ′ | 0.0072722052 rad |
| 30 ′ | 0.0087266463 rad |
| 40 ′ | 0.011635528 rad |
| 50 ′ | 0.01454441 rad |
| 75 ′ | 0.021816616 rad |
| 100 ′ | 0.029088821 rad |
| 250 ′ | 0.072722052 rad |
| 500 ′ | 0.1454441 rad |
| 1,000 ′ | 0.29088821 rad |
About the units
Arcminute (′)
One sixtieth of a degree. Rifle-scope adjustments are often given in MOA (minutes of angle). One arcminute equals 0.0002908882087 radians (rad).
Radian (rad)
The angle subtended by an arc equal in length to the radius; 2π rad make a full turn, so 1 rad ≈ 57.2958°.
Frequently asked questions
How many radians are in one arcminute?
There are 0.0002908882087 radians in one arcminute, and this value is exact by definition.
How do I convert arcminutes to radians?
Multiply the number of arcminutes by 0.0002908882087. For example, 10 ′ × 0.0002908882087 = 0.002908882087 rad.
How many arcminutes are in one radian?
One radian equals 3,437.746771 arcminutes. That is the reverse factor, 1 ÷ 0.0002908882087.
What is 10 arcminutes in radians?
10 ′ = 0.002908882087 rad.
Is this ′ to rad converter accurate?
Yes. Both units are defined exactly in terms of SI units, so the conversion factor is exact; results are shown to 12 significant figures by default and you can change precision in the converter. Calculations run in your browser using the same tested engine that generated this page.